Unsupervised classification of categorical time series through innovative distances

[Abstract]: In this paper, two novel distances for nominal time series are introduced. Both of them are based on features describing the serial dependence patterns between each pair of categories. The first dissimilarity employs the so-called association measures, whereas the second computes correlation quantities between indicator processes whose uniqueness is guaranteed from standard stationary conditions. The metrics are used to construct crisp algorithms for clustering categorical series. The approaches are able to group series generated from similar underlying stochastic processes, achieve accurate results with series coming from a broad range of models and are computationally efficient. An extensive simulation study shows that the devised clustering algorithms outperform several alternative procedures proposed in the literature. Specifically, they achieve better results than approaches based on maximum likelihhod estimation, which take advantage of knowing the real underlying procedures. Both innovative dissimilarities could be useful for practitioners in the field of time series clustering

Hard and soft clustering of categorical time series based on two novel distances with an application to biological sequences

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG.[Abstract]: Two novel distances between categorical time series are introduced. Both of them measure discrepancies between extracted features describing the underlying serial dependence patterns. One distance is based on well-known association measures, namely Cramer's v and Cohen's κ. The other one relies on the so-called binarization of a categorical process, which indicates the presence of each category by means of a canonical vector. Binarization is used to construct a set of innovative association measures which allow to identify different types of serial dependence. The metrics are used to perform crisp and fuzzy clustering of nominal series. The proposed approaches are able to group together series generated from similar stochastic processes, achieve accurate results with series coming from a broad range of models and are computationally efficient. Extensive simulation studies show that both hard and soft clustering algorithms outperform several alternative procedures proposed in the literature. Two applications involving biological sequences from different species highlight the usefulness of the introduced techniques.Xunta de Galicia; ED431G 2019/01Xunta de Galicia; ED431C-2020-14The research of Ángel López-Oriona and José A. Vilar has been supported by the Ministerio de Economía y Competitividad (MINECO) grants MTM2017-82724-R and PID2020-113578RB-100, the Xunta de Galicia (Grupos de Referencia Competitiva ED431C-2020-14), and the Centro de Investigación del Sistema Universitario de Galicia “CITIC” grant ED431G 2019/01; all of them through the European Regional Development Fund (ERDF). This work has received funding for open access charge by Universidade da Coruña/CISUG. The author Ángel López-Oriona is very grateful to researcher Maite Freire for her lessons about DNA theory

An Efficient kk-modes Algorithm for Clustering Categorical Datasets

Mining clusters from data is an important endeavor in many applications. The $k$-means method is a popular, efficient, and distribution-free approach for clustering numerical-valued data, but does not apply for categorical-valued observations. The $k$-modes method addresses this lacuna by replacing the Euclidean with the Hamming distance and the means with the modes in the $k$-means objective function. We provide a novel, computationally efficient implementation of $k$-modes, called OTQT. We prove that OTQT finds updates to improve the objective function that are undetectable to existing $k$-modes algorithms. Although slightly slower per iteration due to algorithmic complexity, OTQT is always more accurate per iteration and almost always faster (and only barely slower on some datasets) to the final optimum. Thus, we recommend OTQT as the preferred, default algorithm for $k$-modes optimization.Comment: 16 pages, 10 figures, 5 table