Restructuring Sparse High Dimensional Data for Effective Retrieval

The task in text retrieval is to find the subset of a collection of documents relevant to a user's information request, usually expressed as a set of words. Classically, documents and queries are represented as vectors of word counts. In its simplest form, relevance is defined to be the dot product between a document and a query vector--a measure of the number of common terms. A central difficulty in text retrieval is that the presence or absence of a word is not sufficient to determine relevance to a query. Linear dimensionality reduction has been proposed as a technique for extracting underlying structure from the document collection. In some domains (such as vision) dimensionality reduction reduces computational complexity. In text retrieval it is more often used to improve retrieval performance. We propose an alternative and novel technique that produces sparse representations constructed from sets of highly-related words. Documents and queries are represented by their distance to these sets. and relevance is measured by the number of common clusters. This technique significantly improves retrieval performance, is efficient to compute and shares properties with the optimal linear projection operator and the independent components of documents.

Perceptually-based Comparison of Image Similarity Metrics

The image comparison operation ??sessing how well one image matches another ??rms a critical component of many image analysis systems and models of human visual processing. Two norms used commonly for this purpose are L1 and L2, which are specific instances of the Minkowski metric. However, there is often not a principled reason for selecting one norm over the other. One way to address this problem is by examining whether one metric better captures the perceptual notion of image similarity than the other. With this goal, we examined perceptual preferences for images retrieved on the basis of the L1 versus the L2 norm. These images were either small fragments without recognizable content, or larger patterns with recognizable content created via vector quantization. In both conditions the subjects showed a consistent preference for images matched using the L1 metric. These results suggest that, in the domain of natural images of the kind we have used, the L1 metric may better capture human notions of image similarity.