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

Semantic Retrieval and Automatic Annotation: Linear Transformations, Correlation and Semantic Spaces

This paper proposes a new technique for auto-annotation and semantic retrieval based upon the idea of linearly mapping an image feature space to a keyword space. The new technique is compared to several related techniques, and a number of salient points about each of the techniques are discussed and contrasted. The paper also discusses how these techniques might actually scale to a real-world retrieval problem, and demonstrates this though a case study of a semantic retrieval technique being used on a real-world data-set (with a mix of annotated and unannotated images) from a picture library