Moses Charikar

Bio: Moses Charikar is an academic researcher from Stanford University. The author has contributed to research in topics: Approximation algorithm & Upper and lower bounds. The author has an hindex of 64, co-authored 218 publications receiving 19458 citations. Previous affiliations of Moses Charikar include EMC Corporation & Google.

Similarity estimation techniques from rounding algorithms

Abstract: (MATH) A locality sensitive hashing scheme is a distribution on a family $\F$ of hash functions operating on a collection of objects, such that for two objects x,y, PrheF[h(x) = h(y)] = sim(x,y), where sim(x,y) e [0,1] is some similarity function defined on the collection of objects. Such a scheme leads to a compact representation of objects so that similarity of objects can be estimated from their compact sketches, and also leads to efficient algorithms for approximate nearest neighbor search and clustering. Min-wise independent permutations provide an elegant construction of such a locality sensitive hashing scheme for a collection of subsets with the set similarity measure sim(A,B) = \frac{|A ∩ B|}{|A ∪ B|}.(MATH) We show that rounding algorithms for LPs and SDPs used in the context of approximation algorithms can be viewed as locality sensitive hashing schemes for several interesting collections of objects. Based on this insight, we construct new locality sensitive hashing schemes for:A collection of vectors with the distance between → \over u and → \over v measured by O(→ \over u, → \over v)/π, where O(→ \over u, → \over v) is the angle between → \over u) and → \over v). This yields a sketching scheme for estimating the cosine similarity measure between two vectors, as well as a simple alternative to minwise independent permutations for estimating set similarity.A collection of distributions on n points in a metric space, with distance between distributions measured by the Earth Mover Distance (EMD), (a popular distance measure in graphics and vision). Our hash functions map distributions to points in the metric space such that, for distributions P and Q, EMD(P,Q) ≤ Ehe\F [d(h(P),h(Q))] ≤ O(log n log log n). EMD(P, Q).

Finding Frequent Items in Data Streams

Abstract: We present a 1-pass algorithm for estimating the most frequent items in a data stream using limited storage space. Our method relies on a data structure called a COUNT SKETCH, which allows us to reliably estimate the frequencies of frequent items in the stream. Our algorithm achieves better space bounds than the previously known best algorithms for this problem for several natural distributions on the item frequencies. In addition, our algorithm leads directly to a 2-pass algorithm for the problem of estimating the items with the largest (absolute) change in frequency between two data streams. To our knowledge, this latter problem has not been previously studied in the literature.

Min-Wise Independent Permutations

Abstract: We define and study the notion of min-wise independent families of permutations. We say that F?Sn (the symmetric group) is min-wise independent if for any set X?n and any x?X, when ? is chosen at random in F we havePr(min{?(X)}=?(x))=1|X| . In other words we require that all the elements of any fixed set X have an equal chance to become the minimum element of the image of X under ?. Our research was motivated by the fact that such a family (under some relaxations) is essential to the algorithm used in practice by the AltaVista web index software to detect and filter near-duplicate documents. However, in the course of our investigation we have discovered interesting and challenging theoretical questions related to this concept?we present the solutions to some of them and we list the rest as open problems.

Multi-probe LSH: efficient indexing for high-dimensional similarity search

Abstract: Similarity indices for high-dimensional data are very desirable for building content-based search systems for feature-rich data such as audio, images, videos, and other sensor data. Recently, locality sensitive hashing (LSH) and its variations have been proposed as indexing techniques for approximate similarity search. A significant drawback of these approaches is the requirement for a large number of hash tables in order to achieve good search quality. This paper proposes a new indexing scheme called multi-probe LSH that overcomes this drawback. Multi-probe LSH is built on the well-known LSH technique, but it intelligently probes multiple buckets that are likely to contain query results in a hash table. Our method is inspired by and improves upon recent theoretical work on entropy-based LSH designed to reduce the space requirement of the basic LSH method. We have implemented the multi-probe LSH method and evaluated the implementation with two different high-dimensional datasets. Our evaluation shows that the multi-probe LSH method substantially improves upon previously proposed methods in both space and time efficiency. To achieve the same search quality, multi-probe LSH has a similar time-efficiency as the basic LSH method while reducing the number of hash tables by an order of magnitude. In comparison with the entropy-based LSH method, to achieve the same search quality, multi-probe LSH uses less query time and 5 to 8 times fewer number of hash tables.

Aggregating inconsistent information: Ranking and clustering

Abstract: We address optimization problems in which we are given contradictory pieces of input information and the goal is to find a globally consistent solution that minimizes the extent of disagreement with the respective inputs. Specifically, the problems we address are rank aggregation, the feedback arc set problem on tournaments, and correlation and consensus clustering. We show that for all these problems (and various weighted versions of them), we can obtain improved approximation factors using essentially the same remarkably simple algorithm. Additionally, we almost settle a long-standing conjecture of Bang-Jensen and Thomassen and show that unless NP⊆BPP, there is no polynomial time algorithm for the problem of minimum feedback arc set in tournaments.

ORB: An efficient alternative to SIFT or SURF

Abstract: Feature matching is at the base of many computer vision problems, such as object recognition or structure from motion. Current methods rely on costly descriptors for detection and matching. In this paper, we propose a very fast binary descriptor based on BRIEF, called ORB, which is rotation invariant and resistant to noise. We demonstrate through experiments how ORB is at two orders of magnitude faster than SIFT, while performing as well in many situations. The efficiency is tested on several real-world applications, including object detection and patch-tracking on a smart phone.

k-means++: the advantages of careful seeding

Abstract: The k-means method is a widely used clustering technique that seeks to minimize the average squared distance between points in the same cluster. Although it offers no accuracy guarantees, its simplicity and speed are very appealing in practice. By augmenting k-means with a very simple, randomized seeding technique, we obtain an algorithm that is Θ(logk)-competitive with the optimal clustering. Preliminary experiments show that our augmentation improves both the speed and the accuracy of k-means, often quite dramatically.

Clustering by Passing Messages Between Data Points

Abstract: Clustering data by identifying a subset of representative examples is important for processing sensory signals and detecting patterns in data. Such "exemplars" can be found by randomly choosing an initial subset of data points and then iteratively refining it, but this works well only if that initial choice is close to a good solution. We devised a method called "affinity propagation," which takes as input measures of similarity between pairs of data points. Real-valued messages are exchanged between data points until a high-quality set of exemplars and corresponding clusters gradually emerges. We used affinity propagation to cluster images of faces, detect genes in microarray data, identify representative sentences in this manuscript, and identify cities that are efficiently accessed by airline travel. Affinity propagation found clusters with much lower error than other methods, and it did so in less than one-hundredth the amount of time.

Canu: scalable and accurate long-read assembly via adaptive k-mer weighting and repeat separation.

Abstract: Long-read single-molecule sequencing has revolutionized de novo genome assembly and enabled the automated reconstruction of reference-quality genomes. However, given the relatively high error rates of such technologies, efficient and accurate assembly of large repeats and closely related haplotypes remains challenging. We address these issues with Canu, a successor of Celera Assembler that is specifically designed for noisy single-molecule sequences. Canu introduces support for nanopore sequencing, halves depth-of-coverage requirements, and improves assembly continuity while simultaneously reducing runtime by an order of magnitude on large genomes versus Celera Assembler 8.2. These advances result from new overlapping and assembly algorithms, including an adaptive overlapping strategy based on tf-idf weighted MinHash and a sparse assembly graph construction that avoids collapsing diverged repeats and haplotypes. We demonstrate that Canu can reliably assemble complete microbial genomes and near-complete eukaryotic chromosomes using either Pacific Biosciences (PacBio) or Oxford Nanopore technologies and achieves a contig NG50 of >21 Mbp on both human and Drosophila melanogaster PacBio data sets. For assembly structures that cannot be linearly represented, Canu provides graph-based assembly outputs in graphical fragment assembly (GFA) format for analysis or integration with complementary phasing and scaffolding techniques. The combination of such highly resolved assembly graphs with long-range scaffolding information promises the complete and automated assembly of complex genomes.

The PARSEC benchmark suite: characterization and architectural implications

Abstract: This paper presents and characterizes the Princeton Application Repository for Shared-Memory Computers (PARSEC), a benchmark suite for studies of Chip-Multiprocessors (CMPs). Previous available benchmarks for multiprocessors have focused on high-performance computing applications and used a limited number of synchronization methods. PARSEC includes emerging applications in recognition, mining and synthesis (RMS) as well as systems applications which mimic large-scale multithreaded commercial programs. Our characterization shows that the benchmark suite covers a wide spectrum of working sets, locality, data sharing, synchronization and off-chip traffic. The benchmark suite has been made available to the public.