Entropy-scaling search of massive biological data

Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing a dataset's entropy and fractal dimension. We prove that searching scales in time with metric entropy (number of covering hyperspheres), if the fractal dimension of the dataset is low, and scales in space with the sum of metric entropy and information-theoretic entropy (randomness of the data). Using these ideas, we present accelerated versions of standard tools, with no loss in specificity and little loss in sensitivity, for use in three domains---high-throughput drug screening (Ammolite, 150x speedup), metagenomics (MICA, 3.5x speedup of DIAMOND [3,700x BLASTX]), and protein structure search (esFragBag, 10x speedup of FragBag). Our framework can be used to achieve "compressive omics," and the general theory can be readily applied to data science problems outside of biology.Comment: Including supplement: 41 pages, 6 figures, 4 tables, 1 bo

2-Dimensional String Problems: Data Structures and Quantum Algorithms

The field of stringology studies algorithms and data structures used for processing strings efficiently. The goal of this thesis is to investigate 2-dimensional (2D) variants of some fundamental string problems, including \textit{Exact Pattern Matching} and \textit{Longest Common Substring}. In the 2D pattern matching problem, we are given a matrix \M[1\dd n,1\dd n] that consists of $N = n \times n$ symbols drawn from an alphabet $\Sigma$ of size $\sigma$. The query consists of a $m \times m$ square matrix \PP[1\dd m, 1\dd m] drawn from the same alphabet, and the task is to find all the locations of \PP in \M. For such square patterns, data structures such as suffix trees and suffix arrays exist for the task of efficient pattern matching. However, a suffix tree occupies $O(N \log N)$ bits, which is significantly more than that of the original text\u27s size of $N\log \sigma$ bits. Therefore, the design of compressed data structures, that supports pattern matching queries efficiently and occupies space close to the original text\u27s size, is imperative. In this thesis, we show an interesting result by designing a compact text index of size $O(N \log\log N + N \log\sigma)$ bits that at least supports efficient inverse suffix array queries. Although, the question of designing a compressed text index that would lead to efficient pattern matching is still evasive, this index gives a hope on the existence of a full 2D compressed text index with all functionalities similar to that of 1D case. On the other hand, the Longest Common 2D substring problem consists of two 2D strings (matrices), and the task is to report the size of the longest common 2D substring (submatrix) of these 2D strings. It is interesting to know if there exists a sublinear-time algorithm for solving this task. We answer this question positively by presenting a sublinear-time \textit{quantum} algorithm. In addition to this, we prove that any quantum algorithm requires at least $\tilde{\Omega}(N^{2/3})$ time to solve this problem

Circulant temporal encoding for video retrieval and temporal alignment

We address the problem of specific video event retrieval. Given a query video of a specific event, e.g., a concert of Madonna, the goal is to retrieve other videos of the same event that temporally overlap with the query. Our approach encodes the frame descriptors of a video to jointly represent their appearance and temporal order. It exploits the properties of circulant matrices to efficiently compare the videos in the frequency domain. This offers a significant gain in complexity and accurately localizes the matching parts of videos. The descriptors can be compressed in the frequency domain with a product quantizer adapted to complex numbers. In this case, video retrieval is performed without decompressing the descriptors. We also consider the temporal alignment of a set of videos. We exploit the matching confidence and an estimate of the temporal offset computed for all pairs of videos by our retrieval approach. Our robust algorithm aligns the videos on a global timeline by maximizing the set of temporally consistent matches. The global temporal alignment enables synchronous playback of the videos of a given scene

bdbms -- A Database Management System for Biological Data

Biologists are increasingly using databases for storing and managing their data. Biological databases typically consist of a mixture of raw data, metadata, sequences, annotations, and related data obtained from various sources. Current database technology lacks several functionalities that are needed by biological databases. In this paper, we introduce bdbms, an extensible prototype database management system for supporting biological data. bdbms extends the functionalities of current DBMSs to include: (1) Annotation and provenance management including storage, indexing, manipulation, and querying of annotation and provenance as first class objects in bdbms, (2) Local dependency tracking to track the dependencies and derivations among data items, (3) Update authorization to support data curation via content-based authorization, in contrast to identity-based authorization, and (4) New access methods and their supporting operators that support pattern matching on various types of compressed biological data types. This paper presents the design of bdbms along with the techniques proposed to support these functionalities including an extension to SQL. We also outline some open issues in building bdbms.Comment: This article is published under a Creative Commons License Agreement (http://creativecommons.org/licenses/by/2.5/.) You may copy, distribute, display, and perform the work, make derivative works and make commercial use of the work, but, you must attribute the work to the author and CIDR 2007. 3rd Biennial Conference on Innovative Data Systems Research (CIDR) January 710, 2007, Asilomar, California, US

Sequential Compressed Sensing

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable performance by bounding the number of samples required for a given level of signal sparsity. However, using these bounds to minimize the number of samples requires a-priori knowledge of the sparsity of the unknown signal, or the decay structure for near-sparse signals. Furthermore, there are some popular recovery methods for which no such bounds are known. In this paper, we investigate an alternative scenario where observations are available in sequence. For any recovery method, this means that there is now a sequence of candidate reconstructions. We propose a method to estimate the reconstruction error directly from the samples themselves, for every candidate in this sequence. This estimate is universal in the sense that it is based only on the measurement ensemble, and not on the recovery method or any assumed level of sparsity of the unknown signal. With these estimates, one can now stop observations as soon as there is reasonable certainty of either exact or sufficiently accurate reconstruction. They also provide a way to obtain "run-time" guarantees for recovery methods that otherwise lack a-priori performance bounds. We investigate both continuous (e.g. Gaussian) and discrete (e.g. Bernoulli) random measurement ensembles, both for exactly sparse and general near-sparse signals, and with both noisy and noiseless measurements.Comment: to appear in IEEE transactions on Special Topics in Signal Processin