In many applications involving multi-media data, the definition of similarity between items is integral to several key tasks, e.g., nearest-neighbor retrieval, classification, and recommendation. Data in such regimes typically exhibits multiple modalities, such as acoustic and visual content of video. Integrating such heterogeneous data to form a holistic similarity space is therefore a key challenge to be overcome in many real-world applications. We present a novel multiple kernel learning technique for integrating heterogeneous data into a single, unified similarity space. Our algorithm learns an optimal ensemble of kernel transfor- mations which conform to measurements of human perceptual similarity, as expressed by relative comparisons. To cope with the ubiquitous problems of subjectivity and inconsistency in multi- media similarity, we develop graph-based techniques to filter similarity measurements, resulting in a simplified and robust training procedure.

The Aviation Safety Reporting System collects voluntarily submitted reports on aviation safety incidents to facilitate research work aiming to reduce such incidents. To effectively reduce these incidents, it is vital to accurately identify why these incidents occurred. More precisely, given a set of possible causes, or shaping factors, this task of cause identification involves identifying all and only those shaping factors that are responsible for the incidents described in a report. We investigate two approaches to cause identification. Both approaches exploit information provided by a semantic lexicon, which is automatically constructed via Thelen and Riloff's Basilisk framework augmented with our linguistic and algorithmic modifications. The first approach labels a report using a simple heuristic, which looks for the words and phrases acquired during the semantic lexicon learning process in the report. The second approach recasts cause identification as a text classification problem, employing supervised and transductive text classification algorithms to learn models from incident reports labeled with shaping factors and using the models to label unseen reports. Our experiments show that both the heuristic-based approach and the learning-based approach (when given sufficient training data) outperform the baseline system significantly.

Support vector machines (SVMs) are invaluable tools for many practical applications in artificial intelligence, e.g., classification and event recognition. However, popular SVM solvers are not sufficiently efficient for applications with a great deal of samples as well as a large number of features. In this paper, thus, we present NESVM, a fast gradient SVM solver that can optimize various SVM models, e.g., classical SVM, linear programming SVM and least square SVM. Compared against SVM-Perf \cite{SVM_Perf}\cite{PerfML} (its convergence rate in solving the dual SVM is upper bounded by $\mathcal O(1/\sqrt{k})$, wherein $k$ is the number of iterations.) and Pegasos \cite{Pegasos} (online SVM that converges at rate $\mathcal O(1/k)$ for the primal SVM), NESVM achieves the optimal convergence rate at $\mathcal O(1/k^{2})$ and a linear time complexity. In particular, NESVM smoothes the non-differentiable hinge loss and $\ell_1$-norm in the primal SVM. Then the optimal gradient method without any line search is adopted to solve the optimization. In each iteration round, the current gradient and historical gradients are combined to determine the descent direction, while the Lipschitz constant determines the step size. Only two matrix-vector multiplications are required in each iteration round. Therefore, NESVM is more efficient than existing SVM solvers. In addition, NESVM is available for both linear and nonlinear kernels. We also propose "homotopy NESVM" to accelerate NESVM by dynamically decreasing the smooth parameter and using the continuation method. Our experiments on census income categorization, indoor/outdoor scene classification, event recognition and scene recognition suggest the efficiency and the effectiveness of NESVM. The MATLAB code of NESVM will be available on our website for further assessment.

Kernel Induced Random Survival Forests (KIRSF) is a statistical learning algorithm which aims to improve prediction accuracy for survival data. As in Random Survival Forests (RSF), Cumulative Hazard Function is predicted for each individual in the test set. Prediction error is estimated using Harrell's concordance index (C index) [Harrell et al. (1982)]. The C-index can be interpreted as a misclassification probability and does not depend on a single fixed time for evaluation. The C-index also specifically accounts for censoring. By utilizing kernel functions, KIRSF achieves better results than RSF in many situations. In this report, we show how to incorporate kernel functions into RSF. We test the performance of KIRSF and compare our method to RSF. We find that the KIRSF's performance is better than RSF in many occasions.

Following a review of metric, ultrametric and generalized ultrametric, we review their application in data analysis. We show how they allow us to explore both geometry and topology of information, starting with measured data. Some themes are then developed based on the use of metric, ultrametric and generalized ultrametric in logic. In particular we study approximation chains in an ultrametric or generalized ultrametric context. Our aim in this work is to extend the scope of data analysis by facilitating reasoning based on the data analysis; and to show how quantitative and qualitative data analysis can be incorporated into logic programming.

We extend the mixtures of Gaussians (MOG) model to the projected mixture of Gaussians (PMOG) model. In the PMOG model, we assume that q dimensional input data points z_i are projected by a q dimensional vector w into 1-D variables u_i. The projected variables u_i are assumed to follow a 1-D MOG model. In the PMOG model, we maximize the likelihood of observing u_i to find both the model parameters for the 1-D MOG as well as the projection vector w. First, we derive an EM algorithm for estimating the PMOG model. Next, we show how the PMOG model can be applied to the problem of blind source separation (BSS). In contrast to conventional BSS where an objective function based on an approximation to differential entropy is minimized, PMOG based BSS simply minimizes the differential entropy of projected sources by fitting a flexible MOG model in the projected 1-D space while simultaneously optimizing the projection vector w. The advantage of PMOG over conventional BSS algorithms is the more flexible fitting of non-Gaussian source densities without assuming near-Gaussianity (as in conventional BSS) and still retaining computational feasibility.

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing image acquisition in magnetic resonance scanners, can be addressed by querying the SLM posterior covariance, unrelated to the density's mode. We propose a scalable algorithmic framework, with which SLM posteriors over full, high-resolution images can be approximated for the first time, solving a variational optimization problem which is convex iff posterior mode finding is convex. These methods successfully drive the optimization of sampling trajectories for real-world magnetic resonance imaging through Bayesian experimental design, which has not been attempted before. Our methodology provides new insight into similarities and differences between sparse reconstruction and approximate Bayesian inference, and has important implications for compressive sensing of real-world images.

Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many signal and image processing tasks. It is now well understood that the choice of the sparsity regularization term is critical in the success of such models. Based on a codelength minimization interpretation of sparse coding, and using tools from universal coding theory, we propose a framework for designing sparsity regularization terms which have theoretical and practical advantages when compared to the more standard l0 or l1 ones. The presentation of the framework and theoretical foundations is complemented with examples that show its practical advantages in image denoising, zooming and classification.

As increasing amounts of sensitive personal information is aggregated into data repositories, it has become important to develop mechanisms for processing the data without revealing information about individual data instances. The differential privacy model provides a framework for the development and theoretical analysis of such mechanisms. In this paper, we propose an algorithm for learning a discriminatively trained multi-class Gaussian classifier that satisfies differential privacy using a large margin loss function with a perturbed regularization term. We present a theoretical upper bound on the excess risk of the classifier introduced by the perturbation.

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.