Classification of Asymmetric Proximity Data

When clustering asymmetric proximity data, only the average amounts are often considered by assuming that the asymmetry is due to noise. But when the asymmetry is structural, as typically may happen for exchange flows, migration data or confusion data, this may strongly affect the search for the groups because the directions of the exchanges are ignored and not integrated in the clustering process. The clustering model proposed here relies on the decomposition of the asymmetric dissimilarity matrix into symmetric and skew-symmetric effects both decomposed in within and between cluster effects. The classification structures used here are generally based on two different partitions of the objects fitted to the symmetric and the skew-symmetric part of the data, respectively; the restricted case is also presented where the partition fits jointly both of them allowing for clusters of objects similar with respect to the average amounts and directions of the data. Parsimonious models are presented which allow for effective and simple graphical representations of the results.     

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.     

One-Mode Classification of a Three-Way Data Matrix

X is the automatic hierarchical classification of one mode (units or variables or occasions) of X on the basis of the other two. In this paper the case of OMC of units according to variables and occasions is discussed. OMC is the synthesis of a set of hierarchical classifications Delta obtained from X; e.g., the OMC of units is the consensus (synthesis) among the set of dendograms individually defined by clustering units on the basis of variables, separately for each given occasion of X. However, because Delta is often formed by a large number of classifications, it may be unrealistic that a single synthesis is representative of the entire set. In this case, subsets of similar (homegeneous) dendograms may be found in Delta so that a consensus representative of each subset may be identified. This paper proposes, PARtition and Least Squares Consensus cLassifications Analysis (PARLSCLA) of a set of r hierarchical classifications Delta. PARLSCLA identifies the best least-squares partition of Delta into m (1 <= m <= r) subsets of homogeneous dendograms and simultaneously detects the closest consensus classification (a median classification called Least Squares Consensus Dendogram (LSCD) for each subset. PARLSCLA is a generalization of the problem to find a least-squares consensus dendogram for Delta. PARLSCLA is formalized as a mixed-integer programming problem and solved with an iterative, two-step algorithm. The method proposed is applied to an empirical data set.     

Percept Variance,Subadditivity and the Metric Classification of Similarity,and Dissimilarity Data

Percept variance is shown to change the additive property of city-block distances and make city-block distances more subadditive than Euclidean distances. Failure to account for percept variance will result in the misclassification of city-block data as Euclidean. A maximum likelihood estimation procedure is proposed for the multidimensional scaling of similarity data characterized by percept variance. Monte Carlo and empirical experiments are used to evaluate the proposed approach.     

An Evaluation of Two Algorithms for Hierarchical Classes Analysis

k  . In this procedure, a least-squares loss function in terms of discrepancies between D and M is minimized. The present paper describes the original hierarchical classes algorithm proposed by De Boeck and Rosenberg (1988), which is based on an alternating greedy heuristic, and proposes a new algorithm, based on an alternating branch-and-bound procedure. An extensive simulation study is reported in which both algorithms are evaluated and compared according to goodness-of-fit to the data and goodness-of-recovery of the underlying true structure. Furthermore, three heuristics for selecting models of different ranks for a given D are presented and compared. The simulation results show that the new algorithm yields models with slightly higher goodness-of-fit and goodness-of-recovery values.     

Data Model and Classification by Trees: The Minimum Variance Reduction (MVR) Method

O (n ⁴), where n is the number of objects. We describe the application of the MVR method to two data models: the weighted least-squares (WLS) model (V is diagonal), where the MVR method can be reduced to an O(n ³) time complexity; a model arising from the study of biological sequences, which involves a complex non-diagonal V matrix that is estimated from the dissimilarity matrix Δ. For both models, we provide simulation results that show a significant error reduction in the reconstruction of T, relative to classical agglomerative algorithms.     

Free Knot Splines for Supervised Classification

Data in many different fields come to practitioners through a process naturally described as functional. We propose a classification procedure of oxidation curves. Our algorithm is based on two stages: fitting the functional data by linear splines with free knots and classifying the estimated knots which estimate useful oxidation parameters. A real data set on 57 oxidation curves is used to illustrate our approach.     

Default Priors for Neural Network Classification

Feedforward neural networks are a popular tool for classification, offering a method for fully flexible modeling. This paper looks at the underlying probability model, so as to understand statistically what is going on in order to facilitate an intelligent choice of prior for a fully Bayesian analysis. The parameters turn out to be difficult or impossible to interpret, and yet a coherent prior requires a quantification of this inherent uncertainty. Several approaches are discussed, including flat priors, Jeffreys priors and reference priors.     

Variable Selection for Clustering and Classification

As data sets continue to grow in size and complexity, effective and efficient techniques are needed to target important features in the variable space. Many of the variable selection techniques that are commonly used alongside clustering algorithms are based upon determining the best variable subspace according to model fitting in a stepwise manner. These techniques are often computationally intensive and can require extended periods of time to run; in fact, some are prohibitively computationally expensive for high-dimensional data. In this paper, a novel variable selection technique is introduced for use in clustering and classification analyses that is both intuitive and computationally efficient. We focus largely on applications in mixture model-based learning, but the technique could be adapted for use with various other clustering/classification methods. Our approach is illustrated on both simulated and real data, highlighted by contrasting its performance with that of other comparable variable selection techniques on the real data sets.     

Robust Functional Supervised Classification for Time Series

We propose using the integrated periodogram to classify time series. The method assigns a new time series to the group that minimizes the distance between the series integrated periodogram and the group mean of integrated periodograms. Local computation of these periodograms allows the application of this approach to nonstationary time series. Since the integrated periodograms are curves, we apply functional data depth-based techniques to make the classification robust, which is a clear advantage over other competitive procedures. The method provides small error rates for both simulated and real data. It improves existing approaches and presents good computational behavior.     

Oscillation Heuristics for the Two-group Classification Problem

We propose a new nonparametric family of oscillation heuristics for improving linear classifiers in the two-group discriminant problem. The heuristics are motivated by the intuition that the classification accuracy of a separating hyperplane can be improved through small perturbations to its slope and position, accomplished by substituting training observations near the hyperplane for those used to generate it. In an extensive simulation study, using data generated from multivariate normal distributions under a variety of conditions, the oscillation heuristics consistently improve upon the classical linear and logistic discriminant functions, as well as two published linear programming-based heuristics and a linear Support Vector Machine. Added to any of the methods above, they approach, and frequently attain, the best possible accuracy on the training samples, as determined by a mixed-integer programming (MIP) model, at a much smaller computational cost. They also improve expected accuracy on the overall populations when the populations overlap significantly and the heuristics are trained with large samples, at least in situations where the data conditions do not explicitly favor a particular classifier.     

Comparing Optimization Algorithms for Item Selection in Mokken Scale Analysis

Mokken scale analysis uses an automated bottom-up stepwise item selection procedure that suffers from two problems. First, when selected during the procedure items satisfy the scaling conditions but they may fail to do so after the scale has been completed. Second, the procedure is approximate and thus may not produce the optimal item partitioning. This study investigates a variation on Mokken’s item selection procedure, which alleviates the first problem, and proposes a genetic algorithm, which alleviates both problems. The genetic algorithm is an approximation to checking all possible partitionings. A simulation study shows that the genetic algorithm leads to better scaling results than the other two procedures.     

俄英医学同义术语的类型划分及英俄、汉俄医学词典编纂启示

同义现象是术语学界长期关注的热点问题,也是当代极具现实意义和有争议的问题。术语的同义现象是建立在表达同一个专业概念的不同术语单位基础上的一种语义关系。通过对医学各领域同义术语(主要是俄语和英语)的分析和描写,划分同义术语的类型,确定现代医学术语的特点,进而发现现代医学双语(主要是英俄、汉俄)词典中暂时还缺乏关于在术语系统功能化条件下使用某一同义术语的相关信息。因此,英俄、汉俄医学词典应对同义术语做相关的信息标注,以帮助使用者选取某一具体医学领域最适合的同义术语。