Results 1  10
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14
A Cheeger inequality for the graph connection laplacian. available online
, 2012
"... Abstract. The O(d) Synchronization problem consists of estimating a set of n unknown orthogonal d × d matrices O1,..., On from noisy measurements of a subset of the pairwise ratios OiO −1 j. We formulate and prove a Cheegertype inequality that relates a measure of how well it is possible to solve t ..."
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Cited by 7 (4 self)
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Abstract. The O(d) Synchronization problem consists of estimating a set of n unknown orthogonal d × d matrices O1,..., On from noisy measurements of a subset of the pairwise ratios OiO −1 j. We formulate and prove a Cheegertype inequality that relates a measure of how well it is possible to solve the O(d) synchronization problem with the spectra of an operator, the graph Connection Laplacian. We also show how this inequality provides a worst case performance guarantee for a spectral method to solve this problem.
Flows and Decompositions of Games: Harmonic and Potential Games
"... In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze na ..."
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Cited by 5 (2 self)
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In this paper we introduce a novel flow representation for finite games in strategic form. This representation allows us to develop a canonical direct sum decomposition of an arbitrary game into three components, which we refer to as the potential, harmonic and nonstrategic components. We analyze natural classes of games that are induced by this decomposition, and in particular, focus on games with no harmonic component and games with no potential component. We show that the first class corresponds to the wellknown potential games. We refer to the second class of games as harmonic games, and study the structural and equilibrium properties of this new class of games. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents the conflicts between the interests of the players. We make this intuition precise, by studying the properties of these two classes, and show that indeed they have quite distinct and remarkable characteristics. For instance, while finite potential games always have pure Nash equilibria, harmonic games generically never do. Moreover, we show that the nonstrategic component does not affect the
Classifying actions and measuring action similarity by modeling the mutual context of objects and human poses
 In Proc. ICML
, 2011
"... In this paper, we consider two action recognition problems in still images. One is the conventional action classification task where we assign a class label to each action image; the other is a new problem where we measure the similarity between action images. We achieve the goals by using a mutual ..."
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Cited by 4 (1 self)
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In this paper, we consider two action recognition problems in still images. One is the conventional action classification task where we assign a class label to each action image; the other is a new problem where we measure the similarity between action images. We achieve the goals by using a mutual context model to jointly model the objects and human poses in images of human actions. Experimental results show that our method not only improves action classification accuracy, but also learns a similarity measure that is largely consistent with human perception. 1.
A Flexible Generative Model for Preference Aggregation
"... Many areas of study, such as information retrieval, collaborative filtering, and social choice face the preference aggregation problem, in which multiple preferences over objects must be combined into a consensus ranking. Preferences over items can be expressed in a variety of forms, which makes the ..."
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Cited by 2 (0 self)
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Many areas of study, such as information retrieval, collaborative filtering, and social choice face the preference aggregation problem, in which multiple preferences over objects must be combined into a consensus ranking. Preferences over items can be expressed in a variety of forms, which makes the aggregation problem difficult. In this work we formulate a flexible probabilistic model over pairwise comparisons that can accommodate all these forms. Inference in the model is very fast, making it applicable to problems with hundreds of thousands of preferences. Experiments on benchmark datasets demonstrate superior performance to existing methods.
ANALYSIS AND APPROXIMATION OF NONLOCAL DIFFUSION PROBLEMS WITH VOLUME CONSTRAINTS
, 2012
"... Abstract. A recently developed nonlocal vector calculus is exploited to provide a variational analysis for a general class of nonlocal diffusion problems described by a linear integral equation on bounded domains in Rn. The nonlocal vector calculus also enables striking analogies to be drawn between ..."
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Abstract. A recently developed nonlocal vector calculus is exploited to provide a variational analysis for a general class of nonlocal diffusion problems described by a linear integral equation on bounded domains in Rn. The nonlocal vector calculus also enables striking analogies to be drawn between the nonlocal model and classical models for diffusion, including a notion of nonlocal flux. The ubiquity of the nonlocal operator in applications is illustrated by a number of examples ranging from continuum mechanics to graph theory. In particular, it is shown that fractional Laplacian and fractional derivative models for anomalous diffusion are special cases of the nonlocal model for diffusion we consider. The numerous applications elucidate different interpretations of the operator and the associated governing equations. For example, a probabilistic perspective explains that the nonlocal spatial operator appearing in our model corresponds to the infinitesimal generator for a symmetric jump process. Sufficient conditions on the kernel of the nonlocal operator and the notion of volume constraints are shown to lead to a wellposed problem. Volume constraints are a proxy for boundary conditions that may not be defined for a given kernel. In particular, we demonstrate for a general class of kernels that the nonlocal operator is a mapping between a constrained subspace of a fractional Sobolev subspace and its dual. We also demonstrate for other particular kernels that the inverse of the operator does not smooth but does correspond to diffusion. The impact of our results is that both a continuum analysis and a numerical method for the modeling of anomalous diffusion on bounded domains in Rn are provided. The analytical framework allows us to consider finitedimensional approximations using both discontinuous or continuous Galerkin methods, both of which are conforming for the nonlocal diffusion equation we consider; error and condition number estimates are derived.
Learning to Rank By Aggregating Expert Preferences
"... We present a general treatment of the problem of aggregating preferences from several experts into a consensus ranking, in the context where information about a target ranking is available. Specifically, we describe how such problems can be converted into a standard learningtorank one on which exi ..."
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Cited by 1 (1 self)
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We present a general treatment of the problem of aggregating preferences from several experts into a consensus ranking, in the context where information about a target ranking is available. Specifically, we describe how such problems can be converted into a standard learningtorank one on which existing learning solutions can be invoked. This transformation allows us to optimize the aggregating function for any target IR metric, such as Normalized Discounted Cumulative Gain, or Expected Reciprocal Rank. When applied to crowdsourcing and metasearch benchmarks, our new algorithm improves on stateoftheart preference aggregation methods.
Robust Late Fusion With Rank Minimization
"... In this paper, we propose a rank minimization method to fuse the predicted confidence scores of multiple models, each of which is obtained based on a certain kind of feature. Specifically, we convert each confidence score vector obtained from one model into a pairwise relationship matrix, in which e ..."
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In this paper, we propose a rank minimization method to fuse the predicted confidence scores of multiple models, each of which is obtained based on a certain kind of feature. Specifically, we convert each confidence score vector obtained from one model into a pairwise relationship matrix, in which each entry characterizes the comparative relationship of scores of two test samples. Our hypothesis is that the relative score relations are consistent among component models up to certain sparse deviations, despite the large variations that may exist in the absolute values of the raw scores. Then we formulate the score fusion problem as seeking a shared rank2 pairwise relationship matrix based on which each original score matrix from individual model can be decomposed into the common rank2 matrix and sparse deviation errors. A robust score vector is then extracted to fit the recovered low rank score relation matrix. We formulate the problem as a nuclear norm and ℓ1 norm optimization objective function and employ the Augmented Lagrange Multiplier (ALM) method for the optimization. Our method is isotonic (i.e., scale invariant) to the numeric scales of the scores originated from different models. We experimentally show that the proposed method achieves significant performance gains on various tasks including object categorization and video event detection. 1.
HODGE THEORY ON METRIC SPACES
, 2009
"... Remark. This draft modifies the previous draft (February 20, 2009) to account for a mistake pointed out to us by Thomas Schick. Our argument that the image of δ in Theorem 3 was closed was incorrect. 1 ..."
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Remark. This draft modifies the previous draft (February 20, 2009) to account for a mistake pointed out to us by Thomas Schick. Our argument that the image of δ in Theorem 3 was closed was incorrect. 1
Mathematical Models and Methods in Applied Sciences c ○ World Scientific Publishing Company Sandia National Labs SAND 20108353J A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUMECONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
"... A vector calculus for nonlocal operators is developed, including the definition of nonlocal divergence, gradient, and curl operators and the derivation of the corresponding adjoint operators. Nonlocal analogs of several theorems and identities of the vector calculus for differential operators are al ..."
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A vector calculus for nonlocal operators is developed, including the definition of nonlocal divergence, gradient, and curl operators and the derivation of the corresponding adjoint operators. Nonlocal analogs of several theorems and identities of the vector calculus for differential operators are also presented. Relationships between the nonlocal operators and their differential counterparts are established, first in a distributional sense and then in a weak sense by considering weighted integrals of the nonlocal adjoint operators. The operators of the nonlocal calculus are used to define volumeconstrained problems that are analogous to elliptic boundaryvalue problems for differential operators; this nonlocal balance laws and deriving the corresponding nonlocal field equations; this is demonstrated for heat conduction and the peridynamics model for continuum mechanics.