Structural Classification Analysis of Three-Way Dissimilarity Data

The paper presents a methodology for classifying three-way dissimilarity data, which are reconstructed by a small number of consensus classifications of the objects each defined by a sum of two order constrained distance matrices, so as to identify both a partition and an indexed hierarchy. Specifically, the dissimilarity matrices are partitioned in homogeneous classes and, within each class, a partition and an indexed hierarchy are simultaneously fitted. The model proposed is mathematically formalized as a constrained mixed-integer quadratic problem to be fitted in the least-squares sense and an alternating least-squares algorithm is proposed which is computationally efficient. Two applications of the methodology are also described together with an extensive simulation to investigate the performance of the algorithm.     

The location model for mixtures of categorical and continuous variables

Recent research into graphical association models has focussed interest on the conditional Gaussian distribution for analyzing mixtures of categorical and continuous variables. A special case of such models, utilizing the homogeneous conditional Gaussian distribution, has in fact been known since 1961 as the location model, and for the past 30 years has provided a basis for the multivariate analysis of mixed categorical and continuous variables. Extensive development of this model took place throughout the 1970’s and 1980’s in the context of discrimination and classification, and comprehensive methodology is now available for such analysis of mixed variables. This paper surveys these developments and summarizes current capabilities in the area. Topics include distances between groups, discriminant analysis, error rates and their estimation, model and feature selection, and the handling of missing data.     

“道法自然”的现代诠释

道家"道法自然"观念的核心内容即是通过"法天地"而体悟其中的"自然"之道以为人类所用。其主要目的有二:一是为人类安身立命,二是借以救治失性的病态人类。"道法自然"的理论根据在于道家认为大自然是至善至美的,而且还认为正是体现于天地万物之中的理性的自然精神造就了这种至善至美。"道法自然"并非机械模仿天地万物尤其是动物的某些个别的、具体的行为,而是要学习它们的不同行为中所体现出来的某些共同的理性精神,也就是说,"道法自然"一定要透过现象而抓取其本质。     

The generation of random,binary unordered trees

Several techniques are given for the uniform generation of trees for use in Monte Carlo studies of clustering and tree representations. First, general strategies are reviewed for random selection from a set of combinatorial objects with special emphasis on two that use random mapping operations. Theorems are given on how the number of such objects in the set (e.g., whether the number is prime) affects which strategies can be used. Based on these results, methods are presented for the random generation of six types of binary unordered trees. Three types of labeling and both rooted and unrooted forms are considered. Presentation of each method includes the theory of the method, the generation algorithm, an analysis of its computational complexity and comments on the distribution of trees over which it samples. Formal proofs and detailed algorithms are in appendices.     

Automated design of multiple-class piecewise linear classifiers

A new method and a supporting theorem for designing multiple-class piecewise linear classifiers are described. The method involves the cutting of straight line segments joining pairs of opposed points (i.e., points from distinct classes) ind-dimensional space. We refer to such straight line segments aslinks. We show how nearly to minimize the number of hyperplanes required to cut all of these links, thereby yielding a near-Bayes-optimal decision surface regardless of the number of classes, and we describe the underlying theory. This method does not require parameters to be specified by users — an improvement over earlier methods. Experiments on multiple-class data obtained from ship images show that classifiers designed by this method yield approximately the same error rate as the bestk-nearest neighbor rule, while providing faster decisions.This research was supported in part by the Army Research Office under grant DAAG29-84-K-0208 and in part by the University of California MICRO Program. We thank R. W. Doucette of the U.S. Naval Weapons Center and R. D. Holben of Ford Aerospace Corporation for providing the ship images in our experiments.     

Comparison of classifications using measures intermediate between metric dissimilarity and consensus similarity

Two fundamental approaches to the comparison of classifications (e g, partitions on the same finite set of objects) can be distinguished One approach is based upon measures of metric dissimilarity while the other is based upon measures of similarity, or consensus These approaches are not necessarily simple complements of each other Instead, each captures different, limited views of comparison of two classifications The properties of these measures are clarified by their relationships to Day's complexity models and to association measures of numerical taxonomy The two approaches to comparison are equated with the use of separation and minimum value sensitive measures, suggesting the potential application of an intermediate sensitive measure to the problem of comparison of classifications Such a measure is a linear combination of separation sensitive and minimum value sensitive components The application of these intermediate measures is contrasted with the two extremes The intermediate measure for the comparison of classifications is applied to a problem of character weighting arising in the analysis of Australian stream basinsWe thank Bill Day, Mike Austin, Peter Minchin and two anonymous referees for many helpful comments We also thank P Arabie for useful discussion of consensus methods and character weighting