Piotr Indyk

Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions

We present an algorithm for the c-approximate nearest neighbor problem in a d-dimensional Euclidean space, achieving query time of O(dn 1c2/+o(1)) and space O(dn + n1+1c2/+o(1)). This almost matches the lower bound for hashing-based algorithm recently obtained in (R. Motwani et al., 2006). We also obtain a space-efficient version of the algorithm, which uses dn+n logO(1) n space, with a query time of dnO(1/c2). Finally, we discuss practical variants of the algorithms that utilize fast bounded-distance decoders for the Leech lattice

Enhanced hypertext categorization using hyperlinks

A major challenge in indexing unstructured hypertext databases is to automatically extract meta-data that enables structured search using topic taxonomies, circumvents keyword ambiguity, and improves the quality of search and profile-based routing and filtering. Therefore, an accurate classifier is an essential component of a hypertext database. Hyperlinks pose new problems not addressed in the extensive text classification literature. Links clearly contain high-quality semantic clues that are lost upon a purely term-based classifier, but exploiting link information is non-trivial because it is noisy. Naive use of terms in the link neighborhood of a document can even degrade accuracy. Our contribution is to propose robust statistical models and a relaxation labeling technique for better classification by exploiting link information in a small neighborhood around documents. Our technique also adapts gracefully to the fraction of neighboring documents having known topics. We experimented with pre-classified samples from Yahoo!1 and the US Patent Database2. In previous work, we developed a text classifier that misclassified only 13% of the documents in the well-known Reuters benchmark; this was comparable to the best results ever obtained. This classifier misclassified 36% of the patents, indicating that classifying hypertext can be more difficult than classifying text. Naively using terms in neighboring documents increased error to 38%; our hypertext classifier reduced it to 21%. Results with the Yahoo! sample were more dramatic: the text classifier showed 68% error, whereas our hypertext classifier reduced this to only 21%.

Maintaining Stream Statistics over Sliding Windows

We consider the problem of maintaining aggregates and statistics over data streams, with respect to the last N data elements seen so far. We refer to this model as the sliding window model. We consider the following basic problem: Given a stream of bits, maintain a count of the number of 1s in the last N elements seen from the stream. We show that, using

Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions

O(\frac{1}{\epsilon} \log^2 N)

Stable distributions, pseudorandom generators, embeddings, and data stream computation

bits of memory, we can estimate the number of 1s to within a factor of

Combining geometry and combinatorics: A unified approach to sparse signal recovery

1 + \epsilon

Approximate clustering via core-sets

. We also give a matching lower bound of

Sparse Recovery Using Sparse Matrices

\Omega(\frac{1}{\epsilon}\log^2 N)

Algorithmic applications of low-distortion geometric embeddings

memory bits for any deterministic or randomized algorithms. We extend our scheme to maintain the sum of the last N positive integers and provide matching upper and lower bounds for this more general problem as well. We also show how to efficiently compute the Lp norms (

Near-optimal sparse fourier representations via sampling

p \in [1,2]