Directional clustering through matrix factorization

This paper deals with a clustering problem where feature vectors are clustered depending on the angle between feature vectors, that is, feature vectors are grouped together if they point roughly in the same direction. This directional distance measure arises in several applications, including document classification and human brain imaging. Using ideas from the field of constrained low-rank matrix factorization and sparse approximation, a novel approach is presented that differs from classical clustering methods, such as seminonnegative matrix factorization, K-EVD, or k-means clustering, yet combines some aspects of all these. As in nonnegative matrix factorization and K-EVD, the matrix decomposition is iteratively refined to optimize a data fidelity term; however, no positivity constraint is enforced directly nor do we need to explicitly compute eigenvectors. As in k-means and K-EVD, each optimization step is followed by a hard cluster assignment. This leads to an efficient algorithm that is shown here to outperform common competitors in terms of clustering performance and/or computation speed. In addition to a detailed theoretical analysis of some of the algorithm's main properties, the approach is empirically evaluated on a range of toy problems, several standard text clustering data sets, and a high-dimensional problem in brain imaging, where functional magnetic resonance imaging data are used to partition the human cerebral cortex into distinct functional regions

An Independent Component Analysis Based Tool for Exploring Functional Connections in the Brain

This thesis describes the use of independent component analysis (ICA) as a measure of voxel similarity, which allows the user to find and view statistically independent maps of correlated voxel activity. The tool developed in this work uses a specialized clustering technique, designed to find and characterize clusters of activated voxels, to compare the independent component spatial maps across patients. This same method is also used to compare SPM results across patients

Tripartite Graph Clustering for Dynamic Sentiment Analysis on Social Media

The growing popularity of social media (e.g, Twitter) allows users to easily share information with each other and influence others by expressing their own sentiments on various subjects. In this work, we propose an unsupervised \emph{tri-clustering} framework, which analyzes both user-level and tweet-level sentiments through co-clustering of a tripartite graph. A compelling feature of the proposed framework is that the quality of sentiment clustering of tweets, users, and features can be mutually improved by joint clustering. We further investigate the evolution of user-level sentiments and latent feature vectors in an online framework and devise an efficient online algorithm to sequentially update the clustering of tweets, users and features with newly arrived data. The online framework not only provides better quality of both dynamic user-level and tweet-level sentiment analysis, but also improves the computational and storage efficiency. We verified the effectiveness and efficiency of the proposed approaches on the November 2012 California ballot Twitter data.Comment: A short version is in Proceeding of the 2014 ACM SIGMOD International Conference on Management of dat