6 ch6 fuzzy pattern reconition
The Fuzzy C-Means Algorithm
Fuzzy Models for Pattern Recognition
Pattern recognition is a study field concerned with machine recognition of meaningful regularities in noisy or complex environments. In simpler words, pattern recognition is the search for structures in data. For example, Fig. 1 shows four cases of data structures in the plane. Observing Fig. 1, we see that the data in each of the four cases should be classified into two groups, but the definition of a "group" is different.
Hard and Fuzzy c-Partitions
Hard and Fuzzy c-Partitions
Objective Function Clustering and Hard c-Means Algorithm
How to choose the "optimal" partition from the space Mc or Mfc? There are three types of methods:
Fuzzy Models for Pattern Recognition
A key problem in pattern recognition is to find clusters from a set of data points. In the literature, a number of fuzzy clustering algorithms were proposed. We study the most famous fuzzy clustering algorithm: the fuzzy cmeans algorithm proposed by Bezdek [1981]. Pattern recognition using fuzzy models is a rich and currently very active research field; this lecture serves only as a short primer.
pattern recognition模板使用 -回复
pattern recognition模板使用-回复Pattern Recognition模板使用模板下载链接：Pattern Recognition是一种常见的模式识别算法，它可以用于检测和识别各种图案和形状。
它是计算机视觉和机器学习领域的重要工具，被广泛应用于许多领域，如图像处理、医学诊断、自动驾驶等。
在本文中，我们将详细介绍Pattern Recognition模板的使用方法。
一、环境准备在使用Pattern Recognition模板之前，我们需要准备一些必要的环境。
首先，我们需要安装OpenCV库，它是一套开源的计算机视觉库，提供了许多图像处理和模式识别的函数和工具。
可以从OpenCV官方网站（安装完OpenCV库之后，我们需要下载Pattern Recognition模板。
可以通过上面提供的链接下载Pattern Recognition模板的源代码。
下载完成后，我们需要将源代码编译成可执行文件。
具体的编译方法可以参考模板源代码中的README文件。
二、代码分析Pattern Recognition模板的源代码分为两个部分：训练和测试。
首先，我们需要用一组已知样本数据对模板进行训练，然后使用训练好的模板进行测试和识别。
下面我们将详细介绍这两个部分的代码。
1. 训练在训练部分的代码中，我们首先需要加载样本数据集。
样本数据集是一组包含一些已知图案或形状的图像。
可以在代码中指定样本数据集的路径和文件类型。
加载完成后，我们需要将图像转换为特征向量，以便进行模式识别。
在转换图像为特征向量的过程中，我们使用了图像处理和特征提取技术。
这些技术包括直方图均衡化、高斯滤波、边缘检测等。
这些操作可以提取图像中的关键特征，帮助我们更好地区分不同的图案和形状。
完成特征向量的转换后，我们可以使用Pattern Recognition模板提供的训练函数训练模型。
训练函数将根据样本数据集和特征向量生成一个模型，该模型可以用于后续的测试和识别。
Pattern_Recognition
d2 A1
1 2
0 32 .52+ 6.52
A2
25 17 .52+1.52
A3
36+36 8 6.52+0.52
B1
9+4 5 3.52+4.52
B2
25+25 2 5.52+1.52
B3
16+36 4 4.52+0.52
C1
1+64 41 0.52+1.52
C2
4+1 13 2.52+5.52
3
神经网络
• 大规模并行计算 • 学习、推广、自适应、容错、分布表达 和计算
• 优点：可以有效地解决一些复杂的非线 性问题 • 缺点：取少有效的学习理论
模式识别应用
• • • • • • • • • • 文本分类 文本图像分析 工业自动化 数据挖掘 多媒体数据库检索 生物特征识别 语音识别 生物信息学 遥感 ….
29
C1
1+64
C2
4+1
36+36 9+4
25+25 16+36
9+4
1+64
9+9
1+9
16+36
0
1+1
58
1: A1 (2,10)
2:A3, B1,B2, B3, C2 (6, 6)
3: A2, C1 (1.5,3,5)
第二次迭代: 中心为1: (2,10), 2: (6,6), 3: (1.5,3.5)
• 决策 （Decision） • 学习 （Learning） • 普适、推广、概括（Generalization)
PatternRecognition.ppt
What is a Pattern?
• Watanable defines a pattern “as opposite of a chaos; it is an entity, vaguely defined, that could be given a name.”
– a finger print image – A handwritten cursive word – a human face – A speech signal – …..
识别
• Recognition-（Re-Cognition） • 识别——再认识 • 主要研究相似和分类问题
– 有监督分类 – 无监督分类
与其他学科的关系
• 统计学 • 人工智能 • 机器学习 • 运筹学
模式识别系统
• 数据获取与预处理
• 数据表达
• 决策
基本概念
• 识别 （Recognition) • 决策 （Decision） • 学习 （Learning） • 普适、推广、概括（Generalization)
案例：聚类
应用聚类分析的例子
• 市场销售: 帮助市场人员发现客户中的不同群体，然后用这 些知识来开展一个目标明确的市场计划；
• 土地使用: 在一个地球观测数据库中标识那些土地使用相类 似的地区；
• 保险: 对购买了汽车保险的客户，标识那些有较高平均赔偿 成本的客户；
• 城市规划: 根据类型、价格、地理位置等来划分不同类型的 住宅；
率分布决定决策边界
• 判别分析方法——给出带参数的决策边 界，根据某种准则，由训练样本决定 “最优”的参数
句法方些子模式组成所谓“基元”
• 每个模式都可以由基元根据一定的关系来组成 • 基元可以认为是语言中的字母，每个模式都可
pattern recognition格式
文章题目：深度探讨：模式识别的意义与应用一、引言在当今信息爆炸的时代，我们面临着海量的数据和信息，如何从这些信息中提取有用的知识和规律成为了一个重要的问题。
而模式识别作为一种重要的人工智能技术，能够帮助我们从数据中找到隐藏的规律和趋势，提供了一种强大的工具来解决这个问题。
在本文中，我们将深入探讨模式识别的意义与应用，并探讨其在不同领域的作用。
二、模式识别的定义与基本原理模式识别是一种通过数据分析和学习来识别数据中的规律和模式的技术。
它的基本原理是通过对输入的数据进行特征提取和分类，从而识别出数据中的各种模式。
在这个过程中，模式识别涉及到统计学、机器学习、人工智能等多个领域的知识，是一个集成了多种技术和方法的交叉学科。
通过模式识别技术，我们能够从数据中发现隐藏的规律和结构，从而实现对数据的理解和应用。
三、模式识别的意义与应用在现实生活中，模式识别技术得到了广泛的应用。
在医学领域，模式识别可以帮助医生从医学影像中识别出病变的模式，辅助医生进行诊断和治疗。
在金融领域，模式识别可以帮助分析师从市场数据中发现交易的规律和趋势，指导投资决策。
在工业生产中，模式识别可以帮助工程师监测设备运行的模式，预测设备的故障和维护周期。
在自然语言处理中，模式识别可以帮助机器理解和生成自然语言，实现智能对话和翻译。
可以看到，模式识别技术在各个领域都发挥着重要作用，促进了这些领域的发展和进步。
四、模式识别的个人观点与理解在我看来，模式识别是一种强大的工具，能够帮助人类从数据中挖掘出宝贵的知识和规律。
通过模式识别技术，我们能够实现对复杂数据的理解和应用，帮助人类更好地处理现实生活中的各种问题。
在未来，随着人工智能技术的不断发展，模式识别技术将发挥越来越重要的作用，并且将在更多的领域得到应用，实现人类社会的进步和发展。
五、总结通过本文的探讨，我们对模式识别的意义与应用有了更深入的理解。
模式识别作为一种重要的人工智能技术，不仅在医学、金融、工业、自然语言处理等领域得到了广泛的应用，而且在人类生活和工作中起着重要的作用。
pattern recognition letters 的latex模板
pattern recognition letters 的latex模板Pattern Recognition Letters是一个国际性的科学期刊，该期刊主要关注模式识别和人工智能相关的不同方面，如图像处理、模式识别、机器学习等。
这篇文章将介绍Pattern Recognition Letters的LaTeX模板，并提供一些相关的参考内容。
Pattern Recognition Letters的LaTeX模板采用的是Elsevier公式，可以通过Elsevier官方网站下载。
在开始使用该模板之前，需要先安装LaTeX的相关软件，如TeX Live或MiKTeX。
安装完成后，可以下载Pattern Recognition Letters的LaTeX模板文件。
在开始编写正文之前，需要进行一些设置。
首先，需要确定文档类别是article，并设置字体大小为11pt。
可以使用如下代码进行设置：\begin{verbatim}\documentclass[11pt]{article}\end{verbatim}接下来，需要设置页面的边距。
Pattern Recognition Letters的边距设置为上下左右均为 2.5cm。
可以使用如下代码进行设置：\begin{verbatim}\usepackage[top=2.5cm, bottom=2.5cm, left=2.5cm,right=2.5cm]{geometry}\end{verbatim}然后，需要加载Pattern Recognition Letters的LaTeX模板文件。
可以使用如下代码进行加载：\begin{verbatim}\usepackage{prletters}\end{verbatim}接下来，就可以开始正文的编写。
在正文的开头，可以使用\textbackslashbegin\{document\}和\textbackslashend\{document\}进行标识。
pattern recognition格式
pattern recognition格式（原创实用版）目录1.模式识别的定义和重要性2.模式识别的基本任务和方法3.模式识别的应用领域4.我国在模式识别领域的发展正文一、模式识别的定义和重要性模式识别，顾名思义，是指对模式进行识别的过程。
它是指通过计算机系统、人工智能技术等手段，对输入的信号、数据或图像等信息进行处理，分析其内在规律，从而识别出特定的模式或特征。
在信息处理、自动化技术、人工智能等领域，模式识别具有重要的应用价值。
二、模式识别的基本任务和方法模式识别的基本任务是根据输入的信号、数据或图像等信息，提取其特征，进行分类、识别或描述。
模式识别的方法主要包括以下几种：1.数据预处理：对输入的数据进行清洗、归一化等操作，提高数据质量。
2.特征提取：从输入数据中提取有代表性的特征，作为分类或识别的依据。
3.分类：根据提取的特征，将数据划分到不同的类别中。
4.识别：通过比较输入数据与已知的模式，确定其所属的类别。
5.描述：对输入数据的特征进行描述，以便于人们理解和分析。
三、模式识别的应用领域模式识别在多个领域都有广泛的应用，如：1.图像识别：在计算机视觉领域，模式识别技术可以用于图像识别、目标检测等任务。
2.语音识别：将人类的语音信号转换为文字，是语音识别的主要任务。
3.自然语言处理：模式识别在自然语言处理领域也有广泛应用，如文本分类、情感分析等。
4.医学诊断：模式识别可以用于辅助医生进行疾病诊断，提高诊断的准确性。
四、我国在模式识别领域的发展我国在模式识别领域取得了一系列的研究成果和应用，如人脸识别技术、语音识别技术等。
模式识别Pattern Recognition
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根据应用领域的划分
图象识别：染色体分类、遥感图象识别
人脸识别：
文字识别：中外文印刷体、手写体识别
数字识别：0-9印刷体、手写体识别，典型 例子：邮政手写数字识别
指纹识别：
掌纹识别：
语音识别：
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1.1.3 刊登模式识别研究成果的中文期刊
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特征提取和选择
目的：从原始数据中，得到最能反映分类本质的特 征
特征形成：通过各种手段从原始数据中得出反映分 类问题的若干特征（有时需进行数据标准化）
特征选择：从特征中选取若干最能有利于分类的若 干特征
特征提取：通过某些数学变换，降低特征数目
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测量空间：原始测量数据组成的空间 特征空间：进行模式分类的空间。一个模式（样
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模式识别系统的基本构造
模式识别系统的主要组成部分：数据获取、
预处理、特征提取和选择、分类决策
训
练
数据 获取
预 处 理
特征提取 与选择
分类器设计
过 程
分类决策
决 策
过
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说明
1 这一系统构造适合于统计模式识别、模 糊模式识别、人工神经网络中有监督方 法
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模式识别关注的内容
1 特征选择与提取 2 分类器的设计 3 分类决策规则
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1.3 关于模式识别的一些基本问题
1.3.1 模式样本)表示方法
模糊模式识别在小麦亲本鉴别中的应用
模糊模式识别在小麦亲本鉴别中的应用小麦（TriticumaestivumL.）是一种全球性的主要粮食作物，为了提高小麦的品质、生产力和抗逆性，小麦育种学家不断采用多种方法来鉴别小麦品种和亲本，以保障育种成果的有效性。
传统小麦亲本鉴别主要采用植物学和遗传学方法，近年来随着科技的发展，出现了由计算机技术支持的小麦亲本鉴别技术，其中模糊模式识别技术的应用也成为研究者们热衷的话题。
模糊模式识别（Fuzzy Pattern Recognition, FPR）是一种计算机辅助亲本鉴别技术，它是识别研究中典型的模式识别方法之一，其主要特点是能够进行快速、高效、准确的鉴别和分类，满足育种和分子育种研究中关于解析和识别小麦亲本的要求。
可以说，模糊模式识别技术对于小麦种质资源的多样性、学习性和生产性有着重要的意义，它主要用于小麦亲本的特征提取和小麦品种的识别与鉴别。
它在小麦亲本鉴别中发挥着重要作用，首先，模糊模式识别可以快速准确地进行小麦亲本鉴别，避免重复检测，提高育种效率；其次，模糊模式识别也可以有效避免小麦亲本鉴别中的失误和检测误差；最后，模糊模式识别技术可以更有效地处理复杂的小麦亲本鉴别问题，有效控制小麦品种的多样性和生产性。
鉴于模糊模式识别技术的重要性，世界各国的科研机构和大学都在积极开展小麦亲本鉴别技术的研究，其中我国科学家也投入了大量精力。
泰国科技大学和俄罗斯科学院分别从数量角度和质量角度对小麦亲本鉴别技术进行了研究，研究结果表明，模糊模式识别技术的应用能够快速准确地鉴别出小麦品种，并且可以有效地控制和优化小麦种质资源的多样性、学习性和生产性，为小麦育种和改良工作带来新的机遇。
随着技术的发展，模糊模式识别技术不断进步，设备、分析方法和可靠性也在不断提高。
然而，尽管模糊模式识别是一项技术，但它也存在一定的弊端：由于小麦亲本鉴别技术涉及到大量的数据处理和分析过程，它的处理效率也非常低，且容易受到外界因素的干扰，因此，小麦亲本鉴别技术的改良和完善仍需要科学家们的继续努力。
模式识别英文经典论文--Feature subset selection in large dimensionality domains
Pattern Recognition43(2010)5--13Contents lists available at ScienceDirectPattern Recognitionjournal homepage:w w w.e l s e v i e r.c o m/l o c a t e/prFeature subset selection in large dimensionality domains Iffat A.Gheyas∗,Leslie S.SmithDepartment of Computing Science and Mathematics,University of Stirling,Stirling,FK94LA,Scotland,UKA R T I C L E I N F O AB S T R AC TArticle history:Received30January2009Received in revised form31May2009 Accepted17June2009Keywords:Curse of dimensionalityFeature subset selectionHigh dimensionalityDimensionality reduction Searching for an optimal feature subset from a high dimensional feature space is known to be an NP-complete problem.We present a hybrid algorithm,SAGA,for this task.SAGA combines the ability to avoid being trapped in a local minimum of simulated annealing with the very high rate of convergence of the crossover operator of genetic algorithms,the strong local search ability of greedy algorithms and the high computational efficiency of generalized regression neural networks.We compare the performance over time of SAGA and well-known algorithms on synthetic and real datasets.The results show that SAGA outperforms existing algorithms.©2009Elsevier Ltd.All rights reserved.1.IntroductionThe purpose of data mining is knowledge discovery:to gener-ate new knowledge about events and phenomena from existing data sets for classification or forecasting future events.Data sets consist of a number of vectors,each corresponding to some occurrence of an event:each vector consists of a large number of features(or ex-planatory variables).In general,which features matter is not known. As a result,all sorts of information about events of interest are often gathered.Improvements in data acquisition capacity,falling costs of data storage,and development of database and data warehousing technology,have led to more and more high dimensional datasets (with tens or hundreds of thousands of features)emerging[1].Many of these features are irrelevant or redundant.Unnecessary features increase the size of the search space and make generalization more difficult.This curse of dimensionality(each feature is a separate di-mension)is a major obstacle in machine learning and data mining. Hence feature selection is an active area of research in pattern recog-nition[2],machine learning[3],data mining[4]and statistics[5].In particular,the prediction performance of any learning algorithm de-pends on how efficiently the algorithm learns patterns in the data. Irrelevant and redundant features increase the search space size, making patterns more difficult to detect and making it more difficultAbbreviations:ACO,ant colony optimization;GA,genetic algorithm;GRNN, generalized regression neural networks;PSO,particle swarm optimization;SA, simulated annealing;SBS,sequential backward selection;SFBS,sequential float-ing backward selection;SFFS,sequential floating forward selection;SFS,sequen-tial forward selection∗Corresponding author.Tel.:+4401786467430;fax:+4401786464551.E-mail addresses:iag@(I.A.Gheyas),lss@(L.S.Smith).0031-3203/$-see front matter©2009Elsevier Ltd.All rights reserved.doi:10.1016/j.patcog.2009.06.009to capture rules necessary for forecasting or classification,whether by machine or by hand.In addition,the more the features,the higher the risk of overfitting.The probability that some features will coin-cidentally fit the data increases,unless the sample size grows expo-nentially with the number of features.Furthermore,in most prac-tical applications,we want to know the collection of core variables that are most critical in explaining an event.Feature subset selection entails choosing the feature subset that maximizes the prediction or classification accuracy.The feature subset selection approach is based on the principle of parsimony(or Occam's razor)[6].This says that,we prefer the model with the smallest possible number of parameters that adequately represents the data.Einstein is quoted in Parzen[7,p.68]as remarking that “everything should be made as simple as possible,but not simpler”. However,this principle is difficult to apply in feature selection problems.Selecting the best feature subset is proven to be an NP-complete problem[8].The task is challenging because,first,features which do not appear relevant singly may become highly relevant when taken with others.There can be two-way,three-way or com-plex multi-way interactions among features.As a result a feature that is weakly associated with prediction(or classification)can improve prediction accuracy if it is complementary to other features.Second, relevant features may be redundant so that the omission of some of them will remove unnecessary complexity(and noise)from the fore-casting problem.There can be many levels of multi-way redundancy in the feature space.Third,high feature correlation does not imply absence of feature complementarity.Fourth,high levels of multi-collinearity increase the probability that a good predictor of the out-put signal will be found non-significant and rejected from the model.An exhaustive search of all possible subsets of features will guar-antee that the best subset of features is found.Unfortunately this is computationally impractical for even a medium sized database(for6I.A.Gheyas,L.S.Smith/Pattern Recognition43(2010)5--13n features,the number of possible feature subsets is2n,too large to be evaluated even for modest n).A major thrust of current research work is focused on the determination of an optimal feature subset. The choice is a trade-off between computational time and quality of the generated feature subset solutions.In this paper,we present and test a novel hybrid algorithm for selection of optimal feature subsets. The proposed algorithm consistently generates better feature subsets compared to existing search algorithms within a predefined time limit and keeps improving the quality of selected subsets as the algorithm runs.The rest of the paper is organized as follows:a brief review of previous work in Section2,the new algorithm in Section3,(with the procedure for estimating fitness of a feature subset in Section 3.1,an overview of generalized regression neural networks(GRNN) in Section3.2and details of the constituent search algorithms in Section3.3),and comparative performance measurement in Section 4,results and discussions in Section5,followed by summary and conclusions in Section6.2.Review of existing techniquesTwo broad categories of optimal feature subset selection have been proposed:filter and wrapper.In filter approaches,features are scored and ranked based on certain statistical criteria and the features with highest ranking values are selected.Frequently used filter methods include t-test[9],chi-square test[10],Wilcoxon Mann–Whitney test[11],mutual information[12],Pearson correla-tion coefficients[13]and principal component analysis[14].Filter methods are fast but lack robustness against interactions among features and feature redundancy.In addition,it is not clear how to determine the cut-off point for rankings to select only truly important features and exclude noise.In the wrapper approach,feature selection is“wrapped”in a learning algorithm.The learning algorithm is applied to subsets of features and tested on a hold-out set,and prediction accuracy is used to determine the feature set quality.Generally,wrapper methods are more effective than filter methods.Since exhaustive search is not computationally feasible,wrapper methods must em-ploy a search algorithm to search for an optimal subset of fea-tures.Wrapper methods can broadly be classified into two cate-gories based on search strategy:(i)greedy and(ii)randomized/sto-chastic.Greedy wrapper methods use less computer time than other wrapper approaches.Sequential backward selection(SBS)(also known as backward stepwise elimination)[15]and Sequential for-ward selection(SFS)(also known as forward stepwise selection) [16]are the two most commonly used wrapper methods that use a greedy hill-climbing search strategy.SBS starts with the set of all features and progressively eliminates the least promising ones.SBS stops if the performance of learning algorithms drops below a given threshold due to removal of any remaining features.SBS relies heav-ily on the monotonicity assumption[17].This states that prediction accuracy never decreases as the number of features increases.This assumption is dubious because of the difficulties associated with search space dimensionality and overfitting.In reality,the predictive ability of a learning algorithm may decrease as the feature subspace dimensionality increases after a maximum point due to a decreasing number of samples for each feature combination.When faced with high-dimensional data,SBS often finds difficulties in identifying the separate effect of each explanatory variable on the target variable. Because of this,good predictors can be removed early on in the algo-rithm(in SBS,once a feature is removed,it is removed permanently). By contrast,SFS starts with an empty set of features and iteratively selects one feature at a time—starting with the most promising feature—until no improvement in classification accuracy can be achieved.In SFS,once a feature is added,it is never removed.SBS is robust to interaction problems but sensitive to multicollinearity.On the other hand,SFS is robust to multicollinearity problems but sen-sitive to feature interaction.As a result,both SBS and SFS can easily be trapped into local minima.The problem with SFS and SBS is their single-track search.Hence,Pudil et al.[18]suggest floating search methods(SFFS,SFBS)that performs greedy search with provision for backtracking.However,recent empirical studies demonstrate that sequential floating forward selection(SFFS)is not superior to SFS[19]and sequential floating backward selection(SFBS)is not feasible for feature sets of more than about100features[20].The problem with sequentially adding or removing features is that the utility of an individual feature is often not apparent on its own,but only in combinations including just the right other features.Stochastic algorithms developed for solving large scale combina-torial problems such as ant colony optimization(ACO),genetic algo-rithm(GA),particle swarm optimization(PSO)and simulated anneal-ing(SA)are at the forefront of research in feature subset selection [17,21–23].These algorithms efficiently capture feature redundancy and interaction and do not require the restrictive monotonicity as-sumption.However,these algorithms are computationally expensive (though far less so than exhaustive search).Recently,several authors proposed hybrid approaches taking ad-vantages of both filter and wrapper methods.Examples of hybrid algorithms include t-statistics and a GA[24],a correlation-based fea-ture selection algorithm and a genetic algorithm[25],principal com-ponent analysis and an ACO algorithm[26],chi-square approach and a multi-objective optimization algorithm[27],mutual information and a GA[28,29].The idea behind the hybrid method is that filter methods are first applied to select a feature pool and then the wrap-per method is applied to find the optimal subset of features from the selected feature pool.This makes feature selection faster since the filter method rapidly reduces the effective number of features un-der consideration.Advocates of hybrid methods argue that the risk of eliminating good predictors by filter methods is minimized if the filter cut-off point for a ranked list of features is set low.However, hybrids of filter and wrapper methods may suffer in terms of ac-curacy because a relevant feature in isolation may appear no more discriminating than an irrelevant one in the presence of feature in-teractions.Wrapper methods use a learning algorithm to assess the accu-racy of potential subsets in predicting the target.Currently,the most popular learning algorithm used in wrapper schemes is the sup-port vector machine(SVM)[30].However,the accuracy of an SVM is dependent on the choice of kernel function and the parameters (e.g.cost parameter,slack variables,margin of the hyper plane,etc.). Failure to find the optimal parameters for an SVM model affects its prediction accuracy[31].Another drawback of the SVM is its com-putational cost[32].Wrapper methods are computationally more demanding than filter methods because they evaluate the candidate feature subsets using a learning algorithm,and these are usually it-erative methods.This can increase the computational cost.To accel-erate the wrapper approach in feature subset search,it is vital to employ a fast learning algorithm.Furthermore,empirical evidence suggests that SVMs are very sensitive to noisy training data,which can degrade their performance[33].They are also prone to overfit-ting and poor generalization[34].Development of a highly accurate and fast search algorithm for the selection of optimal feature subset is an open issue.3.Proposed algorithmA good search algorithm should provide:(1)good global search capability that allows for the exploration of new regions of the solution space without getting stuck in local minima,(2)rapidI.A.Gheyas,L.S.Smith/Pattern Recognition43(2010)5--137convergence to a near optimal solution,(3)good local search ability, and(4)high computational efficiency.We present a hybrid algorithm(SAGA),named after two ma-jor underlying search algorithms(SA and GA),for selecting optimal feature subsets efficiently.This algorithm is based on a simulated annealing,a genetic algorithm,a generalized regression neural net-works and a greedy search algorithm.SAGA combines the ability to avoid being trapped in a local minimum of SA with a very high rate of convergence of the crossover operator of GA,the strong local search ability of the greedy algorithm and high computational ef-ficiency of GRNN.Our hybrid approach solves the feature selection problem without including filter steps.Hence,unlike existing hybrid algorithms,SAGA does not compromise accuracy for speed.The SA algorithm here is a mutation-based search approach.Mu-tation represents a long jump in the search space.The strength of SA is good global search ability.The major disadvantage of SA is its slow convergence speed.On the other hand,GA implements both crossover and mutation operations.The strength of GA is its rapid convergence,but the combination of crossover and a low fixed mu-tation rate often traps the search in a local minimum.In addition, the local search capability of SA and GA is weak.By contrast,greedy algorithms have good local search ability,but lack global search ability.SAGA organizes a search in three stages.Stage1:SAGA employs a SA to guide the global search in a solution space.As long as the temperature is very high,SA accepts every new solution,thus yielding a near random search through the search space.On the other hand,as the temperature becomes close to zero, only improvements are accepted.The SA is run for approximately 50%of the total time available.Stage2:SAGA employs a GA to perform optimization.The GA population was set at100.The initial population consists of the best solutions detected by SA.The main purpose of crossover in GA is to exchange information between pairs of good solutions to form new(and hopefully better)solutions.The crossover operator thereby assists in rapid convergence to a good solution.The mutation operator in GA introduces new genes into the population and retains genetic diversity.The GA runs for about30%of total time spent by SAGA to find the optimal feature subset solution.Stage3:SAGA applies a hill-climbing feature selection algorithm. The greedy algorithm performs a local search on the k-best solutions (elite)given by two global optimization algorithms(SA and GA)and selects the best neighbours(in our context neighbours are defined in terms of the Euclidean distance between a pair of feature subsets). The hill-climbing algorithm is run in the remaining execution time.Computational efficiency is essential for exploring a huge search space.To enhance it,the following measures were taken.First,SAGA employs a robust and fast learning algorithm(GRNN)for assessing candidate solutions.GRNN,based on fuzzy means clustering,is a`one-pass'algorithm.GRNN has just one parameter(smoothing factor)that needs to be chosen,but our empirical research reveals that the prediction accuracy of GRNN is not very sensitive to the parameter setting.Hence in GRNN we need not to develop and validate many predictive models.Furthermore,GRNN requires no training time other than the time required to pre-process and store the entire training set.Another major reason why we choose GRNN is that it suffers relatively more from the curse of dimensionality than other algorithms[35].This is an advantage when trying to eliminate unnecessary variables because GRNN does not have the luxury of producing good results when there are irrelevant and redundant features.Other advantages of GRNN are its non-parametric nature and its robustness against local minima,overfit-ting and outliers[36–38].Second,Cooper and Hinde(2003)report that evolutionary algorithms spend approximately a third of the time testing on already tested candidate solutions[39].SAGA stores information about the candidate solutions evaluated so far in a database and never evaluates a possible solution more than once.As a result,SAGA has all the four qualities mentioned above.puting fitness of feature subsetsOur proposed algorithm(SAGA)employs GRNN classifiers to eval-uate candidate feature subset solutions.Before the evaluation of fea-ture subsets,each feature was normalized by scaling it between0 and1.We perform10-fold cross validation to estimate the testing accuracy of the GRNN classifier.The higher the accuracy,the fitter the solution.If the accuracies of two solutions are the same,then the solution using the smaller number of features wins.3.2.Generalized regression neural networks learning algorithmGRNN is an instance-based algorithm.In GRNN[40]each obser-vation in the training set forms its own cluster.When a new input pattern x is presented to the GRNN for the prediction of the output value,each training pattern(prototype pattern)y i assigns a mem-bership value h i to x based on the Euclidean distance d as in Eq.(2). The formula for the Euclidean distance between x and y i isd=d(x,y i)=nj=1(x j−y ij)2(1)where x=(x1,...,x n)is the presented pattern and y i=(y i1,...,y in) is the i-th prototype pattern.n is the total number of features in the study.x j is the value of the j-th feature of the presented pattern (features can be multivalued or not).y ij is the value of the j-th feature of the i-th prototype patternh i=1√2exp−d22 2(2)where is the smoothing function parameter(we specify a default value: =0.5).Finally,GRNN calculates the output value z of the pattern x as in Eq.(3).The predicted output is the weighted average of the outputs of all prototype patterns.GRNN can handle continuous output vari-ables and categorical output variables with two categories:event of interest(coded as`1')or not(coded as`0'):z=i(h i×output of y i)ih i(3)If the output variable is binary,then GRNN calculates the prob-ability of the event of interest.If the output variable is continuous, then it estimates the value of the variable.3.3.Implementation of the underlying search algorithms of the SAGAWe encode possible feature subset solutions in ordered,fixed-length binary strings where`1'indicates the presence of the feature and`0'its absence.One of the objectives was realizing exactly how time consuming the feature selection task can be.Hence,a prede-fined time limit instead of the maximum number of total iterations was chosen as the stopping criterion which has inevitably made our algorithm rather complicated(in any practical application,one should therefore use a standard stochastic algorithm with imposing a maximum number of iterations as stopping criterion).A search al-gorithm spends almost99%of its running time evaluating the fitness of solutions.The computation time required to evaluate a feature subset depends on the number of features present in the subset and8I.A.Gheyas,L.S.Smith/Pattern Recognition43(2010)5--13the number of instances in the dataset.Hence,we empirically find out the time t(=t(1:10,000))required to estimate the fitness scores of feature subsets with various dimensionalities from1to10,000 using GRNN and store the information(dimensionalities of subsets and time required to assess their fitness)in database.3.3.1.Pseudocode of simulated annealingStep1:Set the initial temperature(T i):T i is the total run time for SA.Step2:Set the current temperature(T c):T c=T i.Step3:Initialize population:Randomly select100individuals I(=I(1:100))from the pool of individuals for initial population.Step4:Evaluate the fitness of each individual:Based on each in-dividual I,extract a new dataset D new from the(normalized)origi-nal dataset D with the features that are present in the solution of the individual.Evaluate the fitness scores E o(=E o(1:100))of fea-ture subsets using GRNN and store the information(feature subset solutions with fitness scores).Step5:Update the effective temperature(T):Based on the dimen-sionality of each individual evaluated in the previous step,retrieve the time elapsed in evaluating the individual.Calculate the total time spent T spent on evaluating individuals of population by adding the time spent for each individual.Finally update the effective temper-ature:T c=T c−T spent.Step6:For all current feature subset vectors I(=I(1:100)) change the bits of vectors with probability p mutation:p mutation=0.5−0.5exp(T c/ )where =T i/log2(0.5).Step7:Evaluate the fitness E n(=E n(1:100))of the new candidate solutions if not already evaluated.Step8:Determine if this new solution is kept or rejected and update the database.•If E nՆE o,the new solution is accepted.The new solution replaces the old solution and E o is set to E n.•If E n<E o,calculate the Boltzmann acceptance probability P accept. If the acceptance probability is greater than or equal to a random number between0and1,the new solution is accepted and it replaces the old one and E o.If the acceptance probability is less than the random number,the new solution is rejected and the old solution stays the same:P accept=exp(−(E o−E n)/T c).Step9:Update the effective temperature.If the effective temper-ature is greater than or equal to zero,return to step6.Otherwise, the run is finished.3.3.2.Pseudo code of GA(Genetic Algorithm)Step1:Construct a chromosome pool of size100with the100 fittest chromosomes from the list of feature subset solutions evalu-ated so far by the SA.Step2:Select50pairs of chromosomes using rank-based selection strategy.Step3:Perform crossover between the chromosomes using the half uniform crossover scheme(HUX).In HUX,half of the non-matching parents'genes are swapped.Step4:Kill the parent solutions.Step5:Mutate offspring with probability0.001.Step6:Evaluate the fitness of the offspring provided if it has not already been evaluated and if sufficient time is available.Update the database and estimate the time left.Step7:Go back to step2if the time is not up.3.3.3.Pseudocode of hill-climbing algorithmStep1:Select the best-to-date solution.Step2:Create10,000new candidate solutions from the selected solution by changing only one bit(feature)at a time.Step3:Evaluate the new solutions if they are not evaluated before and update the database.Replace the previous solution by the new solution(s)if they are better than the previous solution.Step4:Go back to step2and perform the hill climbing on each of the accepted new solutions.Repeatedly apply the process from steps2to3on selected solutions as long as the process is successful in finding improved solutions in every repetition and as long as the time is available.Step5:Update the database and update the time available.Step6:Select the next best-to-date solution from the database and go back to step2if time is still available.parative performance analysisWe compare our algorithms with the following benchmark algo-rithms:four commonly used greedy search algorithms(sequential backward selection[15],sequential forward selection[16],sequen-tial floating forward selection[18],and sequential floating backward selection[18])and four popular stochastic search algorithms(ant colony optimization[21],genetic algorithm[17],particle swarm op-timization[22]and simulated annealing[23]).We also compare our algorithm against a hybrid of filter and wrapper approaches—filter-wrapper(FW).Many hybrid algorithms have been proposed for fea-ture subset selection with encouraging results[24–29].It was not possible to implement all the methods and empirically assess them. Instead,based on the experience of other authors,we develop a rep-resentative hybrid algorithm FW.This consists of a number of pop-ular filter methods and a stochastic algorithm.FW is a three stage algorithm.Stage1:Since,it is hard to decide which filter method is best for a dataset because the performance of a filter method varies with different datasets[24],we use a number of popular filter methods to filter out irrelevant features.FW eliminates a feature when all of these filter methods—t-test,symmetric uncertainty[38],and Pear-son's correlation coefficients—dismiss the feature as irrelevant at the 0.05level.Stage2:FW uses PCA[14]to filter out redundant features.Stage3:FW uses SA[23]to find an optimal solution since our empirical results suggests that SA is better than other stochastic algorithms.The proposed and benchmark algorithms were tested on30 datasets(descriptions of datasets are provided in Section4.2).4.1.Test strategy for a standardized comparison of search algorithmsThere are a number of strategies employed to ensure fair com-parison of search algorithms.•All algorithms were run on a3.40GHz Intel᭨Pentium᭨D CPU with2GB RAM.•The values of each feature were normalized in a0–1range before the experiment.•All algorithms use GRNN classifiers to evaluate each of the resulting subsets using10-fold cross validation.•No algorithm evaluates the same solution more than once.•Each stochastic search algorithm(ACO,FW,GA,PSO,SA and SAGA) was run10times on each dataset,each time with different ini-tial populations of100individuals.The final performance of each algorithm was calculated by averaging over all10simulations.•Algorithms were ranked based on their performance.Their per-formance is measured in terms of classification accuracy with the best solution found during the entire run.Two different solutions having the same accuracy level are assessed in terms of the num-ber of features present in the feature subset solutions.We assign rank1to the best algorithm and rank m(mՅ10)to the worstI.A.Gheyas,L.S.Smith/Pattern Recognition43(2010)5--139algorithm.The Friedman test is used to test the null hypothesis that the performance is the same for all algorithms.After apply-ing the Friedman test and noting that it is significant,a pairwise comparison test(comparison of groups or conditions with a con-trol[41,p.181])was used in order to test the(null)hypothesis that there is no significant difference between any pair of the10 algorithms.4.2.Descriptions of datasetsWe use11synthetic datasets,18real-world benchmark datasets and one new real-world dataset to perform experiments.All of these datasets are high dimensional.4.2.1.Synthetic datasetsFeature interactions and feature redundancy are two major prob-lems often encountered when reducing the dimensionality of feature space.The principal motivation behind generating synthetic datasets was to recreate these problems on large scale and perform experi-ments on controlled datasets.Each dataset consists of10,000instances each of10,000features. Approximately one third of these features were completely irrele-vant.Among these10,000features only10informative features were included in the model.One third of them were actually the exact copy of the set of these10relevant features.The remaining features are correlated to varying degrees with the relevant features.All fea-tures are continuous-valued.They are highly correlated and they in-teract with one another.The response variable is a binary variable. The following steps were taken to generate these datasets.Step1:Specify different mean vectors and different covariance matrices for all the features for the11different datasets.Since mean vectors and covariance matrices of no two datasets are the same,the joint distribution of features is different in each dataset.Step2:Generate10,000combinations of feature values for each dataset from its unique mean vector and covariance matrix.Step3:The probability of the event of interest for each instance was estimated by the following model(we specified different sets of model parameters for different datasets).Only10features among 10,000features were included in the model.To simulate interactions between features,we included three interaction terms.Interaction terms are formed by the multiplication of two or more explanatory variables.We included one two-way interaction term(− 5X66X5789), one three-way interaction term(− 9X420X1103X8652)and one multi-way interaction term(+ 6X420X6166X6999X7200).P(Y)=1/(1+exp(−Z))(4) Z= 0+ 1X66+ 2X1103+ 3X4447+ 4X5789− 5X66X5789 + 6X420X6166X6999X7200+ 7X8652+ 8X9995− 9X420X1103X8652where P(Y)is the probability of the event of interest;(X1,X2,..., X10,000)represent different features;( 0, 1, 2, 3, 4, 5, 6,7, 8, 9)are the model parameters.We used Eq.(4)to generate all of the synthetic datasets.All the features in the model were arranged in the random order in all datasets.The differences between the datasets are mainly due to dif-ferent combinations of feature values and different values of model parameters.Step4:Generate a uniformly distributed random number in the range(0,1)for each observation.If the random number is greater than the probability of the event of interest,the value of the response variable is1,otherwise0.4.2.2.Benchmark datasets(modified)In addition to11synthetic datasets,we tested these algorithms on18benchmark datasets.Benchmark datasets were taken from UCI machine learning repository.The benchmark datasets are real-world datasets.The benchmark datasets on which the algorithms were tested are:(1)Adult dataset,(2)Annealing dataset,(3)Breast Cancer Wisconsin(Diagnostic)dataset,(4)Breast Cancer Wisconsin (Prognostic)dataset,(5)Chess—King-Rook vs.King-Pawn,(6)Con-gressional Voting Records dataset,(7)Dermatology—Psoriasis,(8) Dermatology—Seboreic Dermatitis,(9)Dermatology—Lichen Planus, (10)Dermatology—Pityriasis Rosea,(11)Dermatology—Cronic Der-matitis,(12)Dermatitis—Pityriasis Rubra,(13)Hepatitis,(14)Mush-room,(15)Spambase,(16)Wine,(17)Yeast,and(18)Zoo.The de-scriptions of the original benchmark datasets are available in[42]. These datasets contain varying number of features and instances,but have fewer than10,000features.Hence,we add a series of randomly generated features to each dataset to make a total of10,000features. We added completely irrelevant features because we did not want to destroy the original properties of the benchmark datasets.We did not change the number of observations of the benchmark datasets.4.2.3.New real-world dataset(smoking dataset)We received a three stage cross sectional survey data on the smoking habits of teenagers from the Centre for Tobacco Control Re-search at the University of Stirling and Open University.The data were collected from Scotland,England,Northern Ireland and Wales in three survey stages:stage1in1999,stage2in2002and stage 3in2004.The response variable is a binary variable(1=smoker, 0=non-smoker).Explanatory variables include socio-demographic characteristics of respondents,their knowledge and attitudes to-wards tobacco promotion of all sorts and their smoking knowledge, attitudes and behaviour.This smoking dataset contains285features, 3321instances but has a large number of missing values.Among the respondents,an overall proportion of11%(355respondents)are smokers.We applied multiple imputation with MCMC(Monte Carlo Markov Chain)algorithm to replace missing values[43].We did not add artificial features to this dataset.5.Results and discussionWe compare our proposed algorithm(SAGA)with the conven-tional search algorithms(ACO,FW,GA,PSO,SA,SBS,SFBS,SFFS and SFS)on30high dimensional datasets.The algorithmswereFig.1.Performance of the different algorithms(accuracy only).。
论文相似性检测原理
论文相似性检测原理相似性检测（也称为抄袭检测）是指通过比较两篇文本的内容、结构和语言特征，来判断它们之间的相似程度。
相似性检测在学术界和商业领域都有广泛应用，可以用于检测学术论文的抄袭、新闻稿件的转载、网上内容的复制粘贴等。
相似性检测的原理通常可以分为三个主要步骤：预处理、特征提取和相似度计算。
首先，预处理阶段负责将文本转换为算法可以理解和处理的形式。
这一阶段包括去除文本中的特殊字符、停用词（如“a”、“the”、“and”等）以及标点符号等。
预处理还可以进行词性标注、词干提取和词形还原等操作，以便更好地表达文本的语义信息。
接下来，特征提取是相似性检测的核心步骤。
特征是用来描述文本的显著属性，常用的特征包括词频、词向量和句法结构等。
词频特征是衡量文本相似性的一种简单且常用方法，通过统计每个单词在文本中出现的次数来表示文本的重要性。
词向量特征是一种将单词表示为向量的方法，能够更好地捕捉单词之间的语义关系。
句法结构特征则通过分析句子的语法结构，如主谓宾关系、修饰关系等，来衡量文本的结构相似性。
最后，相似度计算是用来度量两篇文本之间的相似程度的步骤。
常用的相似度计算方法有余弦相似度和编辑距离等。
余弦相似度是通过计算两个文本向量之间的夹角来衡量它们之间的相似程度，值越接近1表示相似度越高。
编辑距离则是通过计算将一个文本转换为另一个文本所需的最小编辑操作数，如插入、删除和替换等，来衡量它们之间的相似程度，值越接近0表示相似度越高。
除了以上的基本原理之外，还有一些深度学习的方法被应用在相似性检测中，如基于卷积神经网络（CNN）和循环神经网络（RNN）的模型。
这些模型可以对文本进行更深入的学习和表达，以提取更丰富的语义特征。
总之，相似性检测的原理包括预处理、特征提取和相似度计算。
通过将文本转换为可处理的形式，提取文本的显著特征，并使用合适的相似度计算方法，可以准确地比较两篇文本之间的相似程度，从而实现对抄袭行为的检测。
基于对称模糊相对熵的模糊模式识别(IJISA-V1-N1-8)
Published Online October 2009 in MECS(/)
Fuzzy Pattern Recognition Based on Symmetric Fuzzy Relative Entropy
I.J. Intelligent Systems and Applications, 2009, 1,68-75
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Copyright © 2009 MECS
Fuzzy Pattern Recognition Based on Symmetric Fuzzy Relative Entropy
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information, imprecise measurements, random occurrences, vague descriptions, or conflicting or ambiguous information and can appear in different circumstances, for instance, in definitions of features and, accordingly, objects, or in definitions of classes. Different methods process uncertainty in various ways [17-22]. Statistical methods based on probability theory assume features of objects to be random variables and require numerical information. Feature vectors having imprecise, or incomplete, representation are usually ignored or discarded from the classification process. In contrast, fuzzy set theory can be applied for handling nonstatistical uncertainty, or fuzziness, at various levels [2326]. Together with possibility theory, it can be used to represent fuzzy objects and fuzzy classes. Objects are considered to be fuzzy if at least one feature is described fuzzily, i.e. feature values are imprecise or represented as linguistic information. Classes are considered to be fuzzy, if their decision boundaries are fuzzy with gradual class membership. Fuzzy distance measurement, fuzzy similarity measurement and fuzzy entropy are three basic concepts in fuzzy set theory. Fuzzy distance measurement is used to measure the differences between fuzzy sets, and another commonly used concept is the divergence, some of its definitions and applications were denoted in reference [27] and [28]. In this paper, we will study fuzzy similarity degree, entropy, relative entropy, fuzzy entropy and fuzzy relative entropy, and presents novel fuzzy relative entropy, symmetric fuzzy relative entropy, and then we will discuss the applications of the symmetric fuzzy relative entropy in fuzzy spatial object recognition and classification. II. FUZZY SIMILARITY DEGREE, ENTROPY AND SYMMETRIC
Pattern Recognition
Pattern Recognition 49 (2016) 102–114Yimin Zhou a ,n ,1, Guolai Jiang a ,b ,1, Yaorong Lin baShenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, ChinabSchool of Electronic and Information Engineering, South China University of Technology, Chinaa r t i c l e i n f o ab s t r ac t&2015 Elsevier Ltd. All rights reserved.Article history:Received 17 March 2014 Received in revised form 8 August 2014Accepted 29 July 2015Available online 8 August 2015This paper presents a high-level hand feature extraction method for real-time gesture recognition. Firstly, the fi ngers are modelled as cylindrical objects due to their parallel edge feature. Then a novel algorithm is proposed to directly extract fi ngers from salient hand edges. Considering the hand geometrical characteristics, the hand posture is segmented and described based on the fi nger positions, palm center location and wrist position. A weighted radial projection algorithm with the origin at theKeywords: Computer vision Finger modelling Salient hand edge Convolution operatorReal-time hand gesture recognitionwrist position is applied to localize each fi nger. The developed system can not only extract extensional fi ngers but also fl exional fi ngers with high accuracy. Furthermore, hand rotation and fi nger angle variation have no effect on the algorithm performance. The orientation of the gesture can be calculated without the aid of arm direction and it would not be disturbed by the bare arm area. Experiments have been performed to demonstrate that the proposed method can directly extract high-level hand feature and estimate hand poses in real-time.A novel fi for handreal-time technique estimation pose hand and nger gesture recognitionat available lists Contents ScienceDirec tjournal homepage:/locate/prPattern RecognitionY . Zhou et al. / Pattern Recognition 49 (2016) 102–114 1031. IntroductionHand gesture recognition based on computer vision technology has been received great interests recently, due to its natural human-computer interaction characteristics. Hand gestures are generally composed of different hand postures and their motions. However, human hand is an articulated object with over 20 degrees of freedom (DOF) [12], and many self-occlusions would occur in its projection results. Moreover, hand motion is often too fast and complicated compared with current computer image processing speed. Therefore, real-time hand posture estimation is still a challenging research topic with multi-disciplinary work including pattern recognition, image processing, computer vision, arti fi cial intelligence and machine learning. In human –machine interaction history, keyboard input & character text output and mouse input & graphic window display are main traditional interaction forms. With the development of computer techniques, the human –machine interaction via hand posture plays an important role under three dimensional virtual environment. Many methods have been developed for hand pose recognition [3,4,10,18,24,29].A general framework for visual based hand gesture recognition is illustrated in Fig. 1. Firstly, the hand is located and segmented from the input image, which can be achieved via skin-color based segmentation methods [27,31] or direct object recognition algorithms. The second step is to extract useful feature for static hand posture and motion identi fi cation. Then the gesture can be identi fi ed via feature matching. Finally, different human machine interaction can be applied based on the successful hand gesture recognition.There are a lot of constraints and dif fi culties in accurate hand gesture recognition from images since human hand is an object with complex and versatile shapes [25]. Firstly, different from less remarkable metamorphosis objects such as human face, human hand possesses over 20 free degree plus variations in hand gesture location and rotation which make hand posture estimation extremely dif fi cult. Evidence shows that at least 6-dimension information is required for basic hand gesture estimation. The occlusion also could increase the dif fi culty in pose recognition. Since the involved hand gesture images are usually two dimensioned images, it would result in occlusion of some key parts of the hand on the plane project due to various heights of the hand shapes.Besides, the impact of the complex environment to the broadly applied visual-based hand gesture recognition techniques has to/10.1016/j.patcog.2015.07.014 0031-3203/&2015Elsevier Ltd. All rights reserved.nCorresponding author.E-mail addresses: ym.zhou@ (Y . Zhou), gl.jiang@ (G. Jiang). 1fi rst author and second author contribute equally in the paper. Thebe considered. The lightness variation and complex background such factors make it more dif fi cult for the hand gesture segmentation. Up to now, there is no united de fi nition for dynamic hand104Y . Zhou et al. / Pattern Recognition 49 (2016) 102–114Fig. 2. Hand gesture models with different complexities (a) 3D strip model; (b) 3 D surface model; (c) paper model [36]; (d) gesture silhouette; and (e) gesture contour.gesture recognition, which is also an unsolved problem to accommodate human habits and facilitate computer recognition. It should be noted that human hand has deformable shape in front of a camera due to its own characteristics. The extraction of a hand image has to be executed in real-time independent of the users and device. Human motion possesses a fast speed up to 5 m/s for translation and 300 1C/s for rotation. The sampling frequency of a digital camera is about 30–60 Hz, which could result in fuzzi fi cation on the collected images with negative impact on further identi fi cation. On the other hand, with the hand gesture module added in the system, the dealt frame number per second for the computer will be even less, which will bring more serious pressure on the relatively lower sampling speed. Moreover, a large amount of data have to be dealt in computer visual system, especially for high complex versatile objects. Under current computer hardware conditions, a lot of high-precision recognition algorithms are dif fi cult to be operated in real-time.Our developed algorithm focuses on single camera based realtime hand gesture recognition. Some assumptions are made without loss of generality: (a) the background is not too complex without large area skin color disturbance; (b) lightness should avoid too low or too light such worse conditions; (c) the palm is right faced to the camera with distance in the range r 0:5 m. These three limitations are not dif fi cult to be realized in the actual application scenarios.Firstly, a new fi nger detection algorithm is proposed. Compared to previous fi nger detection algorithms, the developed algorithm is independent of the fi nger tip feature but can extract fi ngers directly from the main edge of the whole fi ngers. Considering that each fi nger has two main “parallel ” edges, a fi nger is determined from convolution result of salient hand edge image with a speci fi c operator G. The algorithm can not only extract extensional fi ngers but also fl exional fi ngers with high accuracy, which is the basis for complete hand pose high-level feature extraction. After the fi nger central area has been obtained, the center, orientation of the hand gesture can be calculated. During the procedure, a novel high-level gesture feature extraction algorithm is developed. Through weighted radius projection algorithm, the gesture feature sequence can be extracted and the fi ngers can also be localized from the local maxima of angular projection, thus the gesture can be estimated directly in real-time.The remainder of the paper is organized as follows. Section 2 describes hand gesture recognition procedure and generally used methods. Finger extraction algorithm based on parallel edge characteristics is introduced in Section 3. Salient hand image can also be achieved. The speci fi c operator G and threshold is explained in detail in Section 4. High-level hand feature extraction through convolution is demonstrated in Section 5. Experiments in different scenarios are performed to prove the effectiveness of the proposed algorithm in Section 6. Conclusions and future works are given in Section 7.2. Methods of hand gesture recognition based on computer vision2.1. Hand modellingHand posture modelling plays a key role in the whole hand gesture recognition system. The selection of the hand model is dependent on the actual application environments. The hand model can be categorized as gesture appearance modelling and 3D modelling. Generally used hand gesture models are demonstrated in Fig. 2.3D hand gesture model considers the geometrical structure with histogram or hyperquadric surface to approximate fi nger joints and palm. The model parameters can be estimated from single image or several images. However, the 3D model based gesture modelling has quite a high calculation complexity, and too many linearization and approximation would cause unreliable parameter estimation. As for appearance based gesture models, they are built through appearance characteristics, which have the advantages of less computation load and fast processing speed. The adoption of the silhouette, contour model and paper model can only re fl ect partial hand gesture characteristics. In this paper, based on the simpli fi ed paper gesture model [36], a new gesture model is proposed where each fi nger is represented by extension and fl exion states considering gesture completeness and real-time recognition requirements.Many hand pose recognition methods use skin color-based detection and take geometrical features for hand modelling. Hand pose estimation from 2D to 3D using multi-viewpoint silhouette images is described in [35]. In recent years, 3D sensors, such as binocular cameras, Kinect and leap motion, have been applied for hand gesture recognition with good performance [5]. However, hand gesture recognition has quite a limitation, since 3D sensors are not always available in many systems, i.e., Google Glasses.2.2. Description of hand gesture featureThe feature extraction and matching is the most important component in vision-based hand posture recognition system. In early stage of the hand gesture recognition, colored glove or labeling methods are usually chosen to strengthen the feature in different parts of the hand for extraction and recognition. Mechanical gloves can be used to capture hand motion, however, they are rigid with only certain free movements and relatively expensive cost [23]. Compared with the hand recognition methods with additional assistance of data glove or other devices, computervision based hand gesture recognition will need less or no additional device, which is more adaptable and has bright application prospect. A real-time algorithm to track and recognize hand gesture is described for video game in [23]. Only four gestures can be recognized, which has no generality. Here, the hand gesture images without any markers arediscussed for feature extraction.Fig. 1. The general framework of computer based hand posture recognition.Y . Zhou et al. / Pattern Recognition 49 (2016) 102–114 105The generally used image feature for hand gesture recognition can be divided into two categories, low-level and high-level, as shown in Fig. 3. The low-level features such as edge, edge orientation, histogram of oriented gradients (HOG) contour/silhouette and Haar feature, are basic computer image characteristics and can be extracted conveniently. However, in actual applications, due to the diversities of hand motions, even for the same gesture, the subtle variation in fi nger angle can result in large difference in the image. With rotational changes in hand gesture, it is much more dif fi cult to recognize gestures with direct adoption of low-level feature matching.Since the skin color is a distinctive cue of hands which is invariant to scale and rotation, it is regarded as one of the key features. Skin color segmentation is widely used for hand localization [16,31]. Skin detection are normally achieved by Bayesian decision theory, Bayesian classi fi er model and training images [22]. Edge is another common feature for model-based matching [36]. Histogram of oriented gradients has been implemented in [30]. Combinations of multiple features can improve the accuracy and robustness of the algorithm [8].Fingertip position, fi nger location and gesture orientation such high-level gesture features are related to the hand structure, which has direct relationship to the hand recognition. Therefore, they can be easily matched for various gesture recognition in real-time. However, this type of features is generally dif fi cult to be extracted accurately.In [1], fi ngertips were located from probabilistic models. The detected edge segments of monochrome images are computed by Hough transform for fi ngertip detection. But the light and brightness would seriously affect the quality of the dealt images and detection result. Fingertip detection and fi nger type determination are studied with a model-based method in [5], which is only applicable for static hand pose recognition. In [26], fi ngertips are found by fi ngertip masks considering their characteristics, and they can be located via feature matching. However, objects which share similar fi ngertip shapes could result in a misjudgment.Hand postures can be recognized through the geometric features and external shapes of the palm and fi ngers [4]. It proposes a prediction model for showing the hand postures. The measurement error would be large, however, because of the complexity of the hand gestures and diversi fi ed hand motions. In [3], palm and fi ngers were detected by skin-colored blob and ridge features. In [11], a fi nger detection method using grayscale morphology and blob analysis is described, which can be used for fl exional fi nger detection. In [9,13], high-level hand features were extracted by analyzing hand contour. 2.3. Methods of hand gesture segmentationFast and accurate hand segmentation from image sequences is the fundamental for gesture recognition, which have direct impact on the followed gesture tracking, feature extraction and fi nal recognition performance. Many geometrical characteristics can be used to detect hand existence in image sequences via projection, such as contour, fi ngertip and fi nger orientation [26]. Other non-geometrical features, i.e., color [2], strip [34] and motion can also be used for hand detection. Due to the complex background, unpredictable environmental factors and diversi fi ed hand shapes, hand gesture segmentation is still an open issue.Typical methods for hand segmentation are summarized as follows. Increasing constraints and building hand gesture shape database are usually used for segmentation. Black or white wall and dark color cloth can be applied to simplify the backgrounds. Besides, particular colored gloves can be worn todivide the hand and background through emphasized front view. Although these kinds of methods have good performance, it adds more limitation at the cost of freedom. A database can be built to collect hand sample images at any moment with different positions and ratios for hand segmentation through matching. It is a time consuming process, though, the completeness of thedatabase can never be achieved which has to be updated all the time.Methods of contour tracking include snake-model based segmentation [17], which can track the deformation and non-rigid movement effectively, so as to segment the hand gesture from the backgrounds. Differential method [20] and its improved algorithm can realize the segmentation by the deduction from the object images to the background images. It has a fatal defect that the camera has to be fi xed and the background should be kept invariant during background and hand image extraction.Skin color, assumed as one of the most remarkable surface features of human body, is often applied in gesture segmentation [31]. However, only adoption of this feature would be easily affected by the ambient environmental variations, especially when a large area of skin color disturbance is in the background, i.e., hand gesture overlapped by human face. Motion is another remarkable and easily extracted feature in gesture images. The combination of these two features becomes more and more popular in recent years [15].Depth information (the distance information between the object and the camera) in the object images can also be used for background elimination and segmentation since human hands are the closet objects to the camera. Currently, the normally used depth camera are Swiss Ranger 4000 from Mesa Imaging company, Cam cube 2.0 from PMD Technologies, Kinect from Microsoft and Depth camera from PrimeSense. 2.4. Methods of gesture recognition2.4.1. Methods of static gesture recognitionMethods of static gesture recognition can be classi fi ed into several categories:(1) Edge feature based matching: Gesture recognition based on this type offeature is realized through the calculated relationship between data sets of the features and samples to seek the best matching [22,28,33,36]. Although it is relatively simple for feature extraction and adaptable for complex background and lightness, the data based matching algorithm is quite complicated with heavy computational load and time cost. A large amount of templates should be prepared to identify different gestures.(2) Gesture silhouette based matching: Gesture silhouette is normallydenoted as binary images of the wrapped gesture from segmentation. In [20], matching is calculated through the size of the overlapped area between the template and silhouette.Zernike matrix of the images is used to cope with the gesture rotation [14] and feature set is developed for matching. The disadvantages of this type of method are that not all gestures can be identi fi ed with only silhouette and accurate hand segmentation is required.(3) Harr-like feature based recognition: Harr-like feature based Adaboostrecognition algorithm has achieved good performance in face recognition [21]. This method can be used for hand detection [37] and simple gesture recognition [10]. Experiments demonstrate that the method can recognize speci fi c gestures in real-time under complex background environments. However, Harr-like feature based algorithmFig. 3. The generally used feature and classi fi cation for hand gesture recognition.Extraction Identification106 Y. Zhou et al. / Pattern Recognition 49 (2016) 102–114has high requirement on the consistency for the dealt objects, whereas hand gesture has diversi fi ed shape variations. Currently, this type method can only be applied in prede fi ned static gestures recognition.(4)External contour based recognition: External contour is an importantfeature for gesture. Generally speaking, different gestures have different external contours. The curvature of the external contour is varied in different positions of a hand (i.e., curvature is large at fi ngertip). In [9], curvature is analyzed for CSS (Curvature Scale Space) feature extraction to recognize gesture. Fingertip, fi nger root and joint such high-level features can be extracted from contour analysis [13]. A feature sequence is constructed by the distances from the contour points to the center for gesture recognition [32]. This type of method is adaptable for the angle variation between fi ngers but also dependent on the performance of the segmentation.(5)Finger feature based recognition: Finger is the most widely appliedhigh-level feature in hand pose recognition since the location and states of the fi ngers embody the most intuitional characteristics of different gestures. Only the fi nger positions, fi nger states and hand center are located thus simple hand gestures can be determined directly.Several fi ngertip recognition algorithms are compared in [6]. In [26], circular fi ngertip template is used to seek the fi ngertip location and motion tracking. Combined with skin color feature, Blob and Ridge features are used to recognize palm and fi ngers [3]. However, only extensional fi ngers can be recognized via this type of methods.2.4.2. Methods of motion gesture recognitionTime domain models are normally adopted for motion gesture recognition, which includes HMM (Hidden Markov Model) and DTW (Dynamic Time Warping) based methods:(1)HMM-based method: It has achieved good performance in voicerecognition area and applied in gesture recognition as well. Different motion gesture sequences are modelled via HMM, and each gesture is related to a HMM process. HMMbased method can realize recognition through feature matching at each moment, whose training process is a dynamic programming (DP) process. This method can provide time scale invariance and keep the gestures in time sequence. However, the training process is time consuming and the selection of its topology structure is determined by the expert experience, i.e., trial and error method used for number of invisible states and transfer states determination.(2)DTW-based method: It is widely used in simple tracking recognitionthrough the difference between the dealt gestures and standard gestures for feature matching at each moment. HMM and DTW are essentially dynamic programming processes, and DTW is the simpli fi ed version of HMM. DTW-based recognition has limitation on the word database applications.In summary, methods of hand modelling, gesture segmentation and feature extraction are discussed. Most used hand gesture recognition methods are also illustrated. The following sections will introduce the proposed algorithm for real-time hand gesture recognition in detail. 3.Finger extraction algorithm based on parallel edge featureThe most notable parts of a hand to differentiate other skin objects, i.e, human face, arm, are fi ngers. As it is known, fi nger feature extraction and matching have great signi fi cance in hand segmentation. Contour can be extracted from silhouette of a hand region as the commonly used feature for hand recognition. Due to nearly 30 degrees of freedom in hand motion, hand image extraction will be executed regarding a hand as a whole. Moreover, arm should be eliminated. It should be noted that occlusion among four fi ngers (except thumb) could frequently occur, especially for fl exional fi ngers.To solve these problems associated with hand image extraction, a model-based approach for fi nger extraction is developed in this paper. It can obviate the fi nger joint location in hand motion and extract fi nger features from the silhouette of the segmented hand region. In complex background circumstances, models with fi xed threshold can result in false detection or detection failure. However, fi xed threshold color model is still selected for segmentation in this paper because of its simplicity, low computational load and invariant properties with regard to the various hand shapes. The threshold is prede fi ned to accommodate the general human hand sizes. Then the selected pixels are transformed from RGB-space to YCbCr-space for segmentation. Finger extraction is explained in detail.3.1.Salient hand gesture edge extraction3.1.1. Finger modellingCombined with the skin, edge and external contour such easily extracted low-level features, a novel fi nger extraction algorithm is proposed based on the approximately parallel fi nger edge appearance. It can detect the states of the extensional and fl exional fi ngers accurately, which can also be used for further high-level feature extraction. It is known that fi ngers are cylindrical objects with nearly constant diameter from root to tip. As for human hand motion, it is almost impossible to move the distal interphalangeal (DIP) joint without moving the adjacent proximal interphalangeal (PIP) joint with no external force assistance and vice versa. Therefore, there is almost a linear relationship between these two types of joints, where the fi nger description can be simpli fi ed accordingly.Firstly, each fi nger is modelled by its edges, which is illustrated in Fig. 4(a).C fi, the boundary of the ith fi nger, is the composition of arc edges (C ti, fi ngertip or joints) and a pair of parallel edges (C ei [ C0ei , fi nger body), described asC fi ¼ ðC ei [ C 0ei Þ [ X C ti;j ð1Þj ¼1;2where the arc edge C ti;j denotes the fi nger either in extensional (j¼1) state or fl exional state (j¼2) (see two green circles inFig. 4(b)).The fi nger center line (FCL), C FCLi, is introduced as the center line of the parallel fi nger edges to represent the main fi nger body. The distance between fi nger edges is de fi ned as 2d, which is the averaged diameter of all the fi ngers. Fingertip/joint center O ti is located at the end of FCL, and it is the center of the arc curve C ti as well. The fi nger central area along with C FCLi will be extracted for fi nger detection. Compared with many algorithms based on fi ngertip feature [26], the proposed method is more reliable which can also detect the fl exional fi ngers successfully.Y . Zhou et al. / Pattern Recognition 49 (2016) 102–114 107Fig. 5. The diagram of extracting hand salient edge procedure.3.1.2. Structure of hand gesture edgeThe remarkable hand edge C hand of a gesture can provide concise and clear label for different hand gestures. Considering the hand structure characteristics and the assumed constraints, C hand consists of the following curves:5C hand ¼ X C fi þC p þC nð2Þi ¼ 1where C p is the palm/arm edge curve and C n is the noise edge curve. The diagram of the hand edge is shown in Fig. 4(b). Finger edges and palm/arm edges have direct relationship with the gesture structure, which are the main parts of the hand gesture edges and have to be detected as fully as possible. Edge curves formed by palmprint, skin color variation and skin rumple are noise, which has no connection with the gesture structure and should be eliminated completely.3.1.3. Extracting the salient hand gesture edgeAs for the hand gesture image input with complex background, skin color based segmentation algorithm is selected for initial segmentation. Morphology fi lter is then used to extract hand area mask and gesture contour I contour ðx ; y Þ. The gray image I gray ðx ; y Þof the gesture can be obtained at the same time, where arm area might be included. Canny edge detection algorithm [7] can extract most of the remarkable gesture edges. However, the detection results will also contain some noisy edges formed by the rumple and re fl ection from hand surface, which should be separated from the fi nger edges. handThecontoursalient whichhand edgeincludesimageboundariesI edge ðx ; y Þ ofis mainlyextensional made fi ngers,up offl exional fi ngers and arm/palm. Adduction (approximation) and abduction (separation) movements of the fi ngers can be referenced with fi nger III (middle fi nger), and it has slight movement without external force disturbance during motion. When the fi ngers are in extensional states, they are free to carry out adduction and abduction movements, whose edges areeasily obtained. When the fi ngers are clenched into a fi st or in ‘six ’ numbergesture such fl exional states, as shown in Fig. 4, obvious ravine would be formed in the appressed part with lower gray values in the related pixels. Based on this characteristic, most noisy edges can be eliminated.The procedure of extracting the salient hand edge is depicted in Fig. 5. One of the hand posture shown in Fig. 4(b) is used as an example, where its grayscale hand image can be seen in Fig. 5( a ). The steps of I edge ðx ; y Þ extraction are summarized as follows:1. Extract grayscale hand image I gray ðx ; y Þ (see Fig. 5(a)) and hand contour image I contour ðx ; y Þ (see Fig. 5(b)) from source color image using skin color segmentation method in [16].2. Extract canny edge image I canny ðx ; y Þ (see Fig. 5(c)) from3. ApplyingI gray ðx ; y Þ [7]the. threshold Th black ( prede fi ned) to grayscale handimage for extraction, then the obtained I black ðx ; y Þ (see Fig. 5( d )) is I black ðx ; y Þ ¼ ( 10;; ððII graygray ððxx ;; yy ÞÞZo ThTh blackblack Þ Þ3Þ ðThe boundaries of the fl exional fi ngers are extracted from the overlapped area, i.e., I canny ðx ; y Þ \ I black ðx ; y Þ.4. Then the salient hand edge image I edge ðx ; y Þ is obtained:I edge ðx ; y Þ ¼ I black ðx ; y Þ \ I canny ðx ; y Þ [ I contour ðx ; y Þ ð4ÞThe curve denoted by binary image I edge ðx ; y Þ shown in Fig. 5( e )) is the remarkable edge C hand .3.2. Finger extraction via parallel edge featureFinger edge modelHand gesture edgesFig. 4. The diagram of the fi nger edge model. (For interpretation of the references to color in this fi gure, the reader is referred to the web version of this paper.)ANDORgreyI contourI canny I blackI edgeI ExtentionalfingersFlexionalfingerseiC eiC tiC d2 Fingertip/jointcurveFinger paralleledgesFinger center line ( F CL) tiO Fingertip/jointcenterFingertip or finger joint edge tjCPalm/arm edge pC nC Noise edge The parallel edges of fingersFinger center line (FCL) iFCLC。
PatternRecognition
16
Decision Trees
#holes
0 moment of inertia
1 #strokes
2
#strokes
<t
best axis direction
0
t #strokes 2 x 4 w
0
1 0 1
60
90
-
/
1
0
A
8
B
17
Decision Tree Characteristics
20
Information Gain
The information gain of an attribute A is the expected reduction in entropy caused by partitioning on this attribute. |Sv| Gain(S,A) = Entropy(S) ----- Entropy(Sv) v Values(A) |S| where Sv is the subset of S for which attribute A has value v.
8
Classification using nearest class mean
Compute the
Euclidean distance between feature vector X and the mean of each class.
Choose closest class,
if close enough (reject otherwise)
The data is converted to a discrete structure (such as a grammar or a graph) and the techniques are related to computer science subjects (such as parsing and graph matching).
pattern recognition letters 的latex模板 -回复
pattern recognition letters 的latex模板-回复如何使用中括号内的内容找到Pattern Recognition Letters 的LaTeX 模板。
首先，我们需要明确Pattern Recognition Letters 是一份期刊，它通常会为投稿者提供LaTeX 模板来撰写文章。
在查找LaTeX 模板之前，我们可以先了解一下Pattern Recognition Letters 是什么以及其主要特点。
Pattern Recognition Letters 是一个国际期刊，它致力于准确、快速地发布与模式识别相关的高质量研究成果。
其特点包括高影响因子、广泛的读者群体和严格的审稿流程。
由于期刊具有一定的格式要求，使用其提供的LaTeX 模板有助于确保论文的格式与期刊要求一致，并提高投稿的成功率。
首先，我们可以尝试在Pattern Recognition Letters 的官方网站上查找LaTeX 模板。
我们可以在其网站的"Instructions for Authors"或"Author Guidelines"等栏目下找到相关信息。
这些栏目通常会提供详细的投稿指南、格式要求以及模板下载链接。
若在官方网站上未找到相关的LaTeX 模板信息，我们可以转向其他资源，如学术论坛、模板分享平台或科研社区。
在这些平台上，我们可以搜索关键词"Pattern Recognition Letters LaTeX template"或"Pattern Recognition Letters journal template"，并浏览相关帖子、下载链接以及其他用户的回复。
另外，我们还可以尝试联系Pattern Recognition Letters 的编辑部或主编。
他们通常能够提供最准确和最新的LaTeX 模板信息，并解答相关疑问。
FUZZY综合评估聚类法分区预报二代棉铃虫发生量
FUZZY综合评估聚类法分区预报二代棉铃虫发生量
华尧楠;华崇钊
【期刊名称】《山东农业科学》
【年(卷),期】1989(000)004
【摘要】本文从观测数据不齐全,而实践经验丰富的角度出发,采用Fuzzy综合评估的方法,凭实践经验,组成单因子关系矩阵进行加权处理,给出多因子综合相似矩阵,然后用Fuzzy聚类分析,将某地区的二代棉铃虫集合的某些元素与发生程度等级集合的某一元素聚为一类,即可作出分区预报.不仅提供了一种新的Fuzzy分析预测病虫方法,且解决了过去凭实践经验无法运算的问题.
【总页数】4页(P21-24)
【作者】华尧楠;华崇钊
【作者单位】不详;不详
【正文语种】中文
【中图分类】S435.622.3
【相关文献】
1.二代棉铃虫发生量预报模型的初步研究 [J], 史惠玲;冯少兰
2.玛河流域第二代棉铃虫发生量的预报 [J], 贺福德
3.二代棉铃虫发生量预报技术研究 [J], 靳桂芝;张会孔
4.第二代棉铃虫发生量的多元统计分析 [J], 丁世飞
5.二代棉铃虫发生量与发生期预测预报方法的研究 [J], 张平磊;余秀林
因版权原因，仅展示原文概要，查看原文内容请购买。
elasticsearch fuzzy 原理
elasticsearch fuzzy 原理在Elasticsearch 中，模糊搜索（Fuzzy Search）是一种允许在查询中包含拼写错误或近似匹配的搜索方法。
模糊搜索的实现主要基于编辑距离（Edit Distance）的概念，它度量两个字符串之间的相似性。
编辑距离是通过一系列基本编辑操作将一个字符串转换成另一个字符串所需的步骤数。
这些基本编辑操作包括插入、删除、替换字符。
编辑距离越小，两个字符串越相似。
在Elasticsearch 中，模糊搜索通常使用基于Levenshtein 距离的算法来实现。
Levenshtein 距离是指通过插入、删除、替换字符将一个字符串转换成另一个字符串的最小步骤数。
Elasticsearch 中的Fuzzy Search 使用了Damerau-Levenshtein 距离，这是Levenshtein 距离的变种，允许交换相邻字符。
以下是模糊搜索的一般原理：1. 相似度匹配：用户输入的查询词会与索引中的词进行比较，计算它们之间的相似度。
相似度的计算基于编辑距离，即计算需要多少次基本编辑操作才能将一个词转换成另一个词。
2. 阈值设定：用户可以指定一个阈值，只有相似度小于该阈值的文档才会被返回。
这有助于过滤掉相似度较低的匹配。
3. 模糊搜索的语法：在Elasticsearch 中，模糊搜索可以通过在查询词后面加上波浪符（~）并指定一个模糊度参数来实现。
模糊度参数表示允许的最大编辑距离，例如，`apple~1` 表示查找编辑距离不超过1 的与"apple" 相似的词。
示例：```json{"query": {"fuzzy": {"field_name": {"value": "user_input","fuzziness": 2}}}}```在这个例子中，`field_name` 是你想要进行模糊搜索的字段，而"user_input" 是用户提供的查询词，`fuzziness` 参数指定了允许的最大编辑距离。
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1．Distance between fuzzy sets
Let the universe X x 1 , x 2 , , x n ，A ，B be two fuzzy sets in
~ ~
X，p be a positive real number. Then
acceptable，but its classification effect largely depends on the technique of known pattern class membership function built.
Ex.7.20 Divide people into three classes: the old-aged, the middle-aged, the young-aged. They correspond to three fuzzy sets
membership principle ： Suppose there are M fuzzy sets
universe
X，and the membership
A1 , A 2 , , A M ~ ~ ~ function of A i is ~
in the
Ai ~
x ，
then for any given x 0 X ，if
dM ( A, B ) A ( xi ) B ( xi ) ~ ~ ~ i 1 ~
n
M-distance of two vectors in clustering
p
1 p
is defined as the Minkowski distance between fuzzy sets A and B .
Block distance
n
A ( xi ) B ( xi )
~ ~
i 1
When p 2 , it is called Euclidean distance ， denoted by
d E ( A, B ) ， ~ ~
d E ( A, B ) ~ ~
Euclidean distance
is approximately a right triangle.
6.4.2 Indirect method——Principle of Fuzzy Closeness Optimization A problem to find closeness degree between fuzzy sets
~ ~ ~
max[ 7 8 ,
1 8,
0 ] 7 8 A 1 65
~
∴ It belongs to the old-aged people
Ai ~
x
middle old
④x=21： A 1 21 0 ，
~
youth
1
A 2 21 1 200 ，
0, x 20 2 ) , 2( 20 The middle： x 45 2 A 2 x 1 2 ( ) , 30 ~ 2 ( x 70 ) 2 , 20 0,
0 x 20 20 x 30 30 x 60 60 x 70 x 70
n 2
A ( xi ) B ( xi )
~ ~
i 1
Other distances：relative distance, weighted distance
2. degree of similarity (贴近度)
Let A ， B ， C be fuzzy sets in the universe X. If a
~
1 60
min A B , B C
right triangle： R A , B , C 1
~
1 90
A 90
Equilateral Triangle： E A , B , C 1
~
1 180
A C
right isosceles triangle： by IR I R ,
Ai x 0
~
max
A1 ~
x 0 , A2 x 0 , , A M
~ ~
x 0
x0
is considered to belong to A i .
~
membership principle is obvious, and public
A1
~
， A 2 ， A 3 ，Their membership functions are：
~
~
The
0, x 50 2 ) , 2( 20 old： A1 x x 70 2 ~ 1 2 ( ) , 20 1,
0 x 50 50 x 60 60 x 70 x 70
~ ~
If X is a finite interval in real field R，
dM b ( A , B ) A ( x ) B ( x ) dx a ~ ~ ~ ~
p 1 p
If X is extended to the entail real field， boundaries a， are replaced by b －∞ and ∞ respectively.
~
A3 21 199 200 ，
~
0.5
∴It belongs to the young.
0 20
45 70
age 100
Ex.6.21 Chromosome recognition (染色体识别) or erythrocytes (or red blood cells,白血球) classification problem. These problems are finally deduced to recognize triangles, i.e. to classify a triangle into one of an isosceles triangle(等腰三角形 (I)), a right triangle(直角三角形(R)), a right isosceles triangle(等腰直角三角形(IR)), Equilateral Triangle(正三角形 (E)), an other triangle(其他三角形(T)).
max[ 0 ,
1,
0 ] 1 A 2 45 ，
~
the person at age 45 belongs to A 2 , the middle-aged.
~
② x=30： A1 30 0 ， A2 30 0 . 5 ， A3 30 0 . 5 ，
6.4.1 direct approach——membership principle Directly compute sample’s membership degree，according to maximum membership to classify. —— used to recognize single pattern
~ ~ ~
IR A , B , C min
~
I A , B , C , ~
R A, B , C
~
Other triangle：by T I E R ,
~
~
~
~
~
T A , B , C min[ 1 I A , B , C , 1 R A , B , C , 1 E A , B , C ]
5 60
0 . 917
R x0 1
~
90
E x0 1
~
1 180
85
45 1
40 180
0 . 778
IR x 0 min 0 . 917 ,
~
0 . 944
0 . 917
T x 0 min 1 0 . 917 ,
• 6.1 Introduction to fuzzy set theory • 6.2 Fuzzy sets • 6.3 Fuzzy relations and Fuzzy matrices
are all omitted here due to timndirect approaches of fuzzy pattern classification
0 x 20 20 x 30 30 x 40 x 40
Ans：① Put x=45 into three membership functions： A1 45 0 ， A 2 45 1 ， A3 45 0 .
~ ~ ~
That is ∴
Chapter 6 Fuzzy Pattern Recognition Methods
6.1 Introduction to fuzzy set theory 6.2 Fuzzy sets 6.3 Fuzzy relations and Fuzzy matrices 6.4 Direct and indirect methods of fuzzy pattern recognition 6.5 Fuzzy Clustering approaches
~
1 0 . 944 , 0 . 222
1 0 . 778
min 0 . 083 ,