Dimensionality Reduction Techniques for Proximity Problems Piotr Indyk Stanford University

Better Algorithms for High-dimensional Proximity Problems via Asymmetri Embeddings

Compressive Image Feature Extraction by Means of Folding

We explore the utility of a dimensionality reducing process we term folding for the purposes of image feature extraction. We seek to discover whether image features are preserved under this process and how to efficiently extract them. The application is in size weight and power constrained imaging scenarios where an efficient implementation of this dimensionality reduction can save power and co...

Scalable Techniques for Clustering the Web

Clustering is one of the most crucial techniques for dealing with the massive amount of information present on the web. Clustering can either be performed once offline, independent of search queries, or performed online on the results of search queries. Our offline approach aims to efficiently cluster similar pages on the web, using the technique of Locality-Sensitive Hashing (LSH), in which we...

Near-Optimal (Euclidean) Metric Compression

The metric sketching problem is defined as follows. Given a metric on n points, and > 0, we wish to produce a small size data structure (sketch) that, given any pair of point indices, recovers the distance between the points up to a 1 + distortion. In this paper we consider metrics induced by `2 and `1 norms whose spread (the ratio of the diameter to the closest pair distance) is bounded by Φ >...

Dimension Reduction in Kernel Spaces from Locality-Sensitive Hashing

We provide novel methods for efficient dimensionality reduction in kernel spaces. That is, we provide efficient and explicit randomized maps from “data spaces” into “kernel spaces” of low dimension, which approximately preserve the original kernel values. The constructions are based on observing that such maps can be obtained from Locality-Sensitive Hash (LSH) functions, a primitive developed f...