In this paper, we propose a general formulation for kernel nonnegative matrix factorization with flexible kernels. Specifically, we propose the Gaussian nonnegative matrix factorization (GNMF) algorithm by using the Gaussian kernel in the framework. Different from a recently developed polynomial NMF (PNMF), GNMF finds basis vectors in the kernel-induced feature space and the computational cost is independent of input dimensions. Furthermore, we prove the convergence and nonnegativity of decomposition of our method. Extensive experiments compared with PNMF and other NMF algorithms on several face databases, validate the effectiveness of the proposed method.

Event detection is a critical task in sensor networks for a variety of real-world applications. Many real-world events often exhibit complex spatio-temporal patterns whereby they manifest themselves via observations over time and space proximities. These spatio-temporal events cannot be handled well by many of the previous approaches. In this paper, we propose a new Spatio-Temporal Event Detection (STED) algorithm in sensor networks based on a dynamic conditional random field (DCRF) model. Our STED method handles the uncertainty of sensor data explicitly and permits neighborhood interactions in both observations and event labels. Experiments on both real data and synthetic data demonstrate that our STED method can provide accurate event detection in near real time even for large-scale sensor networks.

Distance metric has an important role in many machine learning algorithms. Recently, metric learning for semi-supervised algorithms has received much attention. For semi-supervised clustering, usually a set of pairwise similarity and dissimilarity constraints is provided as supervisory information. Until now, various metric learning methods utilizing pairwise constraints have been proposed. The existing methods that can consider both positive (must-link) and negative (cannot-link) constraints find linear transformations or equivalently global Mahalanobis metrics. Additionally, they find metrics only according to the data points appearing in constraints (without considering other data points). In this paper, we consider the topological structure of data along with both positive and negative constraints. We propose a kernel-based metric learning method that provides a non-linear transformation. Experimental results on synthetic and real-world data sets show the effectiveness of our metric learning method.

Domain adaptation solves a learning problem in a target domain by utilizing the training data in a different but related source domain. Intuitively, discovering a good feature representation across domains is crucial. In this paper, we propose to find such a representation through a new learning method, transfer component analysis ( TCA ), for domain adaptation. TCA tries to learn some transfer components across domains in a Reproducing Kernel Hilbert Space (RKHS) using Maximum Mean Discrepancy (MMD). In the subspace spanned by these transfer components , data distributions in different domains are close to each other. As a result, with the new representations in this subspace, we can apply standard machine learning methods to train classifiers or regression models in the source domain for use in the target domain. The main contribution of our work is that we propose a novel feature representation in which to perform domain adaptation via a new parametric kernel using feature extraction methods, which can dramatically minimize the distance between domain distributions by projecting data onto the learned transfer components . Furthermore, our approach can handle large datsets and naturally lead to out-of-sample generalization. The effectiveness and efficiency of our approach in are verified by experiments on two real-world applications: cross-domain indoor WiFi localization and cross-domain text classification.

Sparse coding is an unsupervised learning algorithm for finding concise, slightly higher-level representations of inputs, and has been successfully applied to self-taught learning, where the goal is to use unlabeled data to help on a supervised learning task, even if the unlabeled data cannot be associated with the labels of the supervised task (Raina et al., 2007). However, sparse coding uses a Gaussian noise model and a quadratic loss function, and thus performs poorly if applied to binary valued, integer valued, or other non-Gaussian data, such as text. Drawing on ideas from generalized linear models (GLMs), we present a generalization of sparse coding to learning with data drawn from any exponential family distribution (such as Bernoulli, Poisson, etc). This gives a method that we argue is much better suited to model other data types than Gaussian. We present an algorithm for solving the L1-regularized optimization problem defined by this model, and show that it is especially efficient when the optimal solution is sparse. We also show that the new model results in significantly improved self-taught learning performance when applied to text classification and to a robotic perception task.

Random Forests have been shown to perform very well in propositional learning.  FORF is an upgrade of Random Forests for relational data. In this paper we investigate shortcomings of FORF and propose an alternative algorithm, RF, for generating Random Forests over relational data. RF employs randomly generated relational rules as fully self-contained Boolean tests inside each node in a tree and thus can be viewed as an instance of dynamic propositionalization.  The implementation of RF allows for the simultaneous or parallel growth of all the branches of all the trees in the ensemble in an efficient shared, but still single-threaded way.  Experiments favorably compare RF to both FORF and the combination of static propositionalization together with standard Random Forests. Various strategies for tree initialization and splitting of nodes, as well as resulting ensemble size, diversity, and computational complexity of RF are also investigated.

Modal correspondence theory is a powerful and effective way to guarantee that adding specific syntactic axioms to a modal logic is mirrored by requiring 'corresponding' properties of the underlying Kripke models. However, such axioms not only  quantify over all formulas, but they are also global  in the sense that the corresponding semantic property is assumed to hold for all states. However, in  for instance epistemic logic one would like to have  the flexibility to say that certain properties (like "agent b knows at least what agent a knows") are  true locally in a specific state, but not necessarily  globally, in all states. This would enable one to  say "currently, b knows at least what a knows, but  this is not common knowledge," or ". . . but this is  not always true," or ". . . but this could be changed  by action α." We offer a logic for "knowing at least  as," where the (global) axiom scheme Ka ϕ → Kb ϕ  is replaced by a (local) inference rule. We give  a complete modal system, and discuss some consequences of the axiom in an epistemic setting.  Our completeness proof also suggests how achieving such local properties can be generalized to other  axioms schemes and modal logics. 

This paper considers the problem of composing or scheduling several (non-deterministic) behaviors so as to conform to a specified target behavior as well as satisfying constraints imposed by the environment in which the behaviors are to be performed. This problem has already been considered by several works in the literature and applied to areas such as web service composition, the composition of robot behaviors and co-ordination of distributed devices. We develop a sound and complete algorithm for determining such a composition which has a number of significant advantages over previous proposals: a) our algorithm is different from previous proposals which resort to dynamic logic or simulation relations, b) we realized an implementation in Java as opposed to other approaches for which there are no known implementations, c) our algorithm determines all possible schedulers at once, and d) we can use our framework to define a notion of approximation when the target behavior cannot be realized.

We look at composition of (possibly nonterminating) high-level programs over situation calculus action theories. Specifically the problem we look at is as follows: given a library of available ConGolog programs and a target program not in the library, verify whether the target program executions be realized by composing fragments of the executions of the available programs; and, if so, synthesize a controller that does the composition automatically. This kind of composition problems have been investigated in the CS and AI literature, but always assuming finite states settings. Here, instead, we investigate the issue in the context of infinite domains that may go through an infinite number of states as a result of actions.  Obviously in this context the problem is undecidable. Nonetheless, by exploiting recent results in the AI literature, we devise a sound and well characterized technique to actually solve the problem.

Calendar management tools assist users with coordinating their daily life. Different tasks have to be scheduled according to the user preferences. In many cases, tasks are at different locations and travel times have to be considered. Therefore, these kinds of calendar management problems can be regarded as spatio-temporal optimisation problems and are often variants of traveling salesman problems (TSP) or vehicle routing problems. While standard TSPs require a solution to include all tasks, prize-collecting TSPs are more suited for calendar management problems as they require a solution that optimises the total sum of prizes we assigned to tasks at different locations. If we now add time windows that limit when tasks can occur, these prize-collecting TSPs with time windows (TW-TSP) are excellent abstractions of spatio-temporal optimisation problems such as calendar management. Due to the inherent complexity of TW-TSPs, the existing literature considers mainly approximation algorithms or special cases. We present a novel algorithm for TW-TSPs that enables us to find the optimal solution to TW-TSP problems occurring in real-world calendar management applications efficiently. Our algorithm is a fixed-parameter tractable algorithm that depends on the maximal number of tasks that can be revisited from some other task, a parameter which is small in the application scenario we consider.