We propose a probabilistic latent variable model for unsupervised cluster matching, which is the task of finding correspondences between clusters of objects in different domains. Existing object matching methods find one-to-one matching. The proposed model finds many-to-many matching, and can handle multiple domains with different numbers of objects. The proposed model assumes that there are an infinite number of latent vectors that are shared by all domains, and that each object is generated using one of the latent vectors and a domain-specific linear projection. By inferring a latent vector to be used for generating each object, objects in different domains are clustered in shared groups, and thus we can find matching between clusters in an unsupervised manner. We present efficient inference procedures for the proposed model based on a stochastic EM algorithm. The effectiveness of the proposed model is demonstrated with experiments using synthetic and real data sets.

Classic sparse representation for classification (SRC) method fails to incorporate the label information of training images, and meanwhile has a poor scalability due to the expensive computation for l_1 norm. In this paper, we propose a novel subspace sparse coding method with utilizing label information to effectively classify the images in the subspace. Our new approach unifies the tasks of dimension reduction and supervised sparse vector learning, by simultaneously preserving the data sparse structure and meanwhile seeking the optimal projection direction in the training stage, therefore accelerates the classification process in the test stage. Our method achieves both flat and structured sparsity for the vector representations, therefore making our framework more discriminative during the subspace learning and subsequent classification. The empirical results on 4 benchmark data sets demonstrate the effectiveness of our method.

Spectral clustering has been a popular data clustering algorithm. This category of approaches often resort to other clustering methods, such as K-Means, to get the final cluster. The potential flaw of such common practice is that the obtained relaxed continuous spectral solution could severely deviate from the true discrete solution. In this paper, we propose to impose an additional orthonormal constraint to better approximate the optimal continuous solution to the graph cut objective functions. Such a method, called spectral rotation in literature, optimizes the spectral clustering objective functions better than K -Means, and improves the clustering accuracy. We would provide efficient algorithm to solve the new problem rigorously, which is not significantly more costly than K-Means. We also establish the connection between our method andK-Means to provide theoretical motivation of our method. Experimental results show that our algorithm consistently reaches better cut and meanwhile outperforms in clustering metrics than classic spectral clustering methods.

Most existing matrix completion methods seek the matrix global structure in the real number domain and produce predictions that are inappropriate for applications retaining discrete structure, where an additional step is required to post-process prediction results with either heuristic threshold parameters or complicated mappings. Such an ad-hoc process is inefficient and impractical. In this paper, we propose a novel robust discrete matrix completion algorithm that produces the prediction from the collection of user specified discrete values by introducing a new discrete constraint to the matrix completion model. Our method achieves a high prediction accuracy, very close to the most optimal value of competitive methods with threshold values tuning. We solve the difficult integer programming problem via incorporating augmented Lagrangian method in an elegant way, which greatly accelerates the converge process of our method and provides the asymptotic convergence in theory. The proposed discrete matrix completion model is applied to solve three real-world applications, and all empirical results demonstrate the effectiveness of our method.

We present a novel framework for shape-based template matching in images. While previous approaches required brittle contour extraction, considered only local information, or used coarse statistics, we propose to match the shape explicitly on low-level gradients by formulating the problem as traversing paths in a gradient network. We evaluate our algorithm on a challenging dataset of objects in cluttered environments and demonstrate significant improvement over state-of-the-art methods for shape matching and object detection.

Multiple sequence alignment (MSA) is a central problem in computational biology. It is well known that MSA can be formulated as a shortest path problem and solved using heuristic search, but the memory requirement of A* makes it impractical for all but the smallest problems. Partial Expansion A* (PEA*) reduces the space complexity of A* by generating only the most promising successor nodes. However, even PEA* exhausts available memory on many problems. Another alternative is Iterative Deepening Dynamic Programming, which uses an uninformed search order but stores only the nodes along the search frontier. However, it too cannot scale to the largest problems. In this paper, we propose storing nodes on cheap and plentiful secondary storage. We present a new general-purpose algorithm, Parallel External PEA* (\xppea), that combines PEA* with Delayed Duplicate Detection to take advantage of external memory and multiple processors to solve large MSA problems. In our experiments, \xppea\ is the first algorithm capable of solving the entire Reference Set 1 of the standard BAliBASE benchmark using a biologically accurate cost function. This work suggests that external best-first search can effectively use heuristic information to surpass methods that rely on uninformed search orders.

The blooming of comparison shopping agents (CSAs) in recent years enables buyers in today's markets to query more than a single CSA while shopping, thus substantially expanding the list of sellers whose prices they obtain. From the individual CSA point of view, however, the multi-CSAs querying is definitely non-favorable as most of today's CSAs benefit depends on payments they receive from sellers upon transferring buyers to their websites (and making a purchase). The most straightforward way for the CSA to improve its competence is through spending more resources on getting more sellers' prices, potentially resulting in a more attractive ``best price''. In this paper we suggest a complementary approach that improves the attractiveness of the best price returned to the buyer without having to extend the CSAs' price database. This approach, which we term ``selective price disclosure'' relies on removing some of the prices known to the CSA from the list of results returned to the buyer. The advantage of this approach is in the ability to affect the buyer's beliefs regarding the probability of obtaining more attractive prices if querying additional CSAs. The paper presents two methods for choosing the subset of prices to be presented to a fully-rational buyer, attempting to overcome the computational complexity associated with evaluating all possible subsets. The effectiveness and efficiency of the methods are demonstrated using real data, collected from five CSAs for four products. Furthermore, since people are known to have an inherently bounded rationality, the two methods are also evaluated with human buyers, demonstrating that selective price-disclosing can be highly effective with people, however the subset of prices that needs to be used should be extracted in a different (and more simplistic) manner.

By handling whole sets of indistinguishable objects together, lifted belief propagation approaches have rendered large, previously intractable, probabilistic inference problems quickly solvable. In this paper, we show that Kumar and Zilberstein's likelihood maximization (LM) approach to MAP inference is liftable, too, and actually provides additional structure for optimization. Specifically, it has been recognized that some pseudo marginals may converge quickly, turning intuitively into pseudo evidence. This additional evidence typically changes the structure of the lifted network: it may expand or reduce it. The current lifted network, however, can be viewed as an upper bound on the size of the lifted network required to finish likelihood maximization. Consequently, we re-lift the network only if the pseudo evidence yields a reduced network, which can efficiently be computed on the current lifted network. Our experimental results on Ising models, image segmentation and relational entity resolution demonstrate that this bootstrapped LM via "reduce and re-lift" finds MAP assignments comparable to those found by the original LM approach, but in a fraction of the time.

Learning from multi-view data is important in many applications. In this paper, we propose a novel convex subspace representation learning method for unsupervised multi-view clustering. We first formulate the subspace learning with multiple views as a joint optimization problem with a common subspace representation matrix and a group sparsity inducing norm. By exploiting the properties of dual norms, we then show a convex min-max dual formulation with a sparsity inducing trace norm can be obtained. We develop a proximal bundle optimization algorithm to globally solve the min-max optimization problem. Our empirical study shows the proposed subspace representation learning method can effectively facilitate multi-view clustering and induce superior clustering results than alternative multi-view clustering methods.

Declarative logic programs (LP) based on the well-founded semantics (WFS) are widely used for knowledge representation (KR).  Logical functions are desirable expressively in KR, but when present make LP inferencing become undecidable. In this paper, we present radial restraint : a novel approach to bounded rationality in LP. Radial restraint is parameterized by a norm that measures the syntactic complexity of a term, along with an abstraction function based on that norm.  When a term exceeds a bound for the norm, the term is assigned the WFS's third truth-value of undefined .  If the norm is finitary, radial restraint guarantees finiteness of models and decidability of inferencing, even when logical functions are present.  It further guarantees soundness, even when non-monotonicity is present.  We give a fixed-point semantics for radially restrained well-founded models which soundly approximate well-founded models.  We also show how to perform correct inferencing relative to such models, via SLG_ABS, an extension of tabled SLG resolution that uses norm-based abstraction functions.  Finally we discuss how SLG_ABS is implemented in the engine of XSB Prolog, and scales to knowledge bases with more than 10^8 rules and facts.