A Study of Application Cosine Similarity and HOSVD for Questionnaire Data

Companies often carry out questionnaires, in order to gain a better grasp of consumer trends for the design of marketing strategies. The proper definition of a set of questions presents some difficulties. For example, if respondents take the meaning of two or more questions in one questionnaire to have the same/similar meanings, these questions could be rendered redundant. However, it is difficult to know beforehand how a respondent will interpret the meaning of a question. On the other hand, it is possible to assess the meaning that respondents assumed for questions, and how appropriate the set of questions is, in retrospect. In this paper, we propose a method for visualizing groups of respondents who assumed distinct meanings for questions, by applying Higher Order Singular Value Decomposition (HOSVD) to a tensor consisting of cosine similarity matrices. The proposed method is applied to a Web questionnaire dataset, and it is shown that the new method can identify the respondents’ unique understanding of the meanings of questions, which are not found using the conventional method. We also show that the proposedmethod is the most effective for the visualization of relationships between questions, among the possible ways of applying HOSVD to cosine similarity matrices.