A review of pattern recognition applied to medical diagnosis and consulting is presented. Papers (127-references) are evaluated with respect to a new medical system model incorporating concepts of consulting and decision making, the latter based on a Bayesean approach incorporating problem knowledge. This model introduces the consultant as an essential component of the decision system. The model is that of a system with subsystems. A subsystem contains a set of classes, and each class has a class-feature relationship. Features (defined as functions of measurements), complex features, and class-feature relationships provide for introducing a priori medical knowledge and dimensionality reduction. Special features such as significant features, rule-in or rule-out features, and time-dependent features, and special classes such as subclasses and intermediate classes are introduced. Etiology, a method of tracing from one subsystem to another subsystem, also is part of the system. With respect to this model, papers in numerous application areas are reviewed. No single paper fulfills many of the system's properties, and this may be why there are very few, if any, of the results described in these papers being used in health care delivery. Part of the paper is a complementary literature review of 127 papers on computer assisted medical diagnosis and consulting.

A nonparametric clustering technique incorporating the concept of similarity based on the sharing of near neighbors is presented. In addition to being an essentially paraliel approach, the computational elegance of the method is such that the scheme is applicable to a wide class of practical problems involving large sample size and high dimensionality. No attempt is made to show how a priori problem knowledge can be introduced into the procedure.

An approach to clustering and decision making is presented where a prior problem knowledge is inserted interactively. The problem knowledge inserted is in the form of subcategory mean vectors and covariance matrices and in the expert's confidence that these means and covariances accurately characterize the category. Then observations of patterns from the category are used to update these a priori supplied means and covariances. The extent to which new observations update the a priori values depends upon the expert's a priori confidence.

A decision-directed unsupervised estimation algorithm is used in a receiver that processes signals with unknown intersymbol interference. The estimator utilizes the statistical structure of this dependent sample problem to reduce the computational complexity. Asymptotic and experimental dynamic probability of error results are presented.

A hybrid computer is described for implementing decision-directed estimators for the two-class unsupervised estimation problem. Extensions of the system design to the multiclass problem has significant application to computerized medical diagnosis and other problems in communications and pattern recognition. These problems include resolving multiple target bearings in sonar and radar, clustering data such as arise in cell processing, locating modes in density functions for use in interactive data analysis systems, data compression, elimination of intersymbol interference, and many others.

There are several approaches to unsupervised estimation that have application to problems of communications, control, and pattern recognition. This paper presents properties of several different digitally implemented algorithms suitable for unsupervised estimation. One result is the rate of convergence in mean square of the Bayes solution for a discretized parameter space. A regression function that is the expected value of the natural logarithm of the mixture probability density function naturally arises from the Bayes approach. This regression function can be used to devise unsupervised estimation algorithms of the stochastic approximation form. Also, the asymptotic solution and rates of convergence in mean square of a class of minimum-integral-square-difference algorithms are determined. Two other estimators that use a "net" on the parameter space are also presented.

The unsupervised estimation problem has been conveniently formulated in terms of a mixture density. It has been shown that a criterion naturally arises whose maximum defines the Bayes minimum risk solution. This criterion is the expected value of the natural log of the mixture density. By making the assumptions that the component densities in the mixture are truncated Gaussian, the criterion has a greatly simplified form. This criterion can be used to resolve mixtures when the number of classes as well as the class covariances are unknown. In this paper a technique is presented where an assumed test covariance is supplied by an experimenter who uses a test function as a "portable magnifying glass" to examine data. Because the experimenter supplies the covariance and thus the test function, the technique is especially suited for interactive data analysis.

Two groups ofL-dimensional observations of sizeN_{1}andN_{2}are known to be random vector variables from two unknown probability distribution functions [1]. A method is discussed for obtaining anl-dimensional linear subspace of the observation space in which thel-variate marginal distributions are most separated, based on a nonparametric estimate of probability density functions and a distance criterion. The distance used essentially is theL_{2}norm of the difference between Parzen estimates of the two densities. An algorithm is developed that determines the subspace for which the distance between the two densities is maximized. Computer simulations are performed.

Abstract—The problem considered is the mapping of a functional's multidimensional bounded domain onto a bounded interval of the real line. This transformation is to have the property that "neighboring" points in the bounded interval are necessarily mapped from "neighboring" points in the bounded domain. The multidimensional bounded domain is partitioned into a finite number of elementary regions while the bounded interval is partitioned into the same finite number of elementary intervals. A one-to-one correspondence is defined between the elementary regions and intervals such that neighboring elementary intervals have corresponding multidimensional elementary regions that are neighboring. The degree of neighborliness is controlled by controlling the fineness of partitioning. By suitably defining an equivalent function over the bounded interval, properties of the original functional can be displayed.

The unsupervised estimation problem has received considerable attention during the last three years. The problem usually considered, however, is only one of a class of unsupervised estimation problems. In this paper, a "mixture approach" defined previously is used to define this class of unsupervised estimation problems, and state precisely the a priori knowledge used to define each problem. After using available a priori knowledge to construct precisely the mixture appropriate to the unsupervised problem, the parameters characterizing this particular unsupervised problem can be estimated, or a Bayes minimum conditional risk receiver can be constructed. The class of unsupervised estimation problems includes the following cases: unknown number of pattern classes, dependent observation vectors, nonstationary class probabilities, more than one vector observation taken with a single class active, lack of synchronization, and unsupervised learning control and communications.

The asymptotic probability of error for an unsupervised learning system with two unknown mean vectors, which are estimated by "decision-directed" estimators, is investigated. Theoretical solutions are obtained for various class probabilities and signal-to-noise ratios by utilizing a digital computer.

A Bayes approach to nonsupervised pattern recognition is given wheren l-dimensional vector samplesX_{1}, X_{2}, \cdots , X_{n}are received unclassified, i.e., any one ofMpattern sources\omega_{1}, \omega_{2}, \cdots, \omega_{M}, with corresponding probabilities of occurrenceQ_{1_{o}}, Q_{2_{o}} , \cdots , Q_{M_{o}}, caused each sampleX_{s}, s=1,2, \cdots , n. The approach utilizes the fact that the cumulative distribution function (c.d.f.) ofX_{s}is a mixture c.d.f.,F(X_{s})= \sum_{i=1}^{M} F(X_{s}|\omega_{i}) Q_{i_{o}}. It is assumed that available a priori knowledge includes knowledge ofMand the family\{F(X_{s}|\omega_{i})\}, whereF(X_{s}|\omega_{i})is characterized by a vectorB_{i_{o}}. In general,B_{i_{o}}andQ_{i_{o}}, i = 1,2, \cdots , Mare considered fixed but unknown, and conditional probability of error in deciding which source causedX_{n}is minimized. When the functional form ofF(X_{s}|\omega_{i})in terms ofB_{i_{o}}is unknown, the family\{F(X_{s}|\omega_{i})\}is taken to be the family of multinomial c.d.f.'s--an application of the histogram concept to the nonsupervisory problem. Additional nonparameteric a priori knowledge about the family--such asF(X_{s}|\omega_{i})is symmetrical, and/orF(X_{s}|\omega_{i})differs fromF(X_{s}|\omega_{j})only by a translational vector--can be utilized in the Bayes solution.