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In the past, automatic procedures for the design of pattern classifiers have usually used a machine of fixed size. These procedures require that prior to learning we know, or can guess, the complexity of the decision surface used by the teacher. Techniques have been discovered for changing the complexity of a pattern classifier by adding or removing parts of it. These methods, respectively called “growing” and “pruning” use well established learning rules applied alternately with the addition or removal of comput,ing equipment. Growing is thus a process by which we can increase the complexity of a classifier until it fits the problem. Pruning removes computing equipment from a classifier whose performance is satisfactory, but inefficient. The paper describes our experimental evaluation of these procedures. These studies have shown that these techniques are capable of designing a classifier which closely models a complex teacher with a minimum of storage.

This paper considers the problem of pattern classification in the frequency domain. The test statistic depends on the spectral density of each pattern class which may or may not be known. When the spectral density of the unknown input pattern to be classified is not known then the technique of time series analysis is applied to estimate its spectra, and asymptotic properties of the test statistic are investigated. A simple example is solved to illustrate the validity of this approach.

This paper proposes the concept of equivocation from information theory as a criterion for feature selection. An expression for equivocation is derived in terms of class conditional probabilities. By making the assumption that the patterns in each class are normally distributed, a transformation matrix that minimizes the equivocation in the reduced dimension is obtained. Furthermore, a relationship between the equivocation and the expected divergence between any pair of classes is presented.

One approach to abstract pattern recognition is to represent the discriminant functions such that they are characterized by linearly appearing parameters, e.g., a general multivariate polynomial. This paper discusses a class of methods for deriving values for these parameters given a finite set of samples of each pattern class; the methods discussed are those which use least-square or least-mean-square approximation to an unknown probability density or partially specified discriminant function. The algorithms which result are feasible for the solution of complex problems using a general-purpose digital computer. This viewpoint emphasizes the common denominator of many procedures in abstract pattern recognition.

This paper uses optimization theory and continuous invariant imbedding in order to derive computationally efficient sequential algorithms for the maximum likelihood estimation of bias errors in recursive filtering with noise corrupted input observations and correlated plant and measurement noise. Error analysis algorithms are derived for adaptive and nonadaptive systems with bias and modeling errors. Examples demonstrate the efficacy of the adaptive estimation algorithms and the error analysis algorithms for estimation with bias uncertainty.

This paper presents the problem of unsupervised learning structure and parameter adaptive pattern recognition. Different near optimal solutions that alleviate the infinite or exploding memory requirements of the optimal solution are suggested. The learning capabilities of these methods are compared with that of the optimal supervised scheme by presenting an example.

This paper deals with a new clustering technique using the concept of fuzzy set introduced by Zadeh. A cluster is defined as a subset characterized by a membership function which associates with each element a real number in the unit interval. A membership function is proposed and a method to select the cluster elements is derived using the separation theorem of the fuzzy sets. The clusters obtained by this way are controlled overlapping groupings.

This paper deals with a nonlinear learning algorithm characterized by a threshold effect. The algorithm is derived in relation to a learning process in pattern recognition where steps must be taken to minimize the effect of spurious samples carrying unreliable information. With the assumption of a multivariate normal density for each pattern population, the nonlinear algorithm reduces to discarding the spurious samples with a threshold element and in the meantime performing an ordinary linear algorithm for the remaining samples. Optimal properties of this algorithm are studied and a criterion for selecting a proper threshold is discussed. A computer-simulated experiment in character recognition is presented to illustrate a possible application for the nonlinear algorithm. Results of this experiment have shown significant improvement over an ordinary linear algorithm in handling character samples with various imperfections due to the poor quality in writing or printing encountered in practice.

The Nearest Neighbour Classifier accepts patterns in the form of points in a descriptor space and classifies them by reference to a number of stored labelled points called locates. Training procedures for such classifiers have in the past consisted of a set of rules for selecting various members of the training set for use as locates. This paper describes an alternative approach in which the locates do not necessarily represent real patterns, and the training procedure consists of adjusting the positions of the locates so as to optimise the decision surface.

This paper is concerned with the analysis of a class of problems involving mixture variates (functions of several random variables). The explicit inclusion of a mixture as a separate category in pattern recognition problems is studied and plausible forms for the mixing densities in such problems are derived.

This paper describes the proceedings of the workshop on Biomedical Statistics and Computation of the Fourth Annual Symposium on the Interface. This was a two day symposium held at the University of California at Irvine on September 17 & 18, 1970. It was sponsored jointly by the ACM, ASA, and the California Mathematics Council. Dr. Tarter chaired this workshop. The thirty participants in this workshop represented all of the disciplines which combine to become Biocomputer Statistics. There were physicians both interested in and active in computer applications to medicine, directors of biomathematics and biostatistics programs, computer specialists, and mathematical and applied statisticians, as well as medical students. It should be noted that the three other workshops at the Interface Symposium were more concerned with computer hardware and software and thus attracted most of the pure computer specialists. This tended to weight this workshop with a large proportion of statisticians.

The paper points out that under certain conditions the Nearest Neighbour and Potential Function Classifiers produce similar decision surfaces. A new classifier is defined which is closely related to the Nearest Neighbour Classifier, and which implements a piecewise hyperspherical decision surface. This decision surface is similar to that produced by a Potential Function Classifier under a wider variety of conditions.

In this paper we describe an approach to the artificial recognition of events of a nonsymbolic nature, such as the bidimensional perspective views of scenes of our everyday world. Scenes are presented as colored pictures and the objective of the cognitive task is the labeling of the interpreted scene objects. The method is based on three major components: 1. (i) a preprocessed version of the scene (stimulus), 2. (ii) a semantic map and 3. (iii) an algorithm which performs interpretation of the stimulus under the guidance of the semantic map. The algorithm is sequential and proceeds from general to specific, thereby achieving efficient tree-pruning (contextual elimination). Stimulus interpretation is based on attribute-value matching, but classification relies strongly on the accumulated context. Backtracking provisions are available in the sequential cognitive algorithm for correction of earlier wrong hypotheses. Experiments are presented and described. The major weakness of the approach is the present lack of a satisfactory theory of inference. Flexibility, generalizability, and efficiency appear to be valid merits.