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     

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     

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.     

Statistical properties of large published classifications

Large published classifications typically consist of sets (called taxa) hierarchically arranged according to taxonomic rank. A statistical survey of 23 such classification reveals the following distinctive properties. The pattern of mandatory and optional taxonomic ranks is similar to a Guttman scale. Mean taxon size (defined as the number of next-lower-rank taxa per higher-rank taxon) is a U-shaped function of mandatory rank, and averages about seven across ranks with no significant differences between classifications. The variability of taxon size is a decreasing function of mandatory rank. The generality of these properties across classifications suggests that they are determined by the psychology of the classification process. In contrast, there are significant differences between classifications in the variability of taxon size and in the prevalence of optional ranks, both of which are greater in biological than in nonbiological classifications. These differences may reflect the nature of the materials classified. This research was supported by a research grant from the UCLA Academic Senate and by computer time from the UCLA Office of Academic Computing.     

N-trees as nestings: Complexity,similarity, and consensus

Interpreting a taxonomic tree as a set of objects leads to natural measures of complexity and similarity, and sets natural lower bounds on a consensus tree Interpretations differing as to the kind of objects constituting a tree lead to different measures and consensus Subset nesting is preferred over the clusters (strict consensus) and even the triads interpretations because of its superior expression of shared structure Algorithms for computing the complexity and similarity of trees, as well as a consensus index onto [0,1], are presented for this interpretation The full consensus is defined as the only tree which includes all the nestings shared in a profile of rival trees and whose clusters reflect only nestings shared in the profile The full consensus is proved to exist uniquely for each profile, and to equal the Adams consensusThe author is grateful for the many helpful comments on presentation from Frances McA Adams, William H E Day, and Christopher A Meacham     

Clustering and isolation in the consensus problem for partitions

We examine the problem of aggregating several partitions of a finite set into a single consensus partition We note that the dual concepts of clustering and isolation are especially significant in this connection. The hypothesis that a consensus partition should respect unanimity with respect to either concept leads us to stress a consensus interval rather than a single partition. The extremes of this interval are characterized axiomatically. If a sufficient totality of traits has been measured, and if measurement errors are independent, then a true classifying partition can be expected to lie in the consensus interval. The structure of the partitions in the interval lends itself to partial solutions of the consensus problem Conditional entropy may be used to quantify the uncertainty inherent in the interval as a whole     

理想与现实：可持续发展观分类与比较

与传统意义的发展相比,可持续发展有着深刻的哲理和丰富的内涵。 中外学者对此确有颇多深入的乃至精辟的论述。文章通过分类比较认为,可持续发展无疑是人类的一种崇高的理想,它可以通过理论研究上的有序突破、行为模式上的有机变革和战略实施上的有效执行逐步实现。同时作者也特别注意到可持续发展在现实操作上的难度,即理想与现实之间存在颇大距离,其实施可谓任重而道远。     

科学革命的本质:科恩与库恩的比较

库恩与科恩都分析了科学中的革命的重要地位和作用,肯定了科学革命存在的必要性和必然性。但是,两人在对科学革命本质的理解上又有着明显的区别：库恩着重剖析了科学革命的结构,将科学革命的发生归缘于科学中的危机,并以范式是否转换来判别科学革命是否发生;科恩则从历史的角度考察科学革命,认为引发科学革命的因素是多样的,而对科学革命的检验必须以历史证据为依据,并因此提出了四项检验标准。库恩和科恩的科学革命观有助于我们理解科学革命的本质,对反思科学探索活动也有较大的启示。     

Fixed Point Clusters for Linear Regression: Computation and Comparison

In this paper an algorithm is developed, which aims to find all FPCs of a dataset corresponding to well separated linear regression subpopulations. Its ability to find such subpopulations under the occurence of outliers is compared to methods based on ML-estimation of mixture models by means of a simulation study. Furthermore, FPC analysis is applied to a real dataset.     

创新与创造之异同

探讨了创新与创造概念之间的异同。认为创新与创造虽然都具有新颖性这一共性,但它们之间仍有一定的区别,即创新概念的外延比创造要小。从学术上讲,人们不应该误把创新等同于创造,更不应该不顾其原始含义,完全用创新去取代创造。     

创新与创造之异同

探讨了创新与创造概念之间的异同。认为创新与创造虽然都具有新颖性这一共性,但它们之间仍有一定的区别,即创新概念的外延比创造要小。从学术上讲,人们不应该误把创新等同于创造,更不应该不顾其原始含义,完全用创新去取代创造。     

政府特许经营与商业特许经营含义辨析

在中国,对于franchise和concession这两个英文单词的具体含义一直没有给出明确的区分,普遍含混地统译为"特许经营".而且,在不同的应用场合经常将这两个概念混用.然而实际上,它们的经济学含义是有区别的.     

从构成到生成——历史与科学的一个比较

历史学与（自然）科学分属不同领域。其研究对象和研究方法以及知识形态都有重大的差异。本文试图以一种新的描述方式对历史和科学的进行比较,发掘二者可能的同构。     

Additive Biclustering: A Comparison of One New and Two Existing ALS Algorithms

The additive biclustering model for two-way two-mode object by variable data implies overlapping clusterings of both the objects and the variables together with a weight for each bicluster (i.e., a pair of an object and a variable cluster). In the data analysis, an additive biclustering model is fitted to given data by means of minimizing a least squares loss function. To this end, two alternating least squares algorithms (ALS) may be used: (1) PENCLUS, and (2) Baier’s ALS approach. However, both algorithms suffer from some inherent limitations, which may hamper their performance. As a way out, based on theoretical results regarding optimally designing ALS algorithms, in this paper a new ALS algorithm will be presented. In a simulation study this algorithm will be shown to outperform the existing ALS approaches.     

Comparison tests for dendrograms: A comparative evaluation

Classifications are generally pictured in the form of hierarchical trees, also called dendrograms. A dendrogram is the graphical representation of an ultrametric (=cophenetic) matrix; so dendrograms can be compared to one another by comparing their cophenetic matrices. Three methods used in testing the correlation between matrices corresponding to dendrograms are evaluated. The three permutational procedures make use of different aspects of the information to compare dendrograms: the Mantel procedure permutes label positions only; the binary tree methods randomize the topology as well; the double-permutation procedure is based on all the information included in a dendrogram, that is: topology, label positions, and cluster heights. Theoretical and empirical investigations of these methods are carried out to evaluate their relative performance. Simulations show that the Mantel test is too conservative when applied to the comparison of dendrograms; the methods of binary tree comparisons do slightly better; only the doublepermutation test provides unbiased type I error. Les arbres utilisés pour illustrés les groupements sont généralement représentés sous la forme de classifications hiérarchiques ou dendrogrammes. Un dendrogramme représente graphiquement l’information contenue dans la matrice ultramétrique (=cophénétique) correspondant à la classification. Dès ultramétriques correspondantes. Nous comparons trois méthodes permettant d’évaluer la signification statistique du coefficient de correlation mesuré entre deux matrices ultramétriques. Ces trois tests par permutations tiennent compte d’aspects différents pour comparer des dendrogrammes: le test de Mantel permute les feuilles de l’arbre, les méthodes pour arbres binaires permutent les feuilles et la topologie, alors que la procédure à double permutation permute les feuilles, la topologie et les niveaux de fusion des dendrogrammes comparés. L’efficacité relative des trois méthodes est évaluée empiriquement et théoriquement. Nos résultats suggèrent l’utilisation préférentielle du test à double permutation pour la comparaison de dendrogrammes: le test de Mantel s’avère trop conservateur, tandis que les méthodes pour arbres binaires ne sont pas toujours adéquates.

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This work was supported by NSERC grant no. A7738 to Pierre Legendre and by a NSERC scholarship to F.-J. Lapointe.     

隐喻与意向性立场——论塞尔对隐喻比较主义的批判

塞尔在对隐喻的比较主义批判的基础上,提出了隐喻性解释的三个步骤和八项原则,以建立一个完备的隐喻理论。但是塞尔重复了布莱克的一些错误,对比较主义的核心论题存在两个方面的误解,他所建立的隐喻解释原则过于宽泛,最后无法避免将隐喻打回术语学解释范围。为了避免把对隐喻的解释仅仅归纳入术语学的范围,文末在分析塞尔关于隐喻的两大反驳论证的基础上,来理清其隐喻理论的核心和缺陷,引入镜像神经元概念来为隐喻的研究提供反驳的基础,并引证来自心理学研究和神经科学研究的其他证据提供支持。