arXiv subjects

Suresh Venkatasubramanian

Publications and source records attributed to Suresh Venkatasubramanian.

71 records · Page 4Linked to original sources

arXiv2013

Multiple Target Tracking with RF Sensor Networks

RF sensor networks are wireless networks that can localize and track people (or targets) without needing them to carry or wear any electronic device. They use the change in the received signal strength (RSS) of the links due to the movements of people to infer their locations. In this paper, we consider real-time multiple target tracking with RF sensor networks. We perform radio tomographic imaging (RTI), which generates images of the change in the propagation field, as if they were frames of a video. Our RTI method uses RSS measurements on multiple frequency channels on each link, combining them with a fade level-based weighted average. We describe methods to adapt machine vision methods to the peculiarities of RTI to enable real time multiple target tracking. Several tests are performed in an open environment, a one-bedroom apartment, and a cluttered office environment. The results demonstrate that the system is capable of accurately tracking in real-time up to 4 targets in cluttered indoor environments, even when their trajectories intersect multiple times, without mis-estimating the number of targets found in the monitored area. The highest average tracking error measured in the tests is 0.45 m with two targets, 0.46 m with three targets, and 0.55 m with four targets.

cs.NI↗

arXiv2012

Efficient Protocols for Distributed Classification and Optimization

In distributed learning, the goal is to perform a learning task over data distributed across multiple nodes with minimal (expensive) communication. Prior work (Daume III et al., 2012) proposes a general model that bounds the communication required for learning classifiers while allowing for $\eps$ training error on linearly separable data adversarially distributed across nodes. In this work, we develop key improvements and extensions to this basic model. Our first result is a two-party multiplicative-weight-update based protocol that uses $O(d^2 \log{1/\eps})$ words of communication to classify distributed data in arbitrary dimension $d$, $\eps$-optimally. This readily extends to classification over $k$ nodes with $O(kd^2 \log{1/\eps})$ words of communication. Our proposed protocol is simple to implement and is considerably more efficient than baselines compared, as demonstrated by our empirical results. In addition, we illustrate general algorithm design paradigms for doing efficient learning over distributed data. We show how to solve fixed-dimensional and high dimensional linear programming efficiently in a distributed setting where constraints may be distributed across nodes. Since many learning problems can be viewed as convex optimization problems where constraints are generated by individual points, this models many typical distributed learning scenarios. Our techniques make use of a novel connection from multipass streaming, as well as adapting the multiplicative-weight-update framework more generally to a distributed setting. As a consequence, our methods extend to the wide range of problems solvable using these techniques.

cs.LG↗

arXiv2012

Protocols for Learning Classifiers on Distributed Data

We consider the problem of learning classifiers for labeled data that has been distributed across several nodes. Our goal is to find a single classifier, with small approximation error, across all datasets while minimizing the communication between nodes. This setting models real-world communication bottlenecks in the processing of massive distributed datasets. We present several very general sampling-based solutions as well as some two-way protocols which have a provable exponential speed-up over any one-way protocol. We focus on core problems for noiseless data distributed across two or more nodes. The techniques we introduce are reminiscent of active learning, but rather than actively probing labels, nodes actively communicate with each other, each node simultaneously learning the important data from another node.

stat.ML↗

arXiv2011

Approximation Analysis of Influence Spread in Social Networks

In the context of influence propagation in a social graph, we can identify three orthogonal dimensions - the number of seed nodes activated at the beginning (known as budget), the expected number of activated nodes at the end of the propagation (known as expected spread or coverage), and the time taken for the propagation. We can constrain one or two of these and try to optimize the third. In their seminal paper, Kempe et al. constrained the budget, left time unconstrained, and maximized the coverage: this problem is known as Influence Maximization. In this paper, we study alternative optimization problems which are naturally motivated by resource and time constraints on viral marketing campaigns. In the first problem, termed Minimum Target Set Selection (or MINTSS for short), a coverage threshold n is given and the task is to find the minimum size seed set such that by activating it, at least n nodes are eventually activated in the expected sense. In the second problem, termed MINTIME, a coverage threshold n and a budget threshold k are given, and the task is to find a seed set of size at most k such that by activating it, at least n nodes are activated, in the minimum possible time. Both these problems are NP-hard, which motivates our interest in their approximation. For MINTSS, we develop a simple greedy algorithm and show that it provides a bicriteria approximation. We also establish a generic hardness result suggesting that improving it is likely to be hard. For MINTIME, we show that even bicriteria and tricriteria approximations are hard under several conditions. However, if we allow the budget to be boosted by a logarithmic factor and allow the coverage to fall short, then the problem can be solved exactly in PTIME. Finally, we show the value of the approximation algorithms, by comparing them against various heuristics.

cs.DM↗

arXiv2011

Generating a Diverse Set of High-Quality Clusterings

We provide a new framework for generating multiple good quality partitions (clusterings) of a single data set. Our approach decomposes this problem into two components, generating many high-quality partitions, and then grouping these partitions to obtain k representatives. The decomposition makes the approach extremely modular and allows us to optimize various criteria that control the choice of representative partitions.

cs.LG↗

arXiv2011

Comparing Distributions and Shapes using the Kernel Distance

Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis, measure theory and geometric measure theory, and have a rich structure that includes an isometric embedding into a (possibly infinite dimensional) Hilbert space. They have recently been applied to numerous problems in machine learning and shape analysis. In this paper, we provide the first algorithmic analysis of these distance metrics. Our main contributions are as follows: (i) We present fast approximation algorithms for computing the kernel distance between two point sets P and Q that runs in near-linear time in the size of (P cup Q) (note that an explicit calculation would take quadratic time). (ii) We present polynomial-time algorithms for approximately minimizing the kernel distance under rigid transformation; they run in time O(n + poly(1/epsilon, log n)). (iii) We provide several general techniques for reducing complex objects to convenient sparse representations (specifically to point sets or sets of points sets) which approximately preserve the kernel distance. In particular, this allows us to reduce problems of computing the kernel distance between various types of objects such as curves, surfaces, and distributions to computing the kernel distance between point sets. These take advantage of the reproducing kernel Hilbert space and a new relation linking binary range spaces to continuous range spaces with bounded fat-shattering dimension.

cs.CG↗

arXiv2011

A Gentle Introduction to the Kernel Distance

This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning, functional analysis and geometric measure theory. The key aspect of the kernel distance developed here is its interpretation as an L_2 distance between probability measures or various shapes (e.g. point sets, curves, surfaces) embedded in a vector space (specifically an RKHS). This structure enables several elegant and efficient solutions to data analysis problems. We conclude with a glimpse into the mathematical underpinnings of this measure, highlighting its recent independent evolution in two separate fields.

cs.CG↗

arXiv2011

Spatially-Aware Comparison and Consensus for Clusterings

This paper proposes a new distance metric between clusterings that incorporates information about the spatial distribution of points and clusters. Our approach builds on the idea of a Hilbert space-based representation of clusters as a combination of the representations of their constituent points. We use this representation and the underlying metric to design a spatially-aware consensus clustering procedure. This consensus procedure is implemented via a novel reduction to Euclidean clustering, and is both simple and efficient. All of our results apply to both soft and hard clusterings. We accompany these algorithms with a detailed experimental evaluation that demonstrates the efficiency and quality of our techniques.

cs.LG↗

arXiv2010

A Unified Algorithmic Framework for Multi-Dimensional Scaling

In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single subroutine in the algorithm, we can switch cost functions and target spaces easily. In addition to the formal guarantees of convergence, our algorithms are accurate; in most cases, they converge to better quality solutions than existing methods, in comparable time. We expect that this framework will be useful for a number of \mds variants that have not yet been studied. Our framework extends to embedding high-dimensional points lying on a sphere to points on a lower dimensional sphere, preserving geodesic distances. As a compliment to this result, we also extend the Johnson-Lindenstrauss Lemma to this spherical setting, where projecting to a random $O((1/\eps^2) \log n)$-dimensional sphere causes $\eps$-distortion.

cs.LG↗

arXiv2009

Computing Hulls And Centerpoints In Positive Definite Space

In this paper, we present algorithms for computing approximate hulls and centerpoints for collections of matrices in positive definite space. There are many applications where the data under consideration, rather than being points in a Euclidean space, are positive definite (p.d.) matrices. These applications include diffusion tensor imaging in the brain, elasticity analysis in mechanical engineering, and the theory of kernel maps in machine learning. Our work centers around the notion of a horoball: the limit of a ball fixed at one point whose radius goes to infinity. Horoballs possess many (though not all) of the properties of halfspaces; in particular, they lack a strong separation theorem where two horoballs can completely partition the space. In spite of this, we show that we can compute an approximate "horoball hull" that strictly contains the actual convex hull. This approximate hull also preserves geodesic extents, which is a result of independent value: an immediate corollary is that we can approximately solve problems like the diameter and width in positive definite space. We also use horoballs to show existence of and compute approximate robust centerpoints in positive definite space, via the horoball-equivalent of the notion of depth.

cs.CG↗

arXiv2009

Streamed Learning: One-Pass SVMs

We present a streaming model for large-scale classification (in the context of $\ell_2$-SVM) by leveraging connections between learning and computational geometry. The streaming model imposes the constraint that only a single pass over the data is allowed. The $\ell_2$-SVM is known to have an equivalent formulation in terms of the minimum enclosing ball (MEB) problem, and an efficient algorithm based on the idea of \emph{core sets} exists (Core Vector Machine, CVM). CVM learns a $(1+\varepsilon)$-approximate MEB for a set of points and yields an approximate solution to corresponding SVM instance. However CVM works in batch mode requiring multiple passes over the data. This paper presents a single-pass SVM which is based on the minimum enclosing ball of streaming data. We show that the MEB updates for the streaming case can be easily adapted to learn the SVM weight vector in a way similar to using online stochastic gradient updates. Our algorithm performs polylogarithmic computation at each example, and requires very small and constant storage. Experimental results show that, even in such restrictive settings, we can learn efficiently in just one pass and get accuracies comparable to other state-of-the-art SVM solvers (batch and online). We also give an analysis of the algorithm, and discuss some open issues and possible extensions.

cs.LG↗

arXiv2006

Rectangular Layouts and Contact Graphs

Contact graphs of isothetic rectangles unify many concepts from applications including VLSI and architectural design, computational geometry, and GIS. Minimizing the area of their corresponding {\em rectangular layouts} is a key problem. We study the area-optimization problem and show that it is NP-hard to find a minimum-area rectangular layout of a given contact graph. We present O(n)-time algorithms that construct $O(n^2)$-area rectangular layouts for general contact graphs and $O(n\log n)$-area rectangular layouts for trees. (For trees, this is an $O(\log n)$-approximation algorithm.) We also present an infinite family of graphs (rsp., trees) that require $Ω(n^2)$ (rsp., $Ω(n\log n)$) area. We derive these results by presenting a new characterization of graphs that admit rectangular layouts using the related concept of {\em rectangular duals}. A corollary to our results relates the class of graphs that admit rectangular layouts to {\em rectangle of influence drawings}.

cs.DS↗

arXiv2006

Restricted Strip Covering and the Sensor Cover Problem

Given a set of objects with durations (jobs) that cover a base region, can we schedule the jobs to maximize the duration the original region remains covered? We call this problem the sensor cover problem. This problem arises in the context of covering a region with sensors. For example, suppose you wish to monitor activity along a fence by sensors placed at various fixed locations. Each sensor has a range and limited battery life. The problem is to schedule when to turn on the sensors so that the fence is fully monitored for as long as possible. This one dimensional problem involves intervals on the real line. Associating a duration to each yields a set of rectangles in space and time, each specified by a pair of fixed horizontal endpoints and a height. The objective is to assign a position to each rectangle to maximize the height at which the spanning interval is fully covered. We call this one dimensional problem restricted strip covering. If we replace the covering constraint by a packing constraint, the problem is identical to dynamic storage allocation, a scheduling problem that is a restricted case of the strip packing problem. We show that the restricted strip covering problem is NP-hard and present an O(log log n)-approximation algorithm. We present better approximations or exact algorithms for some special cases. For the uniform-duration case of restricted strip covering we give a polynomial-time, exact algorithm but prove that the uniform-duration case for higher-dimensional regions is NP-hard. Finally, we consider regions that are arbitrary sets, and we present an O(log n)-approximation algorithm.

cs.DS↗

arXiv2005

The Hunting of the Bump: On Maximizing Statistical Discrepancy

Anomaly detection has important applications in biosurveilance and environmental monitoring. When comparing measured data to data drawn from a baseline distribution, merely, finding clusters in the measured data may not actually represent true anomalies. These clusters may likely be the clusters of the baseline distribution. Hence, a discrepancy function is often used to examine how different measured data is to baseline data within a region. An anomalous region is thus defined to be one with high discrepancy. In this paper, we present algorithms for maximizing statistical discrepancy functions over the space of axis-parallel rectangles. We give provable approximation guarantees, both additive and relative, and our methods apply to any convex discrepancy function. Our algorithms work by connecting statistical discrepancy to combinatorial discrepancy; roughly speaking, we show that in order to maximize a convex discrepancy function over a class of shapes, one needs only maximize a linear discrepancy function over the same set of shapes. We derive general discrepancy functions for data generated from a one- parameter exponential family. This generalizes the widely-used Kulldorff scan statistic for data from a Poisson distribution. We present an algorithm running in $O(\smash[tb]{\frac{1}ε n^2 \log^2 n})$ that computes the maximum discrepancy rectangle to within additive error $ε$, for the Kulldorff scan statistic. Similar results hold for relative error and for discrepancy functions for data coming from Gaussian, Bernoulli, and gamma distributions. Prior to our work, the best known algorithms were exact and ran in time $\smash[t]{O(n^4)}$.

cs.CG↗

arXiv2005

Streaming and Sublinear Approximation of Entropy and Information Distances

In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural measures of distance are not the $\ell_p$ norms and variants, but information-theoretic measures like the Kullback-Leibler distance, the Hellinger distance, and others. Efficient estimation of these distances is a key component in algorithms for manipulating distributions. Thus, sublinear resource constraints, either in time (property testing) or space (streaming) are crucial. We start by resolving two open questions regarding property testing of distributions. Firstly, we show a tight bound for estimating bounded, symmetric f-divergences between distributions in a general property testing (sublinear time) framework (the so-called combined oracle model). This yields optimal algorithms for estimating such well known distances as the Jensen-Shannon divergence and the Hellinger distance. Secondly, we close a $(\log n)/H$ gap between upper and lower bounds for estimating entropy $H$ in this model. In a stream setting (sublinear space), we give the first algorithm for estimating the entropy of a distribution. Our algorithm runs in polylogarithmic space and yields an asymptotic constant factor approximation scheme. We also provide other results along the space/time/approximation tradeoff curve.

cs.DS↗

arXiv2003

The Graphics Card as a Streaming Computer

Massive data sets have radically changed our understanding of how to design efficient algorithms; the streaming paradigm, whether it in terms of number of passes of an external memory algorithm, or the single pass and limited memory of a stream algorithm, appears to be the dominant method for coping with large data. A very different kind of massive computation has had the same effect at the level of the CPU. The most prominent example is that of the computations performed by a graphics card. The operations themselves are very simple, and require very little memory, but require the ability to perform many computations extremely fast and in parallel to whatever degree possible. What has resulted is a stream processor that is highly optimized for stream computations. An intriguing side effect of this is the growing use of a graphics card as a general purpose stream processing engine. In an ever-increasing array of applications, researchers are discovering that performing a computation on a graphics card is far faster than performing it on a CPU, and so are using a GPU as a stream co-processor.

cs.GR↗

arXiv2000

Pattern Matching for sets of segments

In this paper we present algorithms for a number of problems in geometric pattern matching where the input consist of a collections of segments in the plane. Our work consists of two main parts. In the first, we address problems and measures that relate to collections of orthogonal line segments in the plane. Such collections arise naturally from problems in mapping buildings and robot exploration. We propose a new measure of segment similarity called a \emph{coverage measure}, and present efficient algorithms for maximising this measure between sets of axis-parallel segments under translations. Our algorithms run in time $O(n^3\polylog n)$ in the general case, and run in time $O(n^2\polylog n)$ for the case when all segments are horizontal. In addition, we show that when restricted to translations that are only vertical, the Hausdorff distance between two sets of horizontal segments can be computed in time roughly $O(n^{3/2}{\sl polylog}n)$. These algorithms form significant improvements over the general algorithm of Chew et al. that takes time $O(n^4 \log^2 n)$. In the second part of this paper we address the problem of matching polygonal chains. We study the well known \Frd, and present the first algorithm for computing the \Frd under general translations. Our methods also yield algorithms for computing a generalization of the \Fr distance, and we also present a simple approximation algorithm for the \Frd that runs in time $O(n^2\polylog n)$.

cs.CG↗