In various data settings, it is necessary to compare observations from disparate data sources. We assume the data is in the dissimilarity representation and investigate a joint embedding method that results in a commensurate representation of disparate dissimilarities. We further assume that there are "matched" observations from different conditions which can be considered to be highly similar, for the sake of inference. The joint embedding results in the joint optimization of fidelity (preservation of within-condition dissimilarities) and commensurability (preservation of between-condition dissimilarities between matched observations). We show that the tradeoff between these two criteria can be made explicit using weighted raw stress as the objective function for multidimensional scaling. In our investigations, we use a weight parameter, @math , to control the tradeoff, and choose match detection as the inference task. Our results show weights that are optimal (with respect to the inference task) are different than equal weights for commensurability and fidelity and the proposed weighted embedding scheme provides significant improvements in statistical power.
@cite_16 solve the problem in the semi-supervised setting by a similar approach, by optimizing a energy function that has three terms that are analogous to the terms in @cite_15 .
@cite_15 @cite_16
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Recent studies have shown that graph-based approaches are effective for semi-supervised learning. The key idea behind many graph-based approaches is to enforce the consistency between the class assignment of unlabeled examples and the pairwise similarity between examples. One major limitation with most graph-based approaches is that they are unable to explore dissimilarity or negative similarity. This is because the dissimilar relation is not transitive, and therefore is difficult to be propagated. Furthermore, negative similarity could result in unbounded energy functions, which makes most graph-based algorithms unapplicable. In this paper, we propose a new graph-based approach, termed as "mixed label propagation" which is able to effectively explore both similarity and dissimilarity simultaneously. In particular, the new framework determines the assignment of class labels by (1) minimizing the energy function associated with positive similarity, and (2) maximizing the energy function associated with negative similarity. Our empirical study with collaborative filtering shows promising performance of the proposed approach. We consider the problem of speed scaling to conserve energy in a multiprocessor setting where there are precedence constraints between tasks, and where the performance measure is the makespan. That is, we consider an energy bounded version of the classic problem Pm|prec|Cmax . We extend the standard 3-field notation and denote this problem as Sm|prec, energy|Cmax . We show that, without loss of generality, one need only consider constant power schedules. We then show how to reduce this problem to the problem Qm|prec|Cmax to obtain a poly-log(m)-approximation algorithm. This paper addresses the problem of exactly inferring the maximum a posteriori solutions of discrete multi-label MRFs or CRFs with higher order cliques. We present a framework to transform special classes of multi-label higher order functions to submodular second order Boolean functions (referred to as Fs 2), which can be minimized exactly using graph cuts and we characterize those classes. The basic idea is to use two or more Boolean variables to encode the states of a single multi-label variable. There are many ways in which this can be done and much interesting research lies in finding ways which are optimal or minimal in some sense. We study the space of possible encodings and find the ones that can transform the most general class of functions to Fs 2. Our main contributions are two-fold. First, we extend the subclass of submodular energy functions that can be minimized exactly using graph cuts. Second, we show how higher order potentials can be used to improve single view 3D reconstruction results. We believe that our work on exact minimization of higher order energy functions will lead to similar improvements in solutions of other labelling problems. We address the problem of hand pose estimation, formulated as an inverse problem. Typical approaches optimize an energy function over pose parameters using a 'black box' image generation procedure. This procedure knows little about either the relationships between the parameters or the form of the energy function. In this paper, we show that we can significantly improving upon black box optimization by exploiting high-level knowledge of the structure of the parameters and using a local surrogate energy function. Our new framework, hierarchical sampling optimization, consists of a sequence of predictors organized into a kinematic hierarchy. Each predictor is conditioned on its ancestors, and generates a set of samples over a subset of the pose parameters. The highly-efficient surrogate energy is used to select among samples. Having evaluated the full hierarchy, the partial pose samples are concatenated to generate a full-pose hypothesis. Several hypotheses are generated using the same procedure, and finally the original full energy function selects the best result. Experimental evaluation on three publically available datasets show that our method is particularly impressive in low-compute scenarios where it significantly outperforms all other state-of-the-art methods.