第6章(龚尚福) 子程序结构

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数字电子技术基础二版张克农6章习题解答.docx

6章习题题解6」集成施密特触发器及输入波形如图题6.1所示,试画出输出妬的波形图。

施密特触发器的阈值电平S+和U T -如图所示。

［解］集成施密特触发器输出如的波形如图解6」所示。

6.2图题6.2所示为数字系统屮常用的上电复位电路。

试说明其工作原理，并定性画岀 ⑷与心波形图。

若系统为高电平复位，如何改接电路？R\\C 丄I图题6.2［解］工作原理分析如下(1) 当Vcc 刚加上时，由于电容C 上的电压不能突变，尙为低电平，输出“()为低电平；随着电容充电，血按指数规律上升，当 QU T 时，输出仇()变为高电平，完成了低电平复位功能。

波形如图解6.2所示。

(2) 若系统为高电平复位，仅将图中R, C 互换位置即可。

6.3图题6.3是用TTL 与非门、反相器和肚积分电路组成的积分型单稳态触发器。

该电路用图题6.3所示正脉冲触发，R<R试分析电路工作原理，画出w ()i> «i2和坎)的波形图。

JT图解6」1JT图解6.2图题6」［解］工作原理分析如下触发信号未到来时，⑷为低电平，输出问为高电平；正触发脉冲到来时，问I 翻为低电平此时由于均2仍为高电平，输出如为高电平不变，电容通过尺放电，当⑷2下降到S 时仙仍为高电平)，输出“()翻为高电平，暂稳态过程结束。

”()i 、”】2和〃()的波形见图解6.3。

图题6.51 M O1R U 12 Ln __ 1 --- ]・&)—w o"IG|C H 5Ot6.4集成单稳态触发器74121组成的延时电路如图丿 (1) 计算输出脉宽的调节范圉； (2) 电位器旁所串电阻有何作用？图题6.4［解］⑴ 输出脉宽:d=0fi7(R + RQ ，分别代入Rw=O 和22kQ 计算，可得心的调节范围为：3.6mS</w <19mS o(2)电阻/?起保护作用。

若无R,当电位器调到零时，若输出由低变高，则电容C 瞬间相当于短路，将直接加于内部门电路输出而导致电路损坏。

5项目五子程序的应用

化学工业出版社
任务一
子程序的格式和应用
2．从子程序返回 RET/M17/M02
（1）指令格式
RET M17 M02 （2）指令功能
（子程序中）当前程序段的其它指令执行完成后，返回主程序中由P指定的程序段继续执行。
化学工业出版社
任务一
化学工业出版社
任务一
子程序的格式和应用
③在加工较复杂的零件时，往往包含许多独立的工序，有时工序之间需要作适当的调整，为了优化加工程序，把每一个独立的工序编成一个子程序，这样形成了模块式的程序结构，便于对加工顺序的调整，主程序中只有换刀和调用子程序等指令。
化学工业出版社
化学工业出版社
任务一
子程序的格式和应用
2. 子程序结束指令
（1）指令格式 M99 （2）指令功能子程序运行结束，返回主程序（3）指令说明 ①执行到子程序结束M99指令后，返回至主程序，继续执行M98 P××××程序段下面的主程序； ②若子程序结束指令用M99 P___格式时，表示执行完子程序后，返回到主程序中由P___指定的程序段； ③若在主程序中插入M99程序段，则执行完该指令后返回到主程序的起点。
化学工业出版社
任务一
2.子程序的嵌套
子程序的格式和应用
为了进一步简化程序，可以让子程序调用另一个子程序，这种程序的结构称为子程序嵌套。在编程中使用较多的是二重嵌套，其程序的执行情况如图5-1所示。
图5-1 程序的嵌套
化学工业出版社
任务一 3．子程序的应用
任务二
一、加工图纸
子程序综合加工实例
本任务以图5-4为子程序综合应用为例，巩固前面所学习的任务，工件毛坯为经过预先铣削加工过的规则合金铝块，尺寸为80mm×80mm×30mm。

学生课程成绩统计程序设计

《微机原理与接口技术》课程设计（学年论文）说明书课题名称：学生课程成绩统计程序设计（A1 难度系数1）学生学号：专业班级：学生姓名：学生成绩：指导教师：课题工作时间：2013-6-13 至2013-6-18填写说明：1. 一、二、三项由指导教师在课程设计（学年论文）开始前填写并交由学生保管；2. 第五项由学生在完成课程设计后填写，并将此表与课程设计一同装订成册交给指导教师；3. 成绩评定由指导教师按评定标准评分。

4. 此表格填写好后与正文一同装订成册。

课程设计评审标准（指导教师用）学生课程成绩统计程序设计说明书1、方案论证（1）汇编程序设计步骤、要点（2）DOS系统调用2、程序设计（1）总体设计设计分析与思路说明总体框图(框图中每一个模块的功能说明)（2）程序设计流程图程序代码及注释3、程序调试步骤与结果（1）编辑源程序（2）汇编源程序（3）连接程序（4）在TD中调试程序（5）程序运行结果截屏图片结果说明4、结论用结果说明设计成功之处，对某些问题进行分析、展望。

1．方案论证（1）汇编程序设计步骤、要点1 引言汇编语言能充分利用计算机所有的硬件特性并对硬件进行直接控制，汇编语言编制的程序比使用其它语言编制的程序执行速度快、资源占用少，所以，汇编语言在工业自动化控制和智能化产品的生产上有着十分广泛的用途。

但是，汇编语言是一种低级符号语言，与机器指令有着一一对应的关系，与高级语言相比不太符合人的思维习惯，它向寄存器、内存单元，必须通过一种具体的计算机来学习，同时要求初学者应具有一定的硬件基础，真正掌握起来有一定的难度。

2 汇编语言程序设计技巧808618088汇编语言程序设计中一般说来遵循以下几个步骤：首先分析题意，确定解题算法。

然后根据算法由粗到精画程序流程图，最后编写程序。

3 寻址方式的准确使用程序设计的目的是将输入数据加工处理转换成输出数据，获取正确的数据是保证程序处理正确的前提，而获取正确的数据又与正确地使用寻址方式关系密切，所以有必要先从寻址方式谈起。

中职学校《机械基础》重庆高考重点总复习课件(下)(第六章至第九章)(教材：高教版统编)(云天课件)

3．死点位置当以机构的摇杆为主动件、曲柄为从动件，在机构处于压力角 90 的位置时，曲柄不能动作的位置。死点位置有两个，位于连杆与曲柄共线时的位置。死点的害处：影响机构平稳性，特别是启动性能。死点的解决办法：惯性、多组错列。
P.126
死点的用处：用于锁定机构。
第二节平面四杆机构任务实施
P.117
常用机构：平面连杆机构、凸轮机构、棘轮机构等机构。内容：
运动副
低副：转动副、移动副、螺旋副高副：齿轮、凸轮… …
铰链四杆机构的形式铰链四杆机构类型的判定含有一个移动副的四杆机构平面四杆机构的基本特性
平面四杆机构常用机构
凸轮机构
凸轮机构的类型凸轮机构的材料及结构凸轮机构的运动分析平面凸轮轮廓曲线的绘制凸轮机构的传力特性
无论何杆作机架，都是双摇杆机构 “短+长〉另两杆长之和”，（0个曲柄）
以最短杆之相邻杆作机架，得曲柄摇杆机构（1个曲柄）
得双曲柄机构（2个曲柄） “短+长 ≤ 另两杆长之和” 以最短杆作机架，以最短杆之相对杆作机架，得双摇杆机构（0个曲柄）
曲柄摇杆机构
双曲柄机构
双摇杆机构
第二节平面四杆机构三、含有一个移动副的四杆机构
中职学校《机械基础》重庆高考重点总复习课件
P.117
课件制作：重庆市涪陵区职教中心数控组胡志恒
中职学校《机械基础》重庆高考重点总复习课件
P.117
课件制作：重庆市涪陵区职教中心数控组胡志恒
第六章
常用机构
P.117
任务描述
平面连杆机构：基本形式及其演化。机构的组成、运动规律
第六章
常用机构
*四、平面四杆机构的基本特性 1．急回运动特性在曲柄摇杆机构中, 当以曲柄（主动）为匀速旋转时, 摇杆的往返速度不等.

计算机组成与结构 for 期末郝尚富

（期中考试已考）1．己知某计算机有80条指令，平均每条指令由12条微指令组成，其中有一条取指微指令是所有指令公用的，设微指令长度为32位。

请算出控制存储器容量。

解：微指令所占的单元总数：(80×12-80+1) ×32=（80×11+1 ) ×32 =881 ×32所以控制存储器容量可选IK × 32。

2．某机采用微程序控制方式，微指令字长24位，水平型编码控制的微指令格式，断定方式，共有微命令30个，构成4个相斥类，各包含5个、8个、14个和3个微命令，外部条件共3个。

（1）控制存储器的容量应为多少?（2）设计出微指令的具体格式。

解：（1）30个微命令构成4个相斥类，其中5个相斥微命令需3位编码；8个相斥微命令需4位编码，14个相斥微命令需4位编码，3个相斥微命令需2位编码：外部条件3个,采用断定方式需2位控制位。

以上共需15位。

微指令字长24位，采用水平型编码控制的微指令格式，所以还剩9位作为下址字段，这样控制存储器的容量应为512×24.（2）微指令的具体格式如图所示。

3，流水线工作原理：机器的各部分在某些周期内在进行操作，而在某些周期内是空闲的。

如果控制器调度恰当，让各个部件紧张工作，可提高计算机运行速度---流水线结构。

（期中考试已考）4. 已知某运算器的基本结构如图所示，它具有+(加)、-(减)、M(传送)种操作。

（1）写出图中1~12表示的运算器操作的微命令。

（2）指出相斥性微操作。

（3）设计适合此运算器的微指令格式。

解：（1）图中1~12表示的运算器操作的微命令分别为：1：+ 2：- 3：M4：R1→A 5：R2→A 6：R3→A7：R3→B 8：R2→B 9：R1→B10：BUS→R1 11：BUS→R2 12：BUS→R3（2）以下几组微命令是相斥的：1：+ 2：- 3：M4：R1→A 5：R2→A 6：R3→A7：R3→B 8：R2→B 9：R1→B10：BUS→R1 11：BUS→R2 12：BUS→R3（3）此运算器的微指令格式如图所示。

单片机原理及应用课件教学配套课件陈桂友孙同景第6章 C语言程序设计及仿真调试

乘法运算符“*”：双目运算，具有左结合性。除法运算符“/”：双目运算具有左结合性。参与运算量均为整型时，结果也为整型，舍去小数。如果运算量中有一个是实型，则结果为双精度实型。求余运算符（模运算符）“%”：双目运算，具有左结合性。要求参与运算的量均为整型。求余运算的结果等于两数相除后的余数。
a+b，(a*2)／c，(x+r)*8-(a+b)／7，++i， sin(x)+sin(y)，(++i)-(j++)+(k--)。
5:01:31
6/8
版权所有。
单片机原理及应用
9/89
尚辅教学配套课件
6. 赋值运算符和赋值表达式
简单赋值运算符和表达式，简单赋值运算符记为“=”。由“= ” 连接的式子称为赋值表达式。其一般形式为：变量=表达式。例如：
x=a+b
w=sin(a)+sin(b)
如果赋值运算符两边的数据类型不相同，系统将自动进行类型转换，即把赋值号右边的类型换成左边的类型。具体规定如下：
实型赋予整型，舍去小数部分。整型赋予实型，数值不变，但将以浮点形式存放，即增加小数部分(小数部分的值为0)。
字符型赋予整型，由于字符型为一个字节，而整型为二个字节，故将字符的ASCII码值放到整型量的低八位中，高八位为0。
单片机原理及应用
1/89
尚辅教学配套课件
第6章 C语言程序设计及仿真调试
6.1 C语言程序设计基础 6.2 Keil C 和 ANSI C 6.3 C语言程序设计及调试实例
5:01:31
6/8
版权所有。
单片机原理及应用
2/89
尚辅教学配套课件

基于51单片机的音乐盒的设计与实现

基于51单⽚机的⾳乐盒的设计与实现沈阳航空航天⼤学课程设计报告课程设计名称：单⽚机系统综合课程设计课程设计题⽬：基于51单⽚机的⾳乐盒的设计与实现沈阳航空航天⼤学课程设计报告⽬录第1章总体设计⽅案 (1)1.1设计原理 (1)1.2设计思路 (1)1.3实验环境 (2)第2章详细设计⽅案 (3)2.1硬件电路设计 (3)2.2主程序设计 (6)2.3功能模块的设计与实现 (7)第3章结果测试及分析 (10)3.1结果测试 (10)3.2结果分析 (10)参考⽂献 (11)附录1：元件清单 (12)附录2:总电路图 (13)附录3：程序代码 (14)第1章总体设计⽅案1.1设计原理电⼦⾳乐已⼴泛地应⽤于社会⽣活的各个领域。

其类型从⾳乐卡⽚到CD、MP3 等多种多样，制作原理也各不相同。

声⾳是通过振动产⽣的。

单⽚机对某⼀I/O引脚以⼀定的频率循环置1和清0，这⼀引脚便产⽣⼀定频率的⽅波，该⽅波通过放⼤后作⽤于扬声器便产⽣⼀定频率的声⾳。

若改变输出⽅波的频率，产⽣的声⾳也就改变了。

通过控制输出⽅波的时间长短,声⾳的长短也就得到控制。

因此，根据乐谱，单⽚机就可产⽣电⼦⾳乐。

⾳乐中最关键的两个要素是⾳符和节拍。

单⽚机控制的⾳乐发⽣器系统由硬件电路和软件两部分构成。

利⽤单⽚机控制的电⼦⾳乐发⽣器软硬件上具有独特的优点，系统的开发周期短，成本低，电路制作容易。

更换歌曲时，硬件电路⽆需作任何修改，只需修改软件即可实现。

软件编程时，可⽤51系列单⽚机的汇编语⾔。

同时还可根据个⼈的习好通过软件改变节拍的延时时间，增加电⼦⾳乐的趣味性。

1.2 设计思路采⽤汇编语⾔程序设计的⽅法结合硬件电路设计⽅法，利⽤Lab6000实验箱上已有芯⽚来实现⾳乐盒的各项功能。

1)提出⽅案利⽤定时器计时这个半周期时间，每当计时到后就将输出脉冲的I/O反相，然后重复计时此半周期时间再对I/O⼝反相就可在I/O 脚上得到此频率的脉冲。

当键盘有键按下时，判断键值，启动计数器T0，产⽣⼀定频率的脉冲，驱动蜂鸣器，放出乐曲。

六章子程序结构-PPT精选

5
一、子程序指令—返回指令RET的参数
RET i16
；有参数返回
RET指令可以带有一个立即数i16，则堆栈指针SP将增加，即
SP←SP+i16
这个特点使得程序可以方便地废除若干执行CALL指令以前入栈的参数
6
二、子程序的调用与返回
主程序
子程序
CALL label
RET
回到CALL指令后的指令处 ——返回地址
RET
；无参数段内返回
RET i16
；有参数段内返回
RET
；无参数段间返回
பைடு நூலகம்
RET i16
；有参数段间返回
需要弹出CALL指令压入堆栈的返回地址
段内返回——偏移地址IP出栈
IP←SS:[SP]， SP←SP＋2
段间返回——偏移地址IP和段地址CS出栈
IP←SS:[SP]，SP←SP＋2
CS←SS:[SP]，SP←SP＋2
CALL far ptr mem
；段间调用、间接寻址
CALL指令需要保存返回地址：
段内调用——偏移地址IP入栈
SP←SP－2，SS:[SP]←IP
段间调用——偏移地址IP和段地址CS入栈
SP←SP－2，SS:[SP]← CS
SP←SP－2，SS:[SP]← IP
4
一、子程序指令—返回指令
根据段内和段间、有无参数，分成4种类型
① 数据本身（传值） ② 数据的地址（传址）
传递的方法：
① 寄存器 ② 变量 ③ 堆栈
13
例：将两个给定的二进制数转换成为二进制数的ASCII 码形式并加以显示
对两个数进行转换、显示的工作是相同的，没有必要重复编写，以子程序的形式来完成

微机原理与接口技术(第三版) 龚尚福章 (4)

类型属性：变量的类型属性定义该变量所保留的字节数，如BYTE(DB，1个字节长)、WORD(DW，2个字节长)、DWORD(DD， 4个字节长)、FWORD(DF，6个字节长)、QWORD(DQ，8个字节长)、 TBYTE(DT，10个字节长)。
在同一个程序中，同样的标号或变量的定义只允许出现一次，否则汇编程序会指示出错。
第4章汇编语言程序设计
4.2.1 定义符号的伪指令有时程序中多次出现同一个表达式，为方便起见，可以用
赋值伪操作给表达式赋予一个名字。 1. 等值伪指令EQU 格式： <符号名> EQU <表达式> 功能：给符号名定义一个值，赋予一个符号名、表达式或
助记符。
第4章汇编语言程序设计
此后，程序中凡需要用到该表达式之处，就可以用表达式名来代替了。可见，EQU的引入提高了程序的可读性，也使其更加易于修改。上式中的表达式可以是任何有效的操作数格式，可以是任何可以求出常数值的表达式，也可以是任何有效的助记符。举例如下：
第4章汇编语言程序设计
(3) 符号常数。用符号名来代替的常数就是符号常数，如 COUNT EQU 3或COUNT=3定义后COUNT就是一个符号常数，与数值常数3等价。
第4章汇编语言程序设计
2) 表达式
由运算对象和运算符组成的合法式子就是表达式。表达式
分为数值表达式、关系表达式、逻辑表达式和地址表达式等。
类型(TYPE)属性：类型表示该标号所代表的指令的转移范围，分为NEAR和FAR两种。如果为NEAR型，则标号只能在段内引用；如果为FAR型，则标号可以在段间引用。
第4章汇编语言程序设计
(2) 变量。变量在数据段、附加数据段或堆栈段中定义，后面不跟冒号。它也可以用LABEL或EQU伪操作来定义。变量经常在操作数字段出现。它也有段、偏移及类型三种属性。

单片机实用子程序库

《ＭＣＳ－５１单片机实用子程序库（９６年版）》周航慈目前已有若干版本的子程序库公开发表，它们各有特色。

笔者在1988年也编制了两个子程序库（定点子程序库和浮点子程序库），并在相容性、透明性、容错性和算法优化方面作了一些工作。

本程序库中的开平方算法为笔者研究的快速逼近算法，它能达到牛顿迭代法同样的精度，而速度加快二十倍左右，超过双字节定点除法的速度。

经过八年来全国广大用户的实际使用，反馈了不少信息，陆续扩充了一些新的子程序，纠正了一些隐含错误，成为现在这个最新版本。

本子程序库对《单片机应用程序设计技术》一书附录中的子程序库作了重大修订：（１）按当前流行的以IBM PC 为主机的开发系统对汇编语言的规定，将原子程序库的标号和位地址进行了调整，读者不必再进行修改，便可直接使用。

（２）对浮点运算子程序库进行了进一步的测试和优化，对十进制浮点数和二进制浮点数的相互转换子程序进行了彻底改写，提高了运算精度和可靠性。

（３）新增添了若干个浮点子程序（传送、比较、清零、判零等），使编写数据处理程序的工作变得更简单直观。

在使用说明中开列了最主要的几项：标号、入口条件、出口信息、影响资源、堆栈需求，各项目的意义请参阅《单片机应用程序设计技术》第六章 6.3.7 节的内容。

程序清单中开列了四个栏目：标号、指令、操作数、注释。

为方便读者理解，注释尽力详细。

子程序库的使用方法如下：１．将子程序库全部内容链接在应用程序之后，统一编译即可。

优点是简单方便，缺点是程序太长，大量无关子程序也包含在其中。

２．仅将子程序库中的有关部分内容链接在应用程序之后，统一编译即可。

有些子程序需要调用一些低级子程序，这些低级子程序也应该包含在内。

优点是程序紧凑，缺点是需要对子程序库进行仔细删节。

（一）ＭＣＳ－５１定点运算子程序库及其使用说明定点运算子程序库文件名为DQ51.ASM，为便于使用，先将有关约定说明如下：１．多字节定点操作数：用[R0]或[R1]来表示存放在由R0或R1指示的连续单元中的数据。

#ee)

This description includes maximum likelihood, where the moments used are the score vector corresponding to the likelihood function.
1, the use of a large number of moment conditions is problematic. The small-sample properties of GMM and EMM estimators can diﬀer, sometimes dramatically, from the asymptotic properties of these estimators.2 Unfortunately, the time series of interest rates available to econometricians are short, especially when we take into account the welldocumented persistence of interest rates. Accordingly, we advocate that the information in a panel of interest rates should be compressed by ﬁrst imposing the no-arbitrage restrictions implied by the term-structure model of interest. These restrictions are built into the linearized Kalman ﬁlter through parametric restrictions on the ﬁlter’s observation and transition equations.3 We use Monte Carlo simulations to compare the combination of the Kalman ﬁlter/EMM to the combination of SNP/EMM. For the models examined in this paper, and for reasonable sample sizes, the results strongly support the choice of the Kalman ﬁlter. Due primarily to their ﬂexibility, combined with the computational ease with which they can handle multiple factors, much of the academic literature has focused largely on aﬃne models characterized by Duﬃe and Kan (1996). In this class, risk-neutral dynamics are speciﬁed such that bond yields are linear (aﬃne) functions of some underlying set of state variables. Until very recently, the term-structure literature followed Vasicek (1977) and Cox, Ingersoll, and Ross (1985) by augmenting these risk-neutral dynamics with restrictive functional forms for market prices of risk. Essentially, the price of risk is assumed to be a multiple of interest rate volatility, which implies that interest-rate dynamics are aﬃne under the physical measure as well as the risk-neutral measure. This class of models was fully characterized by Dai and Singleton (1998). Recent research has highlighted the limitations of this class of aﬃne models. For example, Ghysels and Ng (1998) and Balduzzi and Eom (1997) ﬁnd evidence against particular aﬃne speciﬁcations using semiparametric tests. Duffee (1999) ﬁnds that these restrictive forms are too inﬂexible to generate realistic behavior of expected excess returns to bonds. Moreover, there is evidence of nonlinearity in expected interest rate movements [see, for example, Pfann et al. (1996), A¨ ıt-Sahalia (1996b), Conley, Hansen, Luttmer, and Scheinkman (1997), and Stanton (1997)] that is inconsistent with the predictions of the aﬃne models that have been estimated to date. Partly in response to these empirical problems, several non-aﬃne term structure models have recently been proposed [see, for example, Longstaﬀ (1989) A¨ ıt-Sahalia (1996a), A¨ ıtSahalia (1996b), Stanton (1997), Boudoukh, Richardson, Stanton, and Whitelaw (1998), Andersen and Lund (1996b), Constantinides (1992), Conley, Hansen, Luttmer, and Scheinkman

计算机控制系统李华范多旺第6章PPT课件

步骤2 设计控制器
1 GIMC(s)Gˆp(s) f(s)
这里 f 为IMC滤波器。选择滤波器的形式，以保证
内模控制器为真分式。
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6
对于阶跃输入信号，可以确定Ⅰ型IMC滤波器的形式
f
(s)
(Tf
1 s1)r
对于斜坡输入信号，可以确定Ⅱ型IMC滤波器的形式为
f
(s)
rTf s1 (Tf s1)r
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2
1.什么是内模控制？
R(s)
GIMC (s)
U (s)
Dˆ (s)
Gp (s)
D(s)

Y (s)
Gˆ p (s)
Ym (s)
图6－1 内模控制结构框图
G p ( s ) ——实际对象； Gˆ p ( s ) ——对象模型；
内模控制器的设计思路是从理想控制器出发，然后考虑
R( s) ——给定值； Y ( s ) ——系统输出；
其反馈信号 D ˆ(s ) [ G p (s ) G ˆp (s )U ] (s ) D (s ) 0
2020/11/6
——内模控制系统具有开环结构。 5
2. 内模控制器的设计
步骤1 因式分解过程模型
Gˆp GˆpGˆp-
式中，Gˆ p 包含了所有的纯滞后和右半平面的零点，并规定其静态增益为1。Gˆ p 为过程模型的最小相位部分。
第6章计算机控制系统的先进控制技术
本章主要内容 1. 内模控制技术 2. 模型预测控制技术
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1
6．1 内模控制技术
内模控制是一种基于过程数学模型进行控制器设计的新型控制策略。它与史密斯预估控制很相似，有一个被称为内部模型的过程模型，控制器设计可由过程模型直接求取。设计简单、控制性能好、鲁棒性强，并且便于系统分析。

编译原理课件chap02(陈火旺)

长度为1的符号串… 与语言的关系：有的构成单词句子，有的不构成
第二章文法和语言
〈7〉正闭包(∑+) ∑+ =∑1 ∪ ∑2∪. …∪∑n
∑+称∑的正闭包。
显然：∑*＝ ∑0∪∑+
∑+
＝
∑∑*＝∑*∑
第二章文法和语言
3.文法和语言的形式定义
（用以上术语对文法的概念进行形式化）
1、规则（重写规则、产生式、生成式）
如： ababa
则长度是5
4 、空符号串：用ε表示，长度为 0 （不含任何符号）若符号串x ,则有εx = xε= x 5、符号串的运算：
(1)
符号串的头和尾
若z=xy,则x是z的头，y是z的尾。
第二章文法和语言
例：设z=abc ,则z的头是
ε，a，ab，abc
则z的尾是
ε，c，bc，abc
N个
则xy=abMN
设x是符号串，则z=xx……xx，称z为x的方幂, 记z=xn。因此 x0=ε, x1=x, x2=xx, x3=xxx 显然n>0时, 有xn =x· x
n-1＝
x
n-1· x
第二章文法和语言
（5）符号串的集合：
若集合 A 中的一切元素都是某字母表上的符号串，则称A为该字母表上的符号串集合。两个符号串集合A、B乘积定义： AB={xy| x∈A且y∈b}
编译原理
第一章第二章第三章第四章第五章第六章第七章第八章第九章编译程序引论文法和语言词法分析自顶向下语法分析方法自底向上优先分析方法 LR分析方法语法制导翻译和中间代码生成运行时存储空间分配代码生成
第二章文法和语言

C++语言程序设计教程(第二版)清华出版杨进才第6章 C++程序的结构

1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
// p6_1_p1.cpp
#include <iostream> using namespace std; extern int G; void p1dispG() { G=11; cout<<"in p1 G="<<G<<endl; } // p6_1_p2.cpp #include <iostream> using namespace std; extern int G; extern int g; void p2dispG() { G=22; cout<<"in p2 G="<<G<<endl; } void p2dispg() { g=33; cout<<"in p2 g="<<g<<endl; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 /************************************** * p6_3.cpp * * 显示各类变量的内存分配 * ***************************************/ #include <iostream> 常变量(常量)、全局变量、局部静 using namespace std; 态变量、字符串常量在程序运 int k=300; 行前在数据区进行分配。并且 const int i=100; 依次按照常变量、全局变量、局部静态变量的顺序从低地址 #define n 10 向高地址分配。常变量按定义 const int j=200; 的先后次序分配，全局变量、 void fun(int i=1,int j=2) 局部变量也一样。 { const int k=3; static int l=0; char *p=new char[n+1]; for(int m=0;m<n;m++) p[m]='A'+m; p[m]='\0'; cout<<"Adddress of parameter variable:"<<endl;

微机原理与接口技术(第三版) 龚尚福章 (5)

第5章微处理器总线时序和系统总线 (2)RQ/GT0、RQ/GT1——请求/允许总线访问控制信号(双向)。这两种信号线是为多处理机应用而设计的，用于对总线控制权的请求和应答，其特点是请求和允许功能由一根信号线来实现。
总线访问的请求/允许时序分为三个阶段，即请求、允许和释放。首先是协处理器向8086输出RQ请求使用总线，然后在 CPU(8086)的T4或下一个总线周期的T1时期，CPU输出一个宽度为一个时钟周期的脉冲信号GT给请求总线的协处理器，作为总线响应信号，从下一个时钟周期开始，CPU释放总线。当协处理器使用总线结束时，再给出一个宽度为一个时钟周期的脉冲信号RQ给CPU，表示总线使用结束，从下一个时钟周期开始，CPU又控制总线。
第5章微处理器总线时序和系统总线
超标量是指在一个时钟周期内CPU可以执行一条以上的指令。只有Pentium级以上的CPU才具有这种超标量结构，这是因为现代的CPU越来越多地采用了RISC技术。486以下的CPU属于低标量结构，即在这类CPU内执行一条指令至少需要一个或一个以上的时钟周期。
第5章微处理器总线时序和系统总线
2. 主频(CPU Clock Speed) 主频也就是CPU内核工作的时钟频率。通常所说的某某CPU 是多少兆赫的，而这个多少兆赫就是“CPU的主频”。主频越高，CPU的运算速度就越快。但主频不等于处理器一秒钟执行的指令条数，因为一条指令的执行可能需要多个时钟周期。对于CPU在有兼容性的前提下，主要看其速度，而主频越高，字节越长，CPU速度就越快。
13
28
14
27
15
26
16
25
17
24
18
23
19
22

课件：第六章xk

3 rotate: mov cl,4 ；循环入口
4
rol bx,cl
；右移一次BX的4位，即BX最高二进制4位移最低4位，
也就最高一位十六进移到最低一位
5 mov al,bl
；把BX最低8位移AL
6 and al,0fh
；保留AL低4位（一位十六进数）
7 add al,30h
；把一般数变成 ASCII数
；输入在AL数字与BX交换，注BX第二次为上次内
；CX置10
( ( 0×10)+A )×10+B )×10+C
；AX中数乘10
；乘后再与BX交换，即BX中数为乘后的数
；每次与上次乘10后再与本次内容相加
；循环出口
1 binihex proc near
；二进数变十六进数
2
mov ch,4 ；置于CH=4，大循环4次，BX中数被移4次
mov
ax, data
movds, axmovbx, offset ary
push bx
mov
bx, offset count
push bx
mov
bx, offset sum
push bx
sum 550d
table 0000 0014 0016
0000 (si)
0014 0016 (di) 0018 (bx)
例：累加数组中的元素（通过堆栈传送参数地址）
data data
segment ary dw 10,20,30,40,50,60,70,80,90,100 count dw 10 sum dw ? ends
P202 例6.4
data segment
ary dw 1,2,3,4,5,6,7,8,9,10

A new cluster isolation criterion based on dissimilarity increments

A New Cluster Isolation Criterion Basedon Dissimilarity IncrementsAna L.N.Fred,Member,IEEE,and Jose´M.N.Leita˜o,Member,IEEE Abstract—This paper addresses the problem of cluster defining criteria by proposing a model-based characterization of interpattern relationships.Taking a dissimilarity matrix between patterns as the basic measure for extracting group structure,dissimilarity increments between neighboring patterns within a cluster are analyzed.Empirical evidence suggests modeling the statistical distribution of these increments by an exponential density;we propose to use this statistical model,which characterizes context,to derive a new cluster isolation criterion.The integration of this criterion in a hierarchical agglomerative clustering framework produces a partitioning of the data, while exhibiting data interrelationships in terms of a dendrogram-type graph.The analysis of the criterion is undertaken through a set of examples,showing the versatility of the method in identifying clusters with arbitrary shape and size;the number of clusters is intrinsically found without requiring ad hoc specification of design parameters nor engaging in a computationally demanding optimization procedure.Index Terms—Clustering,hierarchical methods,context-based clustering,cluster isolation criteria,dissimilarity increments,model-based clustering.æ1I NTRODUCTIONI N this section,we review existing clustering methodolo-gies and algorithms,and outline the goals and the main ideas proposed in this paper.1.1Review of Clustering ApproachesClustering has been applied in a variety of domains,whose main goals are exploratory pattern analysis and data mining, decision-making,and machine learning.Most of the existing work in clustering deals with developing new clustering algorithms.Two main strategies have been adopted:hier-archical methods and partitional methods[1],[2].Partitional methods organize patterns into a small number of clusters.Model-based techniques assume that patterns belonging to a cluster can be given a simple and compact description in terms of a parametrical distribution(such as a Gaussian),a representative element(the centroid or the median,for instance),or some geometrical primitive(lines, planes,circles,ellipses,curves,surfaces,etc.).Such ap-proaches assume particular cluster shapes,partitions being obtained,in general,as a result of an optimization process using a global criterion.Parametric density approaches,such as mixture decomposition techniques[3],[4],[5],[6],and prototype-based methods,such as central clustering[7], square-error clustering[8],K-means[2],[1],or K-medoids clustering[9],emphasize compactness,imposing hyper-spherical clusters in the data.Model order selection is sometimes left as a design parameter or it is incorporated in the clustering procedure[10],[11],[5].The K-means is probably the best known and most widely used algorithm in this category.Assuming a priori knowledge about the number of classes,and based on the square-error criterion,it is a computationally efficient clustering technique that identifies hyperspherical clusters.Extensions of the basic method include:use of Mahalanobis distance to deal with hyperellipsoidal clusters[2];fuzzy algorithms[12];adapta-tions to straight line fitting[13].Optimization-based cluster-ing algorithms adopting shape fitting approaches include [14],[15],[16].Cost-functional clustering methods based on a minimum variance criterion favor spherical clusters.Other optimization-based clustering algorithms do not assume particular cluster shapes,such as the work in[17],proposing a pairwise clustering cost function emphasizing cluster con-nectedness.Nonparametric density-based clustering meth-ods attempt to identify high-density clusters separated by low-density regions by either exploiting regions of high sample density[18]or regions with less data,such as in valley seeking clustering algorithms[19],[20].Hierarchical methods,mostly inspired by graph theory [21],consist of a sequence of nested data partitions in a hierarchical structure,that can be represented graphically as a dendrogram[2].Both agglomerative[2],[22]and divisive approaches[23](such as those based on the minimum spanning tree—MST[2])have been attempted.Variations of the algorithms are obtained depending on the definition of similarity measures between patterns and between clusters [24],the later ultimately determining the structure of the clusters identified.The single-link(SL)and the complete-link (CL)methods[2]are the best known techniques in this class, emphasizing,respectively,connectedness and compactness. Prototype-based hierarchical methods define similarity be-tween clusters based on cluster representatives,such as the centroid or the median;like the prototype-based partitional algorithms,these techniques fail to identify clusters of arbitrary shapes and sizes,imposing spherical structure in the data.Variations of the prototype-based hierarchical clustering include the use of multiple prototypes per cluster, as in the CURE algorithm[25].Other algorithms compute similarity between clusters by the aggregate of the similarities.The authors are with the Instituto de Telecomunicac¸o˜es,Instituto SuperiorTe´cnico,Av.Rovisco Pais1049-001,Lisbon,Portugal.E-mail:{afred,jleitao}@lx.it.pt.Manuscript received14Feb.2001;revised26Mar.2002;accepted27Dec.2002.Recommended for acceptance by R.Kumar.For information on obtaining reprints of this article,please send e-mail to:tpami@,and reference IEEECS Log Number113621.0162-8828/03/$17.00ß2003IEEE Published by the IEEE Computer Society(emphasizing interconnectivity,such as the group-average method[2])among pairs of patterns belonging to distinct clusters,or selecting a particular pair.Other hierarchical agglomerative clustering algorithms follow a split and merge technique;the data being initially split into a high number of small clusters and merging being based on intercluster similarity.A final partition is selected among the clustering hierarchy by thresholding techniques or based on measures of cluster validity.Density-based techniques usually define initial clusters by seeking high-density points(by simple use of K-means clustering[28],applying kernel-based density estimation[18]or using density gradient estimation,the modes being detected with the hill climbing mean shift procedure[29],[30]),density similarity guiding the merging process;simple thresholding[28]or cluster validity indices weighting intercluster connectivity and cluster isolation(low-density regions separating clusters)[18]are used to select a clustering.In the work in[30],an initial random space tessellation is produced to which a mean shift procedure is applied to detect cluster centers.A two phase clustering algorithm is presented in[31],according to which initial subclusters are obtained using a graph partitioning technique to the K-nearest neighbor graph of the data set,followed by a dynamic merging of subclusters under a hierarchical agglom-erative framework.The density-based clustering algorithm presented in[32]explores the idea of intracluster homo-geneity and uniformity,working on links from a complete graph.1.2Goals and Outline of the PaperIn this paper,we address the problem of cluster defining criteria under a model-based framework.A new cluster isolation criterion,briefly outlined in[33],underlying a hypothesis of smooth dissimilarity increments between neighboring patterns,is presented and discussed.It is shown that dissimilarity increments between neighboring patterns within a cluster have a smooth evolution,whose statistical distribution can be modeled by an exponential density function.Dissimilarity increments,by means of their statis-tical model,characterize context.The proposed isolation criterion is supported on a pair-wise context analysis.This isolation criterion is merged in a hierarchical agglomerative clustering algorithm,producing a data partitioning and simultaneous accessibility to the intrinsic data interrelation-ships in terms of a dendrogram-type graph.The structure of the obtained dendrogram,unlike conventional hierarchical clustering methods,is constrained by the isolation criterion, expanding the range of pattern structures handled by these methods,namely,situations containing both sparse and dense clusters.Additionally,the problem of deciding the number of clusters is subsumed and intrinsically dictated by the criterion.Section6studies the distribution of dissimilarity increments,supporting the smooth evolution hypothesis, and outlines the new cluster isolation criterion(Section2.2). Critical evaluation and mathematical manipulation of the parametric context model—exponential distribution—leads to the definition of an intrinsic isolation parameter (Section 2.3).A hierarchical agglomerative algorithm adopting this criterion is described in Section 3.The novelty of the proposed method and its relation to work in the literature is outlined in Section4.The characteristics of the new method are analyzed and illustrated through a set of examples(Section5),covering synthetic data (random data,Gaussian mixtures,concentric patterns, and clusters of arbitrary shape and size)and examples from the UCI Machine Learning Repository[34](Iris data and the Wisconsin Breast Cancer Data Set).Results are compared with the single-link method and the k-means algorithm.A discussion of the proposed method with the SL and the K-means algorithm is presented in Section6. Conclusions are drawn in Section7.2S MOOTHNESS H YPOTHESIS AND C LUSTERI SOLATION C RITERIONLet X be a set of patterns,and x i represent an element in this set.Assume that interpattern relationships are mea-sured by some dissimilarity function,dð:;:Þ.The definition of dð:;:Þis problem and data representation dependent;it may be,for instance,the Euclidean distance for patterns in multidimensional feature spaces;string edit distances[35], [36],[37],[38]are commonly used for quantifying resem-blance between string patterns.The proposed cluster isolation criterion is derived from the following intuitive concepts and assumptions: .A cluster is a set of patterns sharing important characteristics,defining a context..Dissimilarity between neighboring patterns within a cluster should not occur with abrupt changes..The merging of well separated clusters results in abrupt changes in dissimilarity values.The first concept states that a cluster gathers interrelated patterns,the pattern dependence profile being a character-istic of the cluster,thus defining a context;this enables its distinction from other clusters.The last two items state a hypothesis of smooth evolution of dissimilarity changes,or increments,between neighboring patterns within a cluster, nonsatisfaction of this condition being associated with cluster isolation.This smoothness hypothesis is the genesis of the proposed cluster isolation criterion,the dissimilarity increments measuring continuity within a cluster.2.1Distribution of Dissimilarity Increments Consider a set of patterns X.Given x i,an arbitrary element of X and some dissimilarity measure,dð:;:Þ,between patterns,letðx i;x j;x kÞbe the triplet of nearest neighbors, obtained as follows:ðx i;x j;x kÞÀnearest neighborsx j:j¼arg minldðx l;x iÞ;l¼if gx k:k¼arg minldðx l;x jÞ;l¼i;l¼jÈÉ: The dissimilarity increment between the neighboring patterns is defined asd incðx i;x j;x kÞ¼j dðx i;x jÞÀdðx j;x kÞj;which can be seen as the first derivative of the dissimilarity function at the first point of the ordered list of neighboring samples.There is experimental evidence that the increments of the dissimilarity measure between neighboring patterns,as defined above,typically exhibit an exponential distribution, pðxÞ¼ expÀ x;x>0,as illustrated in Fig.1.This figure plots histograms and corresponding fitted distributions of dissim-ilarity increments for a variety of data sets.Two-dimensional examples were chosen for simplicity of representation:FREDAND LEIT~A O:A NEW CLUSTER ISOLATION CRITERION BASED ON DISSIMILARITY INCREMENTS3 Fig.1.Histograms(bar graphs)and fitted exponential distributions(solid line curves)of the dissimilarity increments computed over neighboring patterns in the data.The Euclidean distance was used as the dissimilarity measure.(a)There are2,000uniformly distributed patterns within a square, (b)500patterns generated from a Gaussian distribution(Nð½0;0 ;½100;010 Þ),(c)ring-shaped data(1,000random patterns),(d)1,000patterns generated according to the stochastic model:yðkþ1Þ¼yðkÞþn1ðkÞ,xðkþ1Þ¼xðkÞþn2ðkÞ,with n1ðkÞ,n2ðkÞbeing noise uniformly distributed in the interval½À:25;:25 ,(e)directional expanding data generated by the model:xðkþ1Þ¼xðkÞþn sðkÞk,yðkþ1Þ¼yðkÞþnðkÞ,where n s and nðkÞrepresent uniform noise in the range½À10;10 and½0;10 ,respectively,and(f)grid corrupted by zero mean Gaussian noise,with standard deviation0.1..random samples(uniform distribution),.2D Gaussian process,.noisy ring shaped pattern,.2D stochastic process,.directional expanding pattern,and.grid corrupted by Gaussian noise.The Euclidean distance is used as the dissimilarity measure in these examples.As shown in Fig.2d,the statistical distribution of the dissimilarity increments within the same context or data formation model(cluster)has a smooth evolution,where the parameter of the fitted exponential probability density function characterizes data sparseness.It can be observed that distinct data generation models lead to very similar curves(for instance,patterns in Figs.1c and1d),while an increasing number of observations from the same process (corresponding to decreasing data dispersion levels)results in increasing values for the parameter of the exponential distribution(see Fig.2).Thus,by adopting the dissimilarity derivatives as features for context characterization,a single parametric model(exponential distribution)is obtained for distinct cluster shapes or data generation paradigms.When con-sidering well-separated clusters,it is clear that dissimilarity increments between patterns in different clusters are positioned far on the tail of the distribution associated with the other cluster.We explore this property in defining a cluster isolation criterion in the next section.2.2Isolation CriterionWe extend the previous concept of dissimilarity increments between neighboring patterns to define the concept of gap between clusters.Let C i,C j be two clusters candidate for merging,as the ones shown in Fig.3,and consider the nearest pattern pair,ðx i;x jÞ,linking these clusters,such that x i2C i and x j2C j (x i x12and x j x18Fig.3).We shall represent the dissimilarity between these patterns,dðx i;x jÞ,as dðC i;C jÞ(corresponding to the distance between the two clusters, according to the nearest-neighbor rule).Let x k be the nearest neighbor of x i within C i(pattern x3in Fig.3),and let d tðC iÞ¼dðx i;x kÞ.The tripletðx k;x i;x jÞ,therefore,corre-sponds to neighboring patterns.We define dissimilarity increment or gap between clusters i and j as the asymmetric increase in the dissimilarity value,needed in order to allow the data association into a single cluster:gap i¼j dðC i;C jÞÀd tðC iÞj:ð1Þ4IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,VOL.25,NO.8,AUGUST2003 Fig.2.Fitted exponential distributions for the dissimilarity increments of2D data,randomly generated from a uniform distribution:(a)2,000samples, (b)1,000samples,and(c)500samples.(d)Steep exponentials(higher parameter)correspond to high-densitypatterns.Fig.3.Definition of gap.The figure shows18two-dimensional patternsgrouped in two clusters.The patterns are linked by the minimumspanning tree,adopting the Euclidean distance as the edge weight.In a similar way,we find x l (x 17in Fig.3),the nearestpattern to x j belonging to C j ,and define gap between cluster j and i :gap j ¼j d ðC i ;C j ÞÀd t ðC j Þj ¼j d ðC i ;C j ÞÀd ðx j ;x l Þj .Dissimilarity increments between neighboring patterns within a cluster is a measure of pattern continuity.The statistical distribution of dissimilarity increments is modeledby an exponential distribution.Let ^ i ¼1^ i ,^j ,be the average of dissimilarity increments in cluster C i and C j ,respectively.Tails of these distributions correspond to patterns in frontier or borderline situations,where continuity is broken.The gaps,gap i ,gap j ,represent the increase in neighboring pattern distances needed in order to join the two clusters,measuring intercluster continuity,as seen from each cluster perspective.If the two clusters are well separated,these gaps will have high values (compared to intracluster statistics),being located on the tails of each cluster statistic,and corresponding to a discontinuity in both clusters structure.In situations of touching clusters with distinct densities,as in the example shown in Fig.4,context analysis is needed in order to identify the clusters.The dashed line in Fig.4links the nearest-neighbor patterns connecting the two clusters;remaining lines link the intracluster nearest neighbors to each of these elements.From this figure,it is intuitive to see that the element from the cluster on the right could naturally be included in the left cluster since the increment (gap 1¼0:0150)is small compared to the intracluster statistic (^1¼0:0268).From the context of the cluster on the right,however,the dissimilarity increment (gap 2¼0:0542)is large compared to the average dissimilarity increments within this cluster:^2¼0:0068.Therefore,taking the one-sided perspective of cluster C 1,the two clusters could be merged;from the context of C 2,the clusters are isolated.The cluster isolation criterion consists of setting a limit on the dissimilarity increments,such that most of the patterns exhibiting the same statistical structure or model (densely or sparsely connected)are included in the same cluster,while all others,not satisfying this smoothness hypothesis,are rejected:.Let C i ,C j be two clusters which are candidates for merging,and let i , j be the respective mean values of the dissimilarity increments in each pute the increments for each cluster,gap i and gap j ,as defined in (1).If gap i ! i (gap j ! j ),isolate cluster C i (C j )and continue the clustering strategy with the remaining patterns.If neither cluster exceeds the gap limit,merge them.Notice that the above criterion can be regarded as a context-dependent cluster isolation rule where the context is modeled by the parametric distribution of dissimilarity increments.The isolation rule consists of comparing the value of the dissimilarity increment,seen from the context of each cluster,with a dynamic threshold, i ,computed from this context;inconsistency of gap values in a given context (cluster)determines the isolation of that cluster.The design parameter, ,constrains the degree of isolation;values in the range 3to 5provide reasonable choices,as justified in the next section.2.3Setting the Isolation ParameterAs seen previously,the structure of the dissimilarity increments within a cluster is summarized by an exponen-tial distribution;the parameter of this distribution thus characterizes each cluster.Well-separated clusters are clearly identified by the analysis of these distributions,as samples not belonging to a given cluster will be placed far in the tail of the cluster distribution.A reasonable choice for the isolation parameter, ,is to set it at a point on the tail that does not reject a significant amount of data nor does it allow grouping of patterns that are clearly atypical.Theoretical analysis of the exponential distribution leads to the following interesting result (see Appendix A):The crossing of the tangential line,at points which are multiples ofthe distribution’s mean value,i Â1,with the x axis,is givenby ði þ1ÞÂ1;this is shown in Fig.5.Therefore,setting the threshold, ,to some multiple of the distribution mean,i.e., inside the interval 3to 5is a reasonable choice.In examples throughout the paper,the typical value used is ¼3.3H IERARCHICAL C LUSTERING A LGORITHMIn this section,we incorporate the cluster isolation criterion described in Section 2.2in a hierarchical agglomerative clustering algorithm.Each cluster,C i ,is characterized by: ½i —the estimate of the mean value of the dissimilarity increments within the cluster;jumps ½i —the number of elements used in this estimate.The algorithm starts withFREDAND LEIT ~AO:A NEWCLUSTER ISOLATION CRITERION BASED ON DISSIMILARITY INCREMENTS 5Fig.4.Touching classes with distinct densities.Fig.5.Defining a threshold on the gap values (x axis).Dots are locatedon points which are multiple of the distribution mean,1¼0:05and dashed lines are tangents at those points.The crossing at the x axisoccur at points i,i being a positive integer.Values for i in the range ½3;5 cover the most significant part of the distribution.each pattern in a cluster,the dissimilarity matrix between pattern pairs being computed.It evolves by selecting the most similar pair of clusters and applying the cluster isolation criterion from each cluster context;clusters are thus either isolated(one or both)and frozen on the dendrogram,or merged;frozen clusters are not available for further merging. Statistics ½i are updated along the merging process.Estimates of the mean values ½i are not reliable for very small cluster sizes;this may lead to premature isolation of clusters.In order to overcome this situation,widening of the isolation parameter for small cluster sizes may be adopted [39];alternatively,inhibition of cluster isolation actions may be implemented when clusters are very small[33].In this paper,we replace the term ^ i by the dynamic threshold t dyn Cið ;^ i;ni;njÞ¼ ^ iÂwiden factðni;njÞþdelta factðniÞ:ð2ÞExpression(2)hastwoterms.Thefirsttermincreasesthevalue of the estimate^ i by multiplying it by a factor greater than or equal to1,widen factðni;njÞ,where ni jumps½i and nj jumps½j are the number of elements available for the computation of the distribution means for cluster C i and C j, respectively.We define the amplifying factor widen factðni;njÞas a monotonous decreasing function of ni;nj:widen factðni;njÞ¼1þ Â1À11þeÀ:4ðniÀ10Þ|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}f1ðniÞÂ2À11þeÀ:4ðnjÀ10Þ|ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ}f2ðnjÞ:ð3ÞThe reasoning underlying(3)is the following(see Fig.6).If cluster C i has few samples,the estimate^ ðC iÞshould be enlarged to compensate for possible underestimation of the true distribution mean;this widening effect smoothly vanishes as the number of terms ni used in the computation of the estimate^ ðC iÞincreases(Fig.6a),which is modeled by the term f1ðniÞ,a sigmoid-like function.The term f2ðnjÞexpresses the reinforcement of the widening effect when the number of elements in the competing cluster C j is also low (Fig.6b),taking values greater or equal to1.When both clusters have low cardinality the combined action of f1and f2favors clusters merging.When cluster C i has already a sufficiently large number of elements,the estimate of^ ðC iÞis considered to be reliable and term f1ðniÞtends to zero,thus annihilating the influence of term f2(the size of cluster C j becomes irrelevant—see Fig.6a,ni!25).In(3), is a scaling parameter(default value:3).When the number of elements available for the estima-tion of the dissimilarity increments statistic,n i,is extremely low(such as when the number of cluster’s samples is less than10),the estimate for the parameter is very poor. Applying a multiplicative factor to the threshold term may not solve the underestimation problem in this situation,in particular,when^ is near zero.The second term in(2),with large values vanishing for ni¼10,boosts near zero estimates for extremely small sized clusters:delta factðniÞ¼big valÂ1À11þeÀ10ðniÀ5Þ;ð4Þwhere big val is a large positive number.In order to compute the gap between clusters,one needs to know the distances between nearest neighbor ing the nearest-neighbor rule for updating intercluster dissim-ilarity,dðC i;C jÞgives the desired distance between nearest neighbors in each cluster.Considering that most similar patterns are joined first,dissimilarity values growing along the evolution of the clustering algorithm,we will approximate the exact value of the gap by gap i¼dðC i;C jÞÀd t½i ,with d t½i representing the dissimilarity in the last merging performed in cluster C i(see Fig.7).This approximation prevents further computation of nearest neighbors in each cluster,leading to a computationally more efficient algorithm.The following gives a schematic description of the clustering algorithm.Input:N samples; (default value is3).Output:Data partitioning.Steps:1.Set:Final clusters¼ ;n¼N;Put the i th sample in cluster C i;i¼1;...;n;Clusters¼SiC i;i¼1;...;n;d t½i ¼ ½i ¼jumps½i ¼0;i¼1;...;n;2.If(Clusters¼¼ )or(n¼¼1)6IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,VOL.25,NO.8,AUGUST2003 Fig.6.Amplification term widen fact associated with the estimate^ for cluster C i.(a)Amplification factor as a function of the number of terms used in the computation of the gaps distribution mean for cluster C i( ¼1).(b)Reinforcement of the amplifying term as a function of the number of elements in cluster C j( ¼1).then stop,returning the clusters found in Final clusters S Clusters ;else continue.3.Choose the most similar pair of clusters ðC i ;C j Þfrom Clusters .Letgap i ¼d ðC i ;C j ÞÀd t ½ini ¼jumps ½i gap j ¼d ðC i ;C j ÞÀd t ½jnj ¼jumps ½j 4.If ((gap i <t dyn C i ð ; ½i ;ni;nj Þ)and(gap j <t dyn C j ð ; ½j ;nj;ni Þ))then join the clusters C i ,C j into cluster C i;j :C i;j ¼C i S C j Let I be the index for the merged cluster;Replace C i ,C j by C i;j in Clusters ;d t ½I ¼d ðC i ;C j Þ;jumps ½I ¼jumps ½i þjumps ½j þ2;½I ¼ ½i jumps ½i jumps ½I þ ½j jumps ½jjumps ½I þgap i þgap j jumps ½I ;Go to step 2.else continue.5.If (gap i !t dyn C i ð ; ½i ;ni;nj Þ)then set Final clusters ¼Final clusters S C i ;Remove C i from Clusters ;n ¼n À1.end ifIf (gap j !t dyn C j ð ; ½j ;nj;ni Þ)then set Final clusters ¼Final clusters S C j ;Remove C j from Clusters ;n ¼n À1.end ifGo to step 2.4R ELATED W ORKThe distinctive feature of the proposed scatter measure,which forms the basis of the cluster isolation criterion,consists of analyzing and modeling dissimilarity increments in neighboring patterns,instead of statistical or geometrical manipulations of the dissimilarity values between patterns.Dissimilarity increments measure continuity within a cluster.The work presented in [32]explores the concept of uniformity to detect clusters with similar interior distances.It works on links from a complete graph.Initial clusters are defined by gathering links differing in length by no more than a given threshold.The length difference within these clusters,whichis similar to the dissimilarity increment proposed in this paper,has an a priori fixed upper value;in our method,increments are compared to an adaptive threshold,which depends on individual cluster statistics.The merging process proposed in [32]is based on the comparison of intracluster average distances;in our method,the distribution of increments within a cluster is modeled by a parametric model (exponential distribution),the parameter summariz-ing cluster structure being the average value of increments between neighboring patterns.Increment values computed from the nearest pair of patterns in distinct clusters are compared to each cluster statistic to decide for merging.The proposed cluster isolation criterion has been evaluated in the context of hierarchical agglomerative clustering,adopting a nearest-neighbor rule for measuring the similarity between clusters.This new algorithm is therefore closely related to graph-theoretical methods,in particular,with the single-link method:both methods start with single element clusters,merging most similar clusters first,and updating the similarity matrix according to the nearest-neighbor rule.A major distinction between the two methods is that the standard SL method uses a fixed threshold on dissimilarity values for cutting the resulting dendrogram,while the herein proposed method uses an adaptive threshold on dissimilarity first derivatives,based on the computation of intracluster statistics of dissimilarity increments.These statistics are scatter measures,characterizing density of clusters.With the proposed cluster isolation criterion,the new algorithm is able to identify clusters with different densities,which requires special treatment when using graph-theoretical methods,such as detecting and removing denser clusters,and then clustering the remaining patterns.With the proposed approach,this situation is easily handled as,according to the asymmetric isolation criterion,denser clusters are identified and frozen on the dendrogram,the clustering process based on dissimilarity increments proceeding with the remaining data.Some authors have adopted postproces-sing of the dendrogram produced by the SL method [26],[27]or,equivalently,processing of the minimum spanning tree (MST),in order to obtain a final data partition.Zhan [21]proposed a technique for the identification of clusters from a minimum spanning tree by removing inconsistent links based on the comparison of the link distance (dissimilarity between linked patterns)with the average of nearby link distances on both sides of the link.Inconsistent links removal is therefore based on local dissimilarity statistics;our method,however,evaluates overall clusters statistics (of dissimilarity incre-ments instead of distances)along the clustering process,eventually conditioning the final form of the dendrogram.This dynamic construction of the dendrogram,the final topology being conditioned by intracluster statistics,opposes to the static behavior of the above methods,based on postprocessing of structures.A dynamic hierarchical agglom-erative procedure is proposed in [31].In that work,however,similarity between clusters combines interconnectivity and relative closeness measures based on the K-nearest neighbor graph of the data set,isolation criteria consisting of the comparison of the similarity value with a user specified parameter,controlling,simultaneously with the K parameter,the characteristics of the desired clusters.FREDAND LEIT ~AO:A NEW CLUSTER ISOLATION CRITERION BASED ON DISSIMILARITY INCREMENTS 7Fig.7.Definition of gap on the dendrogram produced by the single-linkmethod for the data in Fig.3.。