Atsuho Nakayama

Reconstructing One-Mode Three-way Asymmetric Data for Multidimensional Scaling

Some models have been proposed to analyze one-mode three-way data [e.g. De Rooij and Gower (J Classification 20:181–220, 2003), De Rooij and Heiser (Br J Math Stat Psychol 53:99–119, 2000)]. These models usually assume triadic symmetric relationships. Therefore, it is general to transform asymmetric data into symmetric proximity data when one-mode three-way asymmetric proximity data are analyzed using multidimensional scaling. However, valuable information among objects is lost by symmetrizing asymmetric proximity data. It is necessary to devise this transformation so that valuable information among objects is not lost. In one-mode two-way asymmetric data, a method that the overall sum of the rows and columns are equal was proposed by Harshman et al. (Market Sci 1:205–242, 1982). Their method is effective to analyze the data that have differences among the overall sum of the rows and columns caused by external factors. Therefore, the present study proposes a method that extends (Harshman et al., Market Sci 1:205–242, 1982) method to one-mode three-way asymmetric proximity data. The proposed method reconstructs one-mode three-way asymmetric data so that the overall sum of the rows, columns and depths is made equal.

The Classification and Visualization of Twitter Trending Topics Considering Time Series Variation

This study attempted to detect trending topics and temporal variation in web communication topics regarding new products among consumers using social media. This was done by classifying words into clusters based on their co-occurrence. We collected Twitter entries about new products based on their specific expressions of sentiment or interest. Because of the desire to identify market trends, the analysis of consumer tweet data has received much attention. To construct appropriate words, we used a complementary similarity measure, a classification method that is widely applied in character recognition. We classified the words extracted from Twitter data using non-negative matrix factorization as a dimensionality reduction model. To help interpret the results, we proposed a visualization method for text classification using a multidimensional scaling model.

An Application of One-mode Three-way Overlapping Cluster Analysis

In recent years, it is possible to more easily obtain multi-way data, and various analysis models for the data have been suggested by several researchers. However, only small number of studies have been done on the one-mode multi-way data analysis model. The authors suggested an overlapping cluster analysis model for one-mode three-way similarity data in our earlier study. In the present study, the authors make an attempt to improve the one of problems of the algorithm and validate the improved algorithm by analyzing the one-mode three-way similarity data which calculated from the panel data of meals. Then, the one-mode three-way result is compared with the results with the one-mode two-way similarity data analysis to show the usefulness of the one-mode three-way similarity data analysis.

Evaluating the Necessity of a Triadic Distance Model

Various studies have examined multi-way proximity generalizations of multidimensional scaling (MDS). Some of these have proposed one-mode three-way proximity data analyses to investigate triadic relationships among three objects. However, the results of a triadic distance model are generally similar to those of a one-mode two-way MDS. Moreover, no technique for judging whether a triadic distance model or one-mode two-way MDS is more appropriate has been developed. Thus, it would be valuable to establish a technique for examining the need for a one-mode three-way MDS analysis. Here, we propose a technique to evaluate the need for a triadic distance model using a log-linear model. When the analysis of the log-linear model shows that three objects, i, j, and k, are not independent, the one-mode three-way proximity data should be analyzed with a triadic distance model. However, one-mode three-way proximity data should not be analyzed with a triadic distance model when the analysis of the log-linear model shows that the three objects i, j, and k are independent.

Analysis of Conditional and Marginal Association in One-Mode Three-Way Proximity Data

The purpose of this study was to examine the necessity for one-mode three-way multidimensional scaling analysis. In many cases, the results of the analysis of one-mode three-way multidimensional scaling are similar to those of one-mode two-way multidimensional scaling for lower dimensions, and, in fact, multidimensional scaling can be used for low dimensional analysis. Our results demonstrated that at lower dimensionality, triadic relationships represented by the results of one-mode three-way multidimensional scaling were almost consistent with the dyadic relationships derived from one-mode two-way multidimensional scaling. However, triadic relationships differ from dyadic relationships in analyses of higher dimensionality. The degree of coincidence obtained for one-mode three- and two-way multidimensional scaling revealed that triadic relationships can only be represented by one-mode three-way multidimensional scaling; specifically, triadic relationships based on conditional associations must be separately explained in terms of marginal associations for higher dimensionality analysis.

A Symmetry Test for One-Mode Three-Way Proximity Data

Recently, several major advances in models of asymmetric proximity data analysis have occurred. These models usually do not deal with the relationships among three or more objects, but instead, those between two objects. However, there exist some approaches for analyzing one-mode three-way asymmetric proximity data that represent triadic relationships among three objects. Nonetheless, a method that evaluates the asymmetry of one-mode three-way asymmetric proximity data has not yet been proposed. There is no measure for judging the necessity of a symmetric model, reconstructed method, or asymmetric model analysis. The present study proposes a method that evaluates the asymmetry of one-mode three-way proximity data. In a square contingency table, a symmetry test is studied to check whether the data are symmetric. We propose a method that extends this symmetry test for square contingency tables to one-mode three-way proximity data.

Analysis of Purchase Intentions at a Department Store by Three-Way Distance Model

This study focused on analyzing the reasons for purchase of ladies’ goods. The analysis used the three-way distance model. The model explains threeway distances as the subtraction of the smallest squared distance among the three squared distances from the sum of these squared distances. The formulation is used to illustrate the idea that relationships with many differences carry more information than relationships with few differences.