Clustering of categorical variables around latent variables

In the framework of clustering, the usual aim is to cluster observations and not variables. However the issue of variable clustering clearly appears for dimension reduction, selection of variables or in some case studies (sensory analysis, biochemistry, marketing, etc.). Clustering of variables is then studied as a way to arrange variables into homogeneous clusters, thereby organizing data into meaningful structures. Once the variables are clustered into groups such that variables are similar to the other variables belonging to their cluster, the selection of a subset of variables is possible. Several specific methods have been developed for the clustering of numerical variables. However concerning categorical variables, much less methods have been proposed. In this paper we extend the criterion used by Vigneau and Qannari (2003) in their Clustering around Latent Variables approach for numerical variables to the case of categorical data. The homogeneity criterion of a cluster of categorical variables is defined as the sum of the correlation ratio between the categorical variables and a latent variable, which is in this case a numerical variable. We show that the latent variable maximizing the homogeneity of a cluster can be obtained with Multiple Correspondence Analysis. Different algorithms for the clustering of categorical variables are proposed: iterative relocation algorithm, ascendant and divisive hierarchical clustering. The proposed methodology is illustrated by a real data application to satisfaction of pleasure craft operators.clustering of categorical variables, correlation ratio, iterative relocation algorithm, hierarchical clustering

Stability of graph communities across time scales

The complexity of biological, social and engineering networks makes it desirable to find natural partitions into communities that can act as simplified descriptions and provide insight into the structure and function of the overall system. Although community detection methods abound, there is a lack of consensus on how to quantify and rank the quality of partitions. We show here that the quality of a partition can be measured in terms of its stability, defined in terms of the clustered autocovariance of a Markov process taking place on the graph. Because the stability has an intrinsic dependence on time scales of the graph, it allows us to compare and rank partitions at each time and also to establish the time spans over which partitions are optimal. Hence the Markov time acts effectively as an intrinsic resolution parameter that establishes a hierarchy of increasingly coarser clusterings. Within our framework we can then provide a unifying view of several standard partitioning measures: modularity and normalized cut size can be interpreted as one-step time measures, whereas Fiedler's spectral clustering emerges at long times. We apply our method to characterize the relevance and persistence of partitions over time for constructive and real networks, including hierarchical graphs and social networks. We also obtain reduced descriptions for atomic level protein structures over different time scales.Comment: submitted; updated bibliography from v

Methods of Hierarchical Clustering

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm.Comment: 21 pages, 2 figures, 1 table, 69 reference

Estimation of instrinsic dimension via clustering

The problem of estimating the intrinsic dimension of a set of points in high dimensional space is a critical issue for a wide range of disciplines, including genomics, finance, and networking. Current estimation techniques are dependent on either the ambient or intrinsic dimension in terms of computational complexity, which may cause these methods to become intractable for large data sets. In this paper, we present a clustering-based methodology that exploits the inherent self-similarity of data to efficiently estimate the intrinsic dimension of a set of points. When the data satisfies a specified general clustering condition, we prove that the estimated dimension approaches the true Hausdorff dimension. Experiments show that the clustering-based approach allows for more efficient and accurate intrinsic dimension estimation compared with all prior techniques, even when the data does not conform to obvious self-similarity structure. Finally, we present empirical results which show the clustering-based estimation allows for a natural partitioning of the data points that lie on separate manifolds of varying intrinsic dimension

Development of a R package to facilitate the learning of clustering techniques

This project explores the development of a tool, in the form of a R package, to ease the process of learning clustering techniques, how they work and what their pros and cons are. This tool should provide implementations for several different clustering techniques with explanations in order to allow the student to get familiar with the characteristics of each algorithm by testing them against several different datasets while deepening their understanding of them through the explanations. Additionally, these explanations should adapt to the input data, making the tool not only adept for self-regulated learning but for teaching too.Grado en Ingeniería Informátic