In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTICS), 2013

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Proc. IEEE International Conference on Data Mining, 2013 (ICDM)

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In this paper, we present a method to attach affinity scores to the implicit labels of individual points in a clustering. The affinity scores capture the confidence level of the cluster that claims to “own” the point. We demonstrate that these scores accurately capture the quality of the label assigned to the point. We also show further applications of these scores to estimate global measures of clustering quality, as well as accelerate clustering algorithms by orders of magnitude using active selection based on affinity.

This method is very general and applies to clusterings derived from any geometric source. It lends itself to easy visualization and can prove useful as part of an interactive visual analytics framework. It is also efficient: assigning an affinity score to a point depends only polynomially on the number of clusters and is independent both of the size and dimensionality of the data. It is based on techniques from the theory of interpolation, coupled with sampling and estimation algorithms from high dimensional computational geometry.

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Links: (older arXiv version: submitted version)

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Notes: the published version of the article has a few errors.

• Moitra’s SODA paper improves the running time from $O((nm)^{2^r r^2})$ to $O((nm)^{r^2})$, which is considerably stronger than what was reported in the article.
• The correct lower bound for computing a nonnegative factorization (assuming ETH) is $O((nm)^{o(r)})$.

This link (PDF) has the corrected article. Thanks to Ankur Moitra for pointing out the errors.

To appear in the IEEE Transactions on Mobile Computing.

http://arxiv.org/abs/1302.4720

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Links: Coming soon.

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Sensor network localization (SNL) is the problem of determining the locations of the sensors given sparse and usually noisy inter-communication distances among them. In this work we propose an iterative algorithm named PLACEMENT to solve the SNL problem.
This iterative algorithm requires an initial estimation of the locations and in each iteration, is guaranteed to reduce the cost function. The proposed algorithm is able to take advantage of the good initial estimation of sensor locations making it suitable for localizing moving sensors, and also suitable for the refinement of the results produced by other algorithms. Our algorithm is very scalable. We have
experimented with a variety of sensor networks and have shown that the proposed algorithm outperforms existing algorithms both in terms of speed and accuracy in almost all experiments. Our algorithm can embed 120,000 sensors in less than 20 minutes.

Links: PDF

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Device-free localization systems pinpoint and track people in buildings using changes in the signal strength measurements made on wireless devices in the building’s wireless network. It has been shown that such systems can locate people who do not participate in the system by wearing any radio device, even through walls, because of the changes that moving people cause to the static wireless network. However, many such systems cannot locate stationary people. We present and evaluate a system which can locate stationary or moving people, with or without calibration, by quantifying the difference between two histograms of signal strength measurements. From five experiments, we show that our kernel distance-based radio tomographic localization system performs better than the state-of-the-art device-free localization systems in different non line-of-sight environments.

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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.

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In recent years, study of influence propagation in social networks has gained tremendous attention. In this context, 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 (or MAXINF for short). 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 η is given and the task is to find the minimum size seed set such that by activating it, at least η nodes are eventually activated in the expected sense. This naturally captures the problem of deploying a viral campaign on a budget. In the second problem, termed MINTIME, the goal is to minimize the time in which a predefined coverage is achieved. More precisely, in MINTIME, a coverage threshold η 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 η nodes are activated in the expected sense, in the minimum possible time. This problem addresses the issue of timing when deploying viral campaigns. 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 this bicriteria approximation is likely to be hard. For MINTIME, we show that even bicriteria and tricriteria approximations are hard under several conditions. We show, however, that if we allow the budget for number of seeds k to be boosted by a logarithmic factor and allow the coverage to fall short, then the problem can be solved exactly in PTIME, i.e., we can achieve the required coverage within the time achieved by the optimal solution to MINTIME with budget k and coverage threshold η. Finally, we establish the value of the approximation algorithms, by conducting an experimental evaluation, comparing their quality against that achieved by various heuristics.

Links: Journal site

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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.

Links: PDF (this is the submitted version, not the final accepted version)