Edward A. Patrick

Clustering Using a Similarity Measure Based on Shared Near Neighbors

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.

A generalized k-nearest neighbor rule

A family of supervised, nonparametric decision rules, based on tolerance regions, is described which includes the k -Nearest Neighbor decision rules when there are two classes. There are two practical reasons for doing so: first, a family of decision rules similar to the k -Nearest Neighbor rules can be specified which applies to a broader collection of pattern recognition problems. This is because in the general class of rules constraints are weakened between the number of training samples required in each training sample set and the respective a priori class probabilities; and, a discrete loss function weighting the importance of the finite number of ways to make a decision error can be introduced. Second, within the family of decision rules based on tolerance regions, there are decision rules which have a property allowing for preprocessing of the training set data resulting in significant data reduction. Theoretical performance for a special case is presented.

Nonparametric feature selection

Two groups of L -dimensional observations of size N_{1} and N_{2} are known to be random vector variables from two unknown probability distribution functions [1]. A method is discussed for obtaining an l -dimensional linear subspace of the observation space in which the l -variate marginal distributions are most separated, based on a nonparametric estimate of probability density functions and a distance criterion. The distance used essentially is the L_{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.

Nonsupervised sequential classification and recognition of patterns

A Bayes approach to nonsupervised pattern recognition is given where n l -dimensional vector samples X_{1}, X_{2}, \cdots , X_{n} are received unclassified, i.e., any one of M pattern sources \omega_{1}, \omega_{2}, \cdots, \omega_{M} , with corresponding probabilities of occurrence Q_{1_{o}}, Q_{2_{o}} , \cdots , Q_{M_{o}} , caused each sample X_{s}, s=1,2, \cdots , n . The approach utilizes the fact that the cumulative distribution function (c.d.f.) of X_{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 of M and the family \{F(X_{s}|\omega_{i})\} , where F(X_{s}|\omega_{i}) is characterized by a vector B_{i_{o}} . In general, B_{i_{o}} and Q_{i_{o}}, i = 1,2, \cdots , M are considered fixed but unknown, and conditional probability of error in deciding which source caused X_{n} is minimized. When the functional form of F(X_{s}|\omega_{i}) in terms of B_{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 as F(X_{s}|\omega_{i}) is symmetrical, and/or F(X_{s}|\omega_{i}) differs from F(X_{s}|\omega_{j}) only by a translational vector--can be utilized in the Bayes solution.

Interactive Use of Problem Knowledge for Clustering and Decision Making

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 experts 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 experts a priori confidence.

Decision-Directed Estimation of a Two-Class Decision Boundary

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.

Expected outcome loss to evaluate medical diagnosis and treatments.

Abstract A model is developed to help evaluate the effect of a treatment on various defined outcomes when the diagnosis can be one of several classes . Loss factors are defined for a particular outcome using one treatment when there is a specific diagnosis (class). After defining appropriate multidimensional probability densities, Expected outcome loss is defined. Clinical examples are presented where the differential diagnosis is foreign body airway obstruction vs cardiac arrest.

Interactive pattern analysis and classification utilizing prior knowledge

Abstract An approach to interactive pattern recognition is described which provides for using a priori problem knowledge. The a priori knowledge is either in the form of uncertain correlation information among features or new features which are nonlinear functions of original features. In effect a problem model is interactively constructed in the computer along with uncertain estimates of the parameters characterizing the model. Provision then exists for updating estimates using supervised or unsupervised training samples. The resulting interactive system is designed for waveforms, pictures, or vectors.

Iterative computation of a posteriori probability for M -ary nonsupervised adaptation (Corresp.)

where {W, WZ, . . . ) is a sequence of uncorrelated random variables, and where t is a specified constant. Such noise sequences arise in simple feed-back systems and in certain digital filtering applications. Recursive filters are basically the same form as (5). If the parameter E is positive and less than unity, (5) represents a digital filter with an exponential “impulse response.” The sequence (Yi, YP, . . . ) has independent increments when E = 1. The Yj’s can be expressed as a linear combination of the Wi)s, namely, (5) u‘w

An algorithm for segmentation of metaphase spreads

Abstract An algorithm is proposed for locating chromosomes in photomicrographs of metaphase spreads. The algorithm resembles closely the method used by human operators to search microscopic fields. The algorithm was specially programmed to be used with small scale computers.