We address an ensemble clustering problem, where reliable clusters are locally embedded in given multiple partitions. We propose a new nonnegative matrix factorization (NMF)-based method, in which locally reliable clusters are explicitly considered by using instance-wise weights over clusters. Our method factorizes the input cluster assignment matrix into two matrices H and W, which are optimized by iteratively 1) updating H and W while keeping the weight matrix constant and 2) updating the weight matrix while keeping H and W constant, alternatively. The weights in the second step were updated by solving a convex problem, which makes our algorithm significantly faster than existing NMF-based ensemble clustering methods. We empirically proved that our method outperformed a lot of cutting-edge ensemble clustering methods by using a variety of datasets.

We consider problems of sequential robot manipulation (aka. combined task and motion planning) where the objective is primarily given in terms of a cost function over the final geometric state, rather than a symbolic goal description. In this case we should leverage optimization methods to inform search over potential action sequences. We propose to formulate the problem holistically as a 1st-order logic extension of a mathematical program: a non-linear constrained program over the full world trajectory where the symbolic state-action sequence defines the (in-)equality constraints. We tackle the challenge of solving such programs by proposing three levels of approximation: The coarsest level introduces the concept of the effective end state kinematics, parametrically describing all possible end state configurations conditional to a given symbolic action sequence. Optimization on this level is fast and can inform symbolic search. The other two levels optimize over interaction keyframes and eventually over the full world trajectory across interactions. We demonstrate the approach on a problem of maximizing the height of a physically stable construction from an assortment of boards, cylinders and blocks.

We address an ensemble clustering problem, where reliable clusters are locally embedded in given multiple partitions. We propose a new nonnegative matrix factorization (NMF)-based method, in which locally reliable clusters are explicitly considered by using instance-wise weights over clusters. Our method factorizes the input cluster assignment matrix into two matrices H and W, which are optimized by iteratively 1) updating H and W while keeping the weight matrix constant and 2) updating the weight matrix while keeping H and W constant, alternatively. The weights in the second step were updated by solving a convex problem, which makes our algorithm significantly faster than existing NMF-based ensemble clustering methods. We empirically proved that our method outperformed a lot of cutting-edge ensemble clustering methods by using a variety of datasets.

The rapidly growing of Location-based Social Networks (LBSNs) provides a vast amount of check-in data, which enables many services, e.g., point-of-interest (POI) recommendation. In this paper, we study the next new POI recommendation problem in which new POIs with respect to users' current location are to be recommended. The challenge lies in the difficulty in precisely learning users' sequential information and personalizing the recommendation model. To this end, we resort to the Metric Embedding method for the recommendation, which avoids drawbacks of the Matrix Factorization technique. We propose a personalized ranking metric embedding method (PRME) to model personalized check-in sequences. We further develop a PRME-G model, which integrates sequential information, individual preference, and geographical influence, to improve the recommendation performance. Experiments on two real-world LBSN datasets demonstrate that our new algorithm outperforms the state-of-the-art next POI recommendation methods.

Distributed word representations have a rising interest in NLP community. Most of existing models assume only one vector for each individual word, which ignores polysemy and thus degrades their effectiveness for downstream tasks. To address this problem, some recent work adopts multi-prototype models to learn multiple embeddings per word type. In this paper, we distinguish the different senses of each word by their latent topics. We present a general architecture to learn the word and topic embeddings efficiently, which is an extension to the Skip-Gram model and can model the interaction between words and topics simultaneously. The experiments on the word similarity and text classification tasks show our model outperforms state-of-the-art methods.

In many settings, we have multiple data sets (also called views) that capture different and overlapping aspects of the same phenomenon. We are often interested in finding patterns that are unique to one or to a subset of the views. For example, we might have one set of molecular observations and one set of physiological observations on the same group of individuals, and we want to quantify molecular patterns that are uncorrelated with physiology. Despite being a common problem, this is highly challenging when the correlations come from complex distributions. In this paper, we develop the general framework of Rich Component Analysis (RCA) to model settings where the observations from different views are driven by different sets of latent components, and each component can be a complex, high-dimensional distribution. We introduce algorithms based on cumulant extraction that provably learn each of the components without having to model the other components. We show how to integrate RCA with stochastic gradient descent into a meta-algorithm for learning general models, and demonstrate substantial improvement in accuracy on several synthetic and real datasets in both supervised and unsupervised tasks. Our method makes it possible to learn latent variable models when we don't have samples from the true model but only samples after complex perturbations.

Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes it possible to estimate expectiles in a non-parametric framework by a support vector machine like approach. In this work we develop an efficient sequential-minimal-optimization-based solver for the underlying optimization problem. The behavior of the solver is investigated by conducting various experiments and the results are compared with the recent R-package ER-Boost.

Recently several methods were proposed for sparse optimization which make careful use of second-order information [10, 28, 16, 3] to improve local convergence rates. These methods construct a composite quadratic approximation using Hessian information, optimize this approximation using a first-order method, such as coordinate descent and employ a line search to ensure sufficient descent. Here we propose a general framework, which includes slightly modified versions of existing algorithms and also a new algorithm, which uses limited memory BFGS Hessian approximations, and provide a novel global convergence rate analysis, which covers methods that solve subproblems via coordinate descent.

Gelfond and Zhang recently proposed a new stable model semantics based on Vicious Circle Principle in order to improve the interpretation of logic programs with aggregates. The paper focuses on this proposal, and analyzes the complexity of both coherence testing and cautious reasoning under the new semantics. Some surprising results highlight similarities and differences versus mainstream stable model semantics for aggregates. Moreover, the paper reports on the design of compilation techniques for implementing the new semantics on top of existing ASP solvers, which eventually lead to realize a prototype system that allows for experimenting with Gelfond-Zhang's aggregates. To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015.

Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different expressions; in particular the \Godel and \Luka fuzzy connectives are usually considered, due to their properties. Although the \Godel conjunction can be easily eliminated from rule heads, we show through complexity arguments that such a simplification is infeasible in general for all other connectives. %, even if bodies are restricted to \Luka or \Godel conjunctions. The paper analyzes a translation of FASP programs into satisfiability modulo theories~(SMT), which in general produces quantified formulas because of the minimality of the semantics. Structural properties of many FASP programs allow to eliminate the quantification, or to sensibly reduce the number of quantified variables. Indeed, integrality constraints can replace recursive rules commonly used to force Boolean interpretations, and completion subformulas can guarantee minimality for acyclic programs with atomic heads. Moreover, head cycle free rules can be replaced by shifted subprograms, whose structure depends on the eliminated head connective, so that ordered completion may replace the minimality check if also \Luka disjunction in rule bodies is acyclic. The paper also presents and evaluates a prototype system implementing these translations. To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015.