Conclusions and Future Work0001

Chapter 8
Conclusions and Future Work
Abstract This chapter summarizes the book and envisions future works.
8.1 Conclusions
Chapter 1 is an overview of this book.
•Pattern recognition is concerned with three central issues: (1) feature extraction, (2) hypothesis selection, and (3) learning algorithm. All issues are involved with prior knowledge about specific applications.
•This book mainly deals with two types of uncertainties in pattern recognition, i.e., randomness and fuzziness.
•Graphical models as hypotheses can (1) statistical-structurally represent patterns, and (2) have efficient learning and decoding algorithms.
•Type-2 fuzzy sets can describe bounded uncertainty in both feature and hypothesis spaces, and handle randomness and fuzziness simultaneously.
•The main contribution of this book lies in four aspects: (1) We introduce graphical models for the statistical-structural pattern recognition paradigm; (2) We use type- 2 fuzzy sets for handling both randomness and fuzziness uncertainties in pattern recognition; (3) We extend classical graphical models such as Gaussian mixture models, hidden Markov models, Markov random fields and latent Dirichlet allocation to type-2 fuzzy graphical models for handling more uncertainties; and (4) We apply the proposed approaches to real-world pattern classification problems such as speech, handwriting, and human action recognition.
In Chap. 2, we formulate pattern recognition as a labeling problem. Many pattern
recognition problems can be posed as labeling problems to which the solution is a set of linguistic labels assigned to extracted features from speech signals, image pixels, and image regions. Graphical models use Markov properties to measure a local probability on the labels within the neighborhood system. The Bayesian decision theory guarantees the best labeling configuration according to the maximum a posteriori criterion.
© Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg 20XX 199 J. Zeng and Z.-Q. Liu, Type-2 Fuzzy Graphical Models for Pattern Recognition.
Chapter 3 introduces type-2 fuzzy sets and type-2 fuzzy logic systems. Type-2 fuzzy sets have two new concepts: secondary membership function and footprint of uncertainty. The secondary membership function evaluates the primary memberships, and the footprint of uncertainty describes bounded uncertainty of the primary memberships. In wavy slice representation, the type-2 fuzzy set can be viewed as embedded with many type-1 fuzzy sets. General type-2 fuzzy sets' operations are prohibitive, whereas interval type-2 fuzzy sets' operations are concerned with simple interval arithmetic. In type-2 fuzzy logic systems, nonsingleton fuzzifier can map crisp input to fuzzy numbers, and the output of the system is a type-2 fuzzy set so that type-reduction and defuzzification are needed. The Karnic-Mendel algorithm is special for the type-reduction of interval type-2 fuzzy set. Using one type-2 fuzzy set for uncertain feature space, and the other type-2 fuzzy set for uncertain hypothesis space, pattern recognition can be performed by a similarity measure of these two sets. On the other hand, if the input feature is nonsingleton fuzzified, and the rule base is modeled by type-2 fuzzy sets, pattern recognition is dependent on the type-reduced set of the type-2 fuzzy logic system. Because of fuzziness, the classical Bayesian decision theory is no longer the best decision rule for classification. Thus, we extend it by type-2 fuzzy set operations referred to as the type-2 fuzzy Bayesian decision theory, which provides a general rule to make decision when both randomness and fuzziness exist in pattern recognition.
In Chap. 4, we introduce type-2 fuzzy Gaussian mixture models (T2 GMMs). In real-world applications, we often encounter uncertain feature space, which results in a mismatch between the GMM-based class-conditional densities and the underlying distributions. To reflect such uncertainty as mismatch, we use type-2 fuzzy sets to describe uncertain parameters in Gaussian mixture models. By information theory, we explain why the lower and upper boundaries of the T2 FGMM can provide additional information for classifying outliers. Multivariate Gaussian primary membership function
with uncertain mean vector and covariance matrix is the most widely used type-2 fuzzy membership functions in this book. In the proposed classification system, we first build a T2 FGMM for each category, and evaluate each training sample by all models. As a result, we obtain a feature vector composed of interval likelihoods. In this case, the maximum likelihood criterion is not suitable for decision-making, so we adopt the generalized linear model to fulfill this task automatically.
Chapter 5 studies type-2 fuzzy hidden Markov models (T2 FHMMs) and their applications to speech recognition. The type-2 fuzzy HMM is an extension of the HMM. The corresponding type-2 fuzzy forward-backward, Viterbi, and Baum- Welch algorithms have been developed using type-2 fuzzy sets operations. Especially, the interval type-2 fuzzy HMM has practical use. The IT2 FHMM can effectively handle babble noise and dialect uncertainties in speech data besides a better classification performance than the classical HMM. We have three methods to make decisions based on the output interval sets from the IT2 FHMM: (1) Rank the output interval sets directly, (2) Use the centroid of interval sets in terms of type-2 fuzzy logic systems, and (3) Use generalized.
Chapter 6 investigates type-2 fuzzy Markov random fields (T2 FMRFs) and their applications to handwritten Chinese character recognition. Stroke segmentation is formulated as the optimal labeling problem. We can use the MRF to detect the ambiguous parts. The MRF can describe the stroke relationships of Chinese characters statistically. The IT2 FMRF shows a better generalization ability than the classical MRF.
Chapter 7 proposes type-2 fuzzy topic models (T2 FTMs) and their applications to topic modeling and human action recognition. We propose a new algorithm, belief propagation (BP), for learning latent Dirichlet allocation (LDA). We also discuss how to speed up BP by residual BP and active BP techniques. We implement two T2 FTMs to perform human action recognition. Results confirm the effectiveness of type-2 fuzzy extensions for differentiating similar actions.
8.2 Future Works
In this book we study the probabilistic graphical models and type-2 fuzzy sets for pattern recognition. The graphical models have been deeply explored for pattern recognition in the past forty years. The question is how to design a suitable graphical model for the problem at hand. Basically, we have three issues in mind: (1) Determine the neighborhood systems (or topology); (2) Design clique potentials (or distance measure);
(3) Develop learning and decoding algorithms. Future works may include applications to protein and gene structure recognition.
Mathematically, the three-dimensional structure of type-2 fuzzy membership function provides us a powerful tool for many complex problems. Furthermore, the type-2 fuzzy sets can be integrated with other methods, such as neural networks, support vector machines, genetic algorithms, to render many new algorithms for handling uncertainty. As far as pattern recognition is concerned, we are still in need of methods to make decisions based on the type-2 fuzzy sets. In the meantime, how to reduce the computational complexity of the general type-2 fuzzy sets operations is an open problem. Future works may integrate type-2 fuzzy sets with deep learning framework for pattern recognition.。