Quantitative properties of the evolution and classification of languages

Statistical analyses of a published phylogenetic classification of languages show some properties attributable to taxonomic methods and others that reflect the nature of linguistic evolution. The inferred phylogenetic tree is less well resolved and more asymmetric at the highest taxonomic ranks, where the tree is constructed mainly by phenetic methods. At lower ranks, where cladistic methods are more prevalent, the asymmetry of well resolved parts of the tree is consistent with a stochastic birth and death process in which languages originate and become extinct at constant rates, although poorly resolved parts of the tree are still more asymmetric than predicted. Other tests applied to a sample of historically recorded languages reveal substantial fluctuations in the rates of origination and extinction, with both rates temporarily reduced when languages enter the historical record. For languages in general, the average origination rate is estimated to be only slightly higher than the average extinction rate, which in turn corresponds to an average lifetime of about 500 years or less.This research was suported by a grant from the UCLA Academic Senate and by computer time from the UCLA Office of the Academic Computing. I thank Merritt Ruhlen, Joseph B. Slowinski, and Thomas D. Wickens for helpful information and suggestions.     

Evolutionary and psychological effects in pre-evolutionary classifications

Relative frequency of genera as a function of number of species per genus is plotted for six eighteenth-century classifications: Linnaeus' classifications of animals, plants, minerals, and diseases, and Sauvages' classifications of plants and diseases. The distributions for animals and plants form positively skewed hollow curves similar but not identical to those found in modern biological classifications and predicted by mathematical models of evolution. The distributions for minerals and diseases, however, are more nearly symmetric and convex. The difference between the eighteenth-century and modern classifications of animals and plants probably reflects psychological properties of the taxonomists' judgments; but the difference between the classifications of animals and plants and those of minerals and diseases reflects evolutionary properties of the materials classified, since all six classifications were constructed by the same taxonomists using the same methods. Consequently, the observable effects of evolution are strong enough to be detected in classifications constructed before the acceptance of evolutionary theory; and traditional classifications can contain substantial scientific information despite their reliance on incompletely understood processes of judgment.I thank Mae Ling Hum for assistance in data collection, and Dennis G. Fisher, David M. Raup, Thomas D. Wickens, and J. Arthur Woodward for helpful comments on earlier versions of the paper. Computer time was provided by the UCLA Office of Academic Computing.     

Numerical taxonomy and the principle of maximum entropy

The standard procedure in numerical classification and identification of micro-organisms based on binary features is given a justification based on the principle of maximum entropy. This principle also strongly supports the assumption that all characteristics upon which the classification is based are equally important and the use of polythetic taxa. The relevance of the principle of maximum entropy in connection with taxonomic structures based on clustering and maximal predictivity is discussed. A result on asymptotic separateness of maximum entropy distributions has implications for minimizing identification errors.The work was partially supported by the Bank of Sweden Tercentenary Foundation, The Swedish Council for Forestry and Agricultural Research, The Carl Trygger Foundation, and the Swedish Cancer Foundation.     

On the use of ordered sets in problems of comparison and consensus of classifications

Ordered set theory provides efficient tools for the problems of comparison and consensus of classifications Here, an overview of results obtained by the ordinal approach is presented Latticial or semilatticial structures of the main sets of classification models are described Many results on partitions are adaptable to dendrograms; many results on n-trees hold in any median semilattice and thus have counterparts on ordered trees and Buneman (phylogenetic) trees For the comparison of classifications, the semimodularity of the ordinal structures involved yields computable least-move metrics based on weighted or unweighted elementary transformations In the unweighted case, these metrics have simple characteristic properties For the consensus of classifications, the constructive, axiomatic, and optimization approaches are considered Natural consensus rules (majoritary, oligarchic, ) have adequate ordinal formalizations A unified presentation of Arrow-like characterization results is given In the cases of n-trees, ordered trees and Buneman trees, the majority rule is a significant example where the three approaches convergeThe authors would like to thank the anonymous referees for helpful suggestions on the first draft of this paper, and W H E Day for his comments and his significant improvements of style     

Significance of the length of the shortest tree

The distribution of lengths of phylogenetic trees under the taxonomic principle of parsimony is compared with the distribution obtained by randomizing the characters of the sequence data. This comparison allows us to define a measure of the extent to which sequence data contain significant hierarchical information. We show how to calculate this measure exactly for up to 10 taxa, and provide a good approximation for larger sets of taxa. The measure is applied to test sequences on 10 and 15 taxa.     

A Thurstonian Ranking Model with Rank-Induced Dependencies

A Thurstonian model for ranks is introduced in which rank-induced dependencies are specified through correlation coefficients among ranked objects that are determined by a vector of rank-induced parameters. The ranking model can be expressed in terms of univariate normal distribution functions, thus simplifying a previously computationally intensive problem. A theorem is proven that shows that the specification given in the paper for the dependencies is the only way that this simplification can be achieved under the process assumptions of the model. The model depends on certain conditional probabilities that arise from item orders considered by subjects as they make ranking decisions. Examples involving a complete set of ranks and a set with missing values are used to illustrate recovery of the objects’ scale values and the rank dependency parameters. Application of the model to ranks for gift items presented singly or as composite items is also discussed.     

A Characterization of Majority Rule for Hierarchies

The majority rule has been a popular method for producing a consensus classification from several different classifications, when the classifications are all on the same set of objects and are structured as hierarchies. In this note, a new axiomatic characterization is proved for this consensus method on hierarchies.     

Kappa Coefficients for Circular Classifications

Circular classifications are classification scales with categories that exhibit a certain periodicity. Since linear scales have endpoints, the standard weighted kappas used for linear scales are not appropriate for analyzing agreement between two circular classifications. A family of kappa coefficients for circular classifications is defined. The kappas differ only in one parameter. It is studied how the circular kappas are related and if the values of the circular kappas depend on the number of categories. It turns out that the values of the circular kappas can be strictly ordered in precisely two ways. The orderings suggest that the circular kappas are measuring the same thing, but to a different extent. If one accepts the use of magnitude guidelines, it is recommended to use stricter criteria for circular kappas that tend to produce higher values.     

A Probability for Classification Based on the Dirichlet Process Mixture Model

In this paper we provide an explicit probability distribution for classification purposes when observations are viewed on the real line and classifications are to be based on numerical orderings. The classification model is derived from a Bayesian nonparametric mixture of Dirichlet process model; with some modifications. The resulting approach then more closely resembles a classical hierarchical grouping rule in that it depends on sums of squares of neighboring values. The proposed probability model for classification relies on a numerical procedure based on a reversible Markov chain Monte Carlo (MCMC) algorithm for determining the probabilities. Some numerical illustrations comparing with alternative ideas for classification are provided.     

A sequential fitting procedure for linear data analysis models

A particular factor analysis model with parameter constraints is generalized to include classification problems definable within a framework of fitting linear models. The sequential fitting (SEFIT) approach of principal component analysis is extended to include several nonstandard data analysis and classification tasks. SEFIT methods attempt to explain the variability in the initial data (commonly defined by a sum of squares) through an additive decomposition attributable to the various terms in the model. New methods are developed for both traditional and fuzzy clustering that have useful theoretic and computational properties (principal cluster analysis, additive clustering, and so on). Connections to several known classification strategies are also stated.The author is grateful to P. Arabie and L. J. Hubert for editorial assistance and reviewing going well beyond traditional levels.     

计算机模拟的认知功能及其可能性

尽管计算机模拟实现了人类认知功能的物化，也为揭示人类认知活动机理开辟了新的途径，但学术界对认知功能的计算机模拟仍存在不同评价。为此，本文从理论层面对认知模拟作了辩证分析，在肯定其具有三项意义的同时，也指出其无法克服的诸多局限。笔者认为，客观评价认知功能的计算机模拟，有助于认知科学家在理论研究中尽早揭示和了解人类认知的规律与机制，在应用研究中能牢牢把握智能模拟的正确方向。     

Minimum Tree Cost Quartet Puzzling

We present a new distance based quartet method for phylogenetic tree reconstruction, called Minimum Tree Cost Quartet Puzzling. Starting from a distance matrix computed from natural data, the algorithm incrementally constructs a tree by adding one taxon at a time to the intermediary tree using a cost function based on the relaxed 4-point condition for weighting quartets. Different input orders of taxa lead to trees having distinct topologies which can be evaluated using a maximum likelihood or weighted least squares optimality criterion. Using reduced sets of quartets and a simple heuristic tree search strategy we obtain an overall complexity of O(n ⁵ log₂ n) for the algorithm. We evaluate the performances of the method through comparative tests and show that our method outperforms NJ when a weighted least squares optimality criterion is employed. We also discuss the theoretical boundaries of the algorithm.     

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     

Generalized measures of association for ranked data with an application to prediction accuracy

A common practice in cross validation research in the behavioral sciences is to employ either the product moment correlation or a simple tabulation of first-choice “hits” for measuring the accuracy with which various preference models predict subjects’ responses to a holdout sample of choice objects. We propose a nonparametric approach for summarizing the accuracy of predicted rankings across a set of holdout-sample options. The methods that we develop contain a novel way to deal with ties and an approach to the different weighting of rank positions.     

海峡两岸土木工程科技名词对照基础研究

海峡两岸土木工程科技名词对照工作是十分必要的。提出了两岸土木工程科技名词对照工作方法与原则,分析了基础对照研究阶段两岸土木工程二级学科分类及名词对应上存在的问题,给出了处理分歧的建议,并对成果的应用和对照的前景做了展望。     

On lattice consensus methods

We investigate the consensus problem for classifications of three types: partitions, dendrograms, and n-trees For partitions or dendrograms, lattice polynomials define natural consensus functions We extend these lattice methods to n-trees, introducing a general class of consensus functions that includes the intersection consensus functions in current use These lattice consensus methods have a number of desirable mathematical properties We prove that they all satisfy the Pareto Axiom For each of the three classification types, we determine which lattice consensus functions satisfy the Betweenness AxiomAuthor partially supported by a research grant from the Faculty Research Committee, Bowling State University     

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.     

美日基础研究成果转移政策浅析

传统认为基础研究的主要目的是发现新现象和新规律以及创造新知识,对基础研究的传统评价主要是看其学术价值。而美国和日本越来越重视基础研究的社会经济价值,基础研究也越来越成为科学技术和产业创新的直接推动力。本文对美国和日本基础研究及成果转移政策进行了介绍和分析,并对我国的基础研究相关政策制定提出了几点建议。     

Using Neural Network Analysis to Define Methods of DINA Model Estimation for Small Sample Sizes

The DINA model is a commonly used model for obtaining diagnostic information. Like many other Diagnostic Classification Models (DCMs), it can require a large sample size to obtain reliable item and examinee parameter estimation. Neural Network (NN) analysis is a classification method that uses a training dataset for calibration. As a result, if this training dataset is determined theoretically, as was the case in Gierl’s attribute hierarchical method (AHM), the NN analysis does not have any sample size requirements. However, a NN approach does not provide traditional item parameters of a DCM or allow for item responses to influence test calibration. In this paper, the NN approach will be implemented for the DINA model estimation to explore its effectiveness as a classification method beyond its use in AHM. The accuracy of the NN approach across different sample sizes, item quality and Q-matrix complexity is described in the DINA model context. Then, a Markov Chain Monte Carlo (MCMC) estimation algorithm and Joint Maximum Likelihood Estimation is used to extend the NN approach so that item parameters associated with the DINA model are obtained while allowing examinee responses to influence the test calibration. The results derived by the NN, the combination of MCMC and NN (NN MCMC) and the combination of JMLE and NN are compared with that of the well-established Hierarchical MCMC procedure and JMLE with a uniform prior on the attribute profile to illustrate their strength and weakness.