The primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques and methods imported from statistical learning theory have bean receiving increasing attention. The design of a recognition system requires careful attention to the following issues: definition of pattern classes, sensing environment, pattern representation, feature extraction and selection, cluster analysis, classifier design and learning, selection of training and test samples, and performance evaluation. In spite of almost 50 years of research and development in this field, the general problem of recognizing complex patterns with arbitrary orientation, location, and scale remains unsolved. New and emerging applications, such as data mining, web searching, retrieval of multimedia data, face recognition, and cursive handwriting recognition, require robust and efficient pattern recognition techniques. The objective of this review paper is to summarize and compare some of the well-known methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.

A reliable and precise classification of tumors is essential for successful diagnosis and treatment of cancer. cDNA microarrays and high-density oligonucleotide chips are novel biotechnologies increasingly used in cancer research. By allowing the monitoring of expression levels in cells for thousands of genes simultaneously, microarray experiments may lead to a more complete understanding of the molecular variations among tumors and hence to a finer and more informative classification. The ability to successfully distinguish between tumor classes (already known or yet to be discovered) using gene expression data is an important aspect of this novel approach to cancer classification. This article compares the performance of different discrimination methods for the classification of tumors based on gene expression data. The methods include nearest-neighbor classifiers, linear discriminant analysis, and classification trees. Recent machine learning approaches, such as bagging and boosting, are also considered. The discrimination methods are applied to datasets from three recently published cancer gene expression studies.

We compare discriminative and generative learning as typified by logistic regression and naive Bayes. We show, contrary to a widely held belief that discriminative classifiers are almost always to be preferred, that there can often be two distinct regimes of performance as the training set size is increased, one in which each algorithm does better. This stems from the observation -- which is borne out in repeated experiments -- that while discriminative learning has lower asymptotic error, a generative classifier may also approach its (higher) asymptotic error much faster.

A non-linear classification technique based on Fisher's discriminant is proposed. The main ingredient is the kernel trick which allows the efficient computation of Fisher discriminant in feature space. The linear classification in feature space corresponds to a (powerful) non-linear decision function in input space. Large scale simulations demonstrate the competitiveness of our approach.

Nearest neighbor classification expects the class conditional probabilities to be locally constant, and suffers from bias in high dimensions. We propose a locally adaptive form of nearest neighbor classification to try to ameliorate this curse of dimensionality. We use a local linear discriminant analysis to estimate an effective metric for computing neighborhoods. We determine the local decision boundaries from centroid information, and then shrink neighborhoods in directions orthogonal to these local decision boundaries, and elongate them parallel to the boundaries. Thereafter, any neighborhood-based classifier can be employed, using the modified neighborhoods. The posterior probabilities tend to be more homogeneous in the modified neighborhoods. We also propose a method for global dimension reduction, that combines local dimension information. In a number of examples, the methods demonstrate the potential for substantial improvements over nearest neighbor classification. Keywords--...

Cluster analysis is the automated search for groups of related observations in a data set. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures and most clustering methods available in commercial software are also of this type. However, there is little systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as \How many clusters are there?", "Which clustering method should be used?" and \How should outliers be handled?". We outline a general methodology for model-based clustering that provides a principled statistical approach to these issues. We also show that this can be useful for other problems in multivariate analysis, such as discriminant analysis and multivariate density estimation. We give examples from medical diagnosis, mineeld detection, cluster recovery from noisy data, and spatial density estimation. Finally, we mention limitations of the methodology, a...

Fisher-Rao linear discriminant analysis (LDA) is a valuable tool for multigroup classification. LDA is equivalent to maximum likelihood classification assuming Gaussian distributions for each class. In this paper, we fit Gaussian mixtures to each class to facilitate effective classification in non-normal settings, especially when the classes are clustered. Low dimensional views are an important by-product of LDA---our new techniques inherit this feature. We are able to control the within-class spread of the subclass centers relative to the between-class spread. Our technique for fitting these models permits a natural blend with nonparametric versions of LDA. Keywords: Classification, Pattern Recognition, Clustering, Nonparametric, Penalized. 1 Introduction In the generic classification or discrimination problem, the outcome of interest G falls into J unordered classes, which for convenience we denote by the set J = f1; 2; 3; \Delta \Delta \Delta Jg. We wish to build a rule for pred...

The K-nearest-neighbor decision rule assigns an object of unknown class to the plurality class among the K labeled "training" objects that are closest to it. Closeness is usually defined in terms of a metric distance on the Euclidean space with the input measurement variables as axes. The metric chosen to define this distance can strongly effect performance. An optimal choice depends on the problem at hand as characterized by the respective class distributions on the input measurement space, and within a given problem, on the location of the unknown object in that space. In this paper new types of K-nearest-neighbor procedures are described that estimate the local relevance of each input variable, or their linear combinations, for each individual point to be classified. This information is then used to separately customize the metric used to define distance from that object in finding its nearest neighbors. These procedures are a hybrid between regular K-nearest-neighbor methods and tree-structured recursive partitioning techniques popular in statistics and machine learning.

Latent Semantic Indexing (LSI) is a novel approach to information retrieval that attempts to model the underlying structure of term associations by transforming the traditional representation of documents as vectors of weighted term frequencies to a new coordinate space where both documents and terms are represented as linear combinations of underlying semantic factors. In previous research, LSI has produced a small improvement in retrieval performance. In this paper, we apply LSI to the routing task, which operates under the assumption that a sample of relevant and non-relevant documents is available to use in constructing the query. Once again, LSI slightly improves performance. However, when LSI is used is conduction with statistical classification, there is a dramatic improvement in performance. 1

There has been much publicity about the ability of artificial neural networks to learn and generalize. In fact, the most commonly used artificial neural networks, called multilayer perceptrons, are nothing more than nonlinear regression and discriminant models that can be implemented with standard statistical software. This paper explains what neural networks are, translates neural network jargon into statistical jargon, and shows the relationships between neural networks and statistical models such as generalized linear models, maximum redundancy analysis, projection pursuit, and cluster analysis.