Spatial versus tree representations of proximity data

In this paper we investigated two of the most common representations of proximities, two-dimensional euclidean planes and additive trees. Our purpose was to develop guidelines for comparing these representations, and to discover properties that could help diagnose which representation is more appropriate for a given set of data. In a simulation study, artificial data generated either by a plane or by a tree were scaled using procedures for fitting either a plane (KYST) or a tree (ADDTREE). As expected, the appropriate model fit the data better than the inappropriate model for all noise levels. Furthermore, the two models were roughly comparable: for all noise levels, KYST accounted for plane data about as well as ADDTREE accounted for tree data. Two properties of the data proved useful in distinguishing between the models: the skewness of the distribution of distances, and the proportion of elongated triangles, which measures departures from the ultrametric inequality, Applications of KYST and ADDTREE to some twenty sets of real data, collected by other investigators, showed that most of these data could be classified clearly as favoring either a tree or a two-dimensional representation.A portable PASCAL program implementing the Sattath and Tversky [1977] ADDTREE algorithm is available from J. Corter, Department of Psychology, Stanford University, Stanford, California 94305.     

Note on ultrametric hierarchical clustering algorithms

Milligan presented the conditions that are required for a hierarchical clustering strategy to be monotonic, based on a formula by Lance and Williams. In the present paper, the statement of the conditions is improved and shown to provide necessary and sufficient conditions.This work was supported in part by the Boris Kidri Fund, Yugoslavia.     

关于短时记忆中范畴群集的定位实验

本研究通过对短时记忆的编码或提取阶段进行注意分散来探讨范畴群集的定位问题。以大学生为被试,应用双作业进行分散注意条件下的记忆实验,并与集中注意条件下的记忆实验进行比较。识记材料均为双范畴词表。结果表现无论在编码还是提取阶段分散注意,都导致范畴群集程度的降低。实验结果不支持认为范畴群集的组织过程仅仅发生在记忆信息加工的某一个阶段的看法,而有利于双重定位观点,即认为范畴群集既与编码阶段有关,也与提取阶段有关。     

Mapclus: A mathematical programming approach to fitting the adclus model

We present a new algorithm, MAPCLUS (MAthematicalProgrammingCLUStering), for fitting the Shepard-Arabie ADCLUS (forADditiveCLUStering) model. MAPCLUS utilizes an alternating least squares method combined with a mathematical programming optimization procedure based on a penalty function approach, to impose discrete (0,1) constraints on parameters defining cluster membership. This procedure is supplemented by several other numerical techniques (notably a heuristically based combinatorial optimization procedure) to provide an efficient general-purpose computer implemented algorithm for obtaining ADCLUS representations. MAPCLUS is illustrated with an application to one of the examples given by Shepard and Arabie using the older ADCLUS procedure. The MAPCLUS solution uses half as many clusters to achieve nearly the same level of goodness-of-fit. Finally, we consider an extension of the present approach to fitting a three-way generalization of the ADCLUS model, called INDCLUS (INdividualDifferencesCLUStering).We are indebted to Scott A. Boorman, W. K. Estes, J. A. Hartigan, Lawrence J. Hubert, Carol L. Krumhansl, Joseph B. Kruskal, Sandra Pruzansky, Roger N. Shepard, Edward J. Shoben, Sigfrid D. Soli, and Amos Tversky for helpful discussions of this work, as well as the anonymous referees for their suggestions and corrections on an earlier version of this paper. We are also grateful to Pamela Baker and Dan C. Knutson for technical assistance. The research reported here was supported in part by LEAA Grant 78-NI-AX-0142 and NSF Grants SOC76-24512 and SOC76-24394.     

Cluster differences scaling with a within-clusters loss component and a fuzzy successive approximation strategy to avoid local minima

Cluster differences scaling is a method for partitioning a set of objects into classes and simultaneously finding a low-dimensional spatial representation ofK cluster points, to model a given square table of dissimilarities amongn stimuli or objects. The least squares loss function of cluster differences scaling, originally defined only on the residuals of pairs of objects that are allocated to different clusters, is extended with a loss component for pairs that are allocated to the same cluster. It is shown that this extension makes the method equivalent to multidimensional scaling with cluster constraints on the coordinates. A decomposition of the sum of squared dissimilarities into contributions from several sources of variation is described, including the appropriate degrees of freedom for each source. After developing a convergent algorithm for fitting the cluster differences model, it is argued that the individual objects and the cluster locations can be jointly displayed in a configuration obtained as a by-product of the optimization. Finally, the paper introduces a fuzzy version of the loss function, which can be used in a successive approximation strategy for avoiding local minima. A simulation study demonstrates that this strategy significantly outperforms two other well-known initialization strategies, and that it has a success rate of 92 out of 100 in attaining the global minimum.     

A parametric procedure for ultrametric tree estimation from conditional rank order proximity data

The psychometric and classification literatures have illustrated the fact that a wide class of discrete or network models (e.g., hierarchical or ultrametric trees) for the analysis of ordinal proximity data are plagued by potential degenerate solutions if estimated using traditional nonmetric procedures (i.e., procedures which optimize a STRESS-based criteria of fit and whose solutions are invariant under a monotone transformation of the input data). This paper proposes a new parametric, maximum likelihood based procedure for estimating ultrametric trees for the analysis of conditional rank order proximity data. We present the technical aspects of the model and the estimation algorithm. Some preliminary Monte Carlo results are discussed. A consumer psychology application is provided examining the similarity of fifteen types of snack/breakfast items. Finally, some directions for future research are provided.     

Ordinal network representation: Representing proximities by graphs

Ordinal network representations are graph-theoretic representations of proximity data. They seek to provide parsimonious representations of the ordinal (nonmetric) information in observed proximity data by means of the minimum-path-length distance of a connected and weighted graph. In contrast to traditional tree-based graph-theoretic approaches, ordinal network representation is not limited to but includes the representation by trees. Asymmetry in the proximity data and violations of zero-minimality are allowed for. The paper explores fundamental representation and uniqueness results and discusses a method of constructing ordinal network representations. A simple strategy for handling the problem of errors in the data is described and illustrated.This work was supported by grant Fe 75/20-2 of the Deutsche Forschungsgemeinschaft. The author is indebted to Hubert Feger for many inspiring discussions.     

关于假设-验证和范畴化认知方式与学业不良的相关研究

该研究采用自行设计的能力问卷量表,结合教师问卷、个案访谈和调查等方法对80名小学四年级学生、94名初中一年级学生、85名高中一年级学生,共259名被试进行了假设一验证和范畴化认知方式与学业不良关系的研究。结果表明：各学习年限段学业不良学生在这两方面的得分均低于学业优秀者,且差异显著;各学习年限段学业不良学生间在这两方面的得分差异显著,呈随年龄增长而增长的趋势。     

创造性思维中语义搜索过程：基于答案累积时间函数和语义相似性的量化分析

通过描绘发散性思维测验(物品多用途, AUT)中答案生成在累积函数和语义相似性等一系列参数上的量化特征, 揭示创造性思维的语义搜索过程。结果发现：(1)新颖AUT条件中, 语义搜索呈现与自由联想类似的负加速特点, 但搜索速度较寻常AUT条件更慢。(2)新颖AUT条件中所生成的答案与题目(即物品)均具有较低的语义相似性, 且显著小于寻常AUT条件。(3)新颖AUT条件中生成的答案比寻常AUT条件表现出显著更低的聚类程度, 其中可聚类答案和未聚类答案与题目的语义相似度均较低, 且不存在显著差异, 二者在新颖性上也不存在显著差异。以上结果说明了创造性思维的语义信息搜索过程具有与自由联想类似的激活扩散特征, 但总体搜索速度较慢。新颖性要求使得个体在最初搜索时便开始摆脱题目的语义限制而进行远距离搜索(避免就近搜索), 并倾向于在每个语义场中只生成一个答案(避免局部搜索), 但也可能会在远离题目的语义场中生成多个同类别答案。