Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Statistical Analysis with Missing Data

An Introduction to MultiAgent Systems.

An overview of the self-organizing map algorithm, on which the papers in this issue are based, is presented in this article.

The Self-Organizing Map

The main subject of this book is the fuzzy c-means proposed by Dunn and Bezdek and their variations including recent studies A main reason why we concentrate on fuzzy c-means is that most methodology and application studies in fuzzy clustering use fuzzy c-means, and hence fuzzy c-means should be considered to be a major technique of clustering in general, regardless whether one is interested in fuzzy methods or not Unlike most studies in fuzzy c-means, what we emphasize in this book is a family of algorithms using entropy or entropy-regularized methods which are less known, but we consider the entropy-based method to be another useful method of fuzzy c-means Throughout this book one of our intentions is to uncover theoretical and methodological differences between the Dunn and Bezdek traditional method and the entropy-based method We do note claim that the entropy-based method is better than the traditional method, but we believe that the methods of fuzzy c-means become complete by adding the entropy-based method to the method by Dunn and Bezdek, since we can observe natures of the both methods more deeply by contrasting these two

Algorithms for Fuzzy Clustering: Methods in c-Means Clustering with Applications

This paper proposes a new fuzzy clustering algorithm for categorical multivariate data. The conventional fuzzy clustering algorithms form fuzzy clusters so as to minimize the total distance from cluster centers to data points. However, they cannot be applied to the case where only cooccurrence relations among individuals and categories are given and the criterion to obtain clusters is not available. The proposed method enables us to handle that kind of data set by maximizing the degree of aggregation among clusters. The clustering results by the proposed method show similarity to those of correspondence analysis or Hayashi's (1952) quantification method Type III. Numerical examples show the usefulness of our method.

Fuzzy clustering for categorical multivariate data

Fuzzy c-means (FCM)-type fuzzy clustering approaches are closely related to Gaussian mixture models (GMMs) and EM-like algorithms have been used in FCM clustering with regularized objective functions. Especially, FCM with regularization by Kullback-Leibler information (KLFCM) is a fuzzy counterpart of GMMs. In this paper, we propose to apply probabilistic principal component analysis (PCA) mixture models to linear clustering following a discussion on the relationship between local PCA and linear fuzzy clustering. Although the proposed method is a kind of the constrained model of KLFCM, the algorithm includes the fuzzy c-varieties (FCV) algorithm as a special case, and the algorithm can be regarded as a modified FCV algorithm with regularization by K-L information. Numerical experiments demonstrate that the proposed clustering algorithm is more flexible than the maximum likelihood approaches and is useful for capturing local substructures properly.

Regularized linear fuzzy clustering and probabilistic PCA mixture models

In this paper, we propose two methods for partitioning an incomplete data set with missing values into several linear fuzzy clusters by extracting local principal components. One is an extension of fuzzy c-varieties clustering that can be regarded as the algorithm for the local principal component analysis of fuzzy covariance matrices. The other is a simultaneous application of fuzzy clustering and principal component analysis of fuzzy correlation matrices. Both methods estimate prototypes ignoring only missing values and they need no preprocessing of data such as the elimination of samples with missing values or the imputation of missing elements. Numerical examples show that the methods provide useful tools for interpretation of the local structures of a database.

/pdf/linear-fuzzy-clustering-techniques-with-missing-values-and-2nbepdlp19.pdf

Linear fuzzy clustering techniques with missing values and their application to local principal component analysis

The Gaussian mixture model or Gaussian mixture density decomposition(GMDD) use the likelihood function as a measure of fit. We show that just the same algorithm as the GMDD can be derived from a modified objective function of fuzzy c-means (FCM) clustering with the regularizer by K-L information, only when the parameter /spl lambda/ equals 2. Although the fixed-point iteration scheme of FCM is similar to that of the GMDD, the FCM has more flexible structure since the algorithm is based on the objective function method. In a slightly different manner such as installing a deterministic annealing or an addition of Gustafson and Kessel's (1979) constraint, the proposed algorithm is likely to provide more valid clustering results.

/pdf/fuzzy-c-means-clustering-with-regularization-by-k-l-2bu2gwzquo.pdf

Katsuhiro Honda

Papers

Algorithms for Fuzzy Clustering: Methods in c-Means Clustering with Applications

Fuzzy clustering for categorical multivariate data

Regularized linear fuzzy clustering and probabilistic PCA mixture models

Linear fuzzy clustering techniques with missing values and their application to local principal component analysis

Fuzzy c-means clustering with regularization by K-L information