Clustering categorical sequences is an important and difficult data mining task. Despite recent efforts, the challenge remains, due to the lack of an inherently meaningful measure of pairwise similarity. In this paper, we propose a novel variable-order Markov framework, named weighted conditional probability distribution (WCPD), to model clusters of categorical sequences. We propose an efficient and effective approach to solve the challenging problem of model initialization. To initialize the WCPD model, we propose to use a first-order Markov model built on a weighted fuzzy indicator vector representation of categorical sequences, which we call the WFI Markov model. Based on a cascade optimization framework that combines the WCPD and WFI models, we design a new divisive hierarchical clustering algorithm for clustering categorical sequences. Experimental results on data sets from three different domains demonstrate the promising performance of our models and clustering algorithm.

Recommender systems are becoming a widespread technology used to promote cross-selling. Collaborative filtering is one of the main paradigms employed to offer recommendations to users. However, while most collaborative filtering methods require explicit user feedback, such as ratings, it is a well-established fact that users rate only a small portion of all available products. Subsequently, the rating system often acquires insufficient explicit feedback, thus leading to unsatisfactory recommendations. We propose a novel approach in the implicit feedback recommender system domain that combines clustering and matrix factorization to yield good results while using only implicit feedback on users purchase history and without requiring any parameter. We use a high-dimensional, parameter-free, divisive hierarchical clustering technique and, based on the clustering results, create personalized recommendations of high interest for each user. This easy to implement and very effective technique can be applied to any data sets where we can identify users with a purchase history.

Clustering categorical sequences remains an open and challenging task due to the lack of an inherently meaningful measure of pair wise similarity between sequences. Model initialization is an unsolved problem in model-based clustering algorithms for categorical sequences. In this paper, we propose a simple and effective Markov model to approximate the conditional probability distribution (CPD) model, and use it to design a novel two-tier Markov model to represent a sequence cluster. Furthermore, we design a novel divisive hierarchical algorithm for clustering categorical sequences based on the two-tier Markov model. The experimental results on the data sets from three different domains demonstrate the promising performance of our models and clustering algorithm.

Clustering categorical data faces two challenges, one is lacking of inherent similarity measure, and the other is that the clusters are prone to being embedded in different subspace. In this paper, we propose the first divisive hierarchical clustering algorithm for categorical data. The algorithm, which is based on multiple correspondence analysis (MCA), is systematic, efficient and effective. In our algorithm, MCA plays an important role in analyzing the data globally. The proposed algorithm has five merits. First, our algorithm yields a dendrogram representing nested groupings of patterns and similarity levels at different granularities. Second, it is parameter-free, fully automatic and, most importantly, requires no assumption regarding the number of clusters. Third, it is independent of the order in which the data are processed. Forth, it is scalable to large data sets; and finally, using the novel data representation and Chi-square distance measures makes our algorithm capable of seamlessly discovering the clusters embedded in the subspaces. Experiments on both synthetic and real data demonstrate the superior performance of our algorithm.