We describe a data complexity approach to kernel selection based on the behavior of polynomial and Gaussian kernels. Our resultsshow how the use of a Gaussian kernel produces a gram matrix with useful local information that has no equivalent counterpart inpolynomial kernels.By exploiting neighborhood information embedded by data complexity measures, we are able to carry out a form of meta-generalization.Our goal is to predict which data sets are more favorable to particular kernels (Gaussian or polynomial).The end result is a framework to improve the model selection process in Support Vector Machines.

Dropout and other feature noising schemes have shown promising results in controlling over-fitting by artificially corrupting the training data. Though extensive theoretical and empirical studies have been performed for generalized linear models, little work has been done for support vector machines (SVMs), one of the most successful approaches for supervised learning. This paper presents dropout training for linear SVMs. To deal with the intractable expectation of the non-smooth hinge loss under corrupting distributions, we develop an iteratively re-weighted least square (IRLS) algorithm by exploring data augmentation techniques. Our algorithm iteratively minimizes the expectation of a re-weighted least square problem, where the re-weights have closed-form solutions. The similar ideas are applied to develop a new IRLS algorithm for the expected logistic loss under corrupting distributions. Our algorithms offer insights on the connection and difference between the hinge loss and logistic loss in dropout training. Empirical results on several real datasets demonstrate the effectiveness of dropout training on significantly boosting the classification accuracy of linear SVMs.

A combination of the sparse coding and transfer learning techniques was shown to be accurate and robust in classification tasks where training and testing objects have a shared feature space but are sampled from different underlying distributions, i.e., belong to different domains. The key assumption in such case is that in spite of the domain disparity, samples from different domains share some common hidden factors. Previous methods often assumed that all the objects in the target domain are unlabeled, and thus the training set solely comprised objects from the source domain. However, in real world applications, the target domain often has some labeled objects, or one can always manually label a small number of them. In this paper, we explore such possibility and show how a small number of labeled data in the target domain can significantly leverage classification accuracy of the state-of-the-art transfer sparse coding methods. We further propose a unified framework named supervised transfer sparse coding (STSC) which simultaneously optimizes sparse representation, domain transfer and classification. Experimental results on three applications demonstrate that a little manual labeling and then learning the model in a supervised fashion can significantly improve classification accuracy.

Recent literature has demonstrated the difficulty of classifying between composers who write in extremely similar styles (homogeneous style). Additionally, machine learning studies in this field have been exclusively of technical import with little musicological interpretability or significance. We present a supervised machine learning system which addresses the difficulty of differentiating between stylistically homogeneous composers using foundational elements of music, their complexity and interaction. Our work expands on previous style classification studies by developing more complex features as well as introducing a new class of musical features which focus on local irregularities within musical scores. We demonstrate the discriminative power of the system as applied to Haydn and Mozart's string quartets. Our results yield interpretable musicological conclusions about Haydn's and Mozart's stylistic differences while distinguishing between the composers with higher accuracy than previous studies in this domain.

Trust has been used to replace or complement rating-based similarity in recommender systems, to improve the accuracy of rating prediction. However, people trusting each other may not always share similar preferences. In this paper, we try to fill in this gap by decomposing the original single-aspect trust information into four general trust aspects, i.e. benevolence, integrity, competence, and predictability, and further employing the support vector regression technique to incorporate them into the probabilistic matrix factorization model for rating prediction in recommender systems. Experimental results on four datasets demonstrate the superiority of our method over the state-of-the-art approaches.

Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g., support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as we will show-is universal, which limits their ability to approximate a target function arbitrarily well. Here, we introduce several positive definite Grassmannian kernels, including universal ones, and demonstrate their superiority over previously-known kernels in various tasks, such as classification, clustering, sparse coding and hashing.

Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size of the data. Many natural measures of similarity between pairs of samples are not PSD e.g. invariant kernels, and those that are implicitly or explicitly defined by latent variable models. In this paper, we investigate scalable approaches for using indefinite similarity measures in large margin frameworks. In particular we show that a normalization of similarity to a subset of the data points constitutes a representation suitable for linear classifiers. The result is a classifier which is competitive to kernelized SVM in terms of accuracy, despite having better training and test time complexities. Experimental results demonstrate that on CIFAR-10 dataset, the model equipped with similarity measures invariant to rigid and non-rigid deformations, can be made more than 5 times sparser while being more accurate than kernelized SVM using RBF kernels.

Dimensionality reduction (DR) is often used as a preprocessing step in classification, but usually one first fixes the DR mapping, possibly using label information, and then learns a classifier (a filter approach). Best performance would be obtained by optimizing the classification error jointly over DR mapping and classifier (a wrapper approach), but this is a difficult nonconvex problem, particularly with nonlinear DR. Using the method of auxiliary coordinates, we give a simple, efficient algorithm to train a combination of nonlinear DR and a classifier, and apply it to a RBF mapping with a linear SVM. This alternates steps where we train the RBF mapping and a linear SVM as usual regression and classification, respectively, with a closed-form step that coordinates both. The resulting nonlinear low-dimensional classifier achieves classification errors competitive with the state-of-the-art but is fast at training and testing, and allows the user to trade off runtime for classification accuracy easily. We then study the role of nonlinear DR in linear classification, and the interplay between the DR mapping, the number of latent dimensions and the number of classes. When trained jointly, the DR mapping takes an extreme role in eliminating variation: it tends to collapse classes in latent space, erasing all manifold structure, and lay out class centroids so they are linearly separable with maximum margin.

Electronic discovery is an interesting subproblem of information retrieval in which one identifies documents that are potentially relevant to issues and facts of a legal case from an electronically stored document collection (a corpus). In this paper, we consider representing documents in a topic space using the well-known topic models such as latent Dirichlet allocation and latent semantic indexing, and solving the information retrieval problem via finding document similarities in the topic space rather doing it in the corpus vocabulary space. We also develop an iterative SMART ranking and categorization framework including human-in-the-loop to label a set of seed (training) documents and using them to build a semi-supervised binary document classification model based on Support Vector Machines. To improve this model, we propose a method for choosing seed documents from the whole population via an active learning strategy. We report the results of our experiments on a real dataset in the electronic discovery domain.

This paper presents a study where semantic frames are used to mine financial news so as to quantify the impact of news on the stock market. We represent news documents in a novel semantic tree structure and use tree kernel support vector machines to predict the change of stock price. We achieve an efficient computation through linearization of tree kernels. In addition to two binary classification tasks, we rank news items according to their probability to affect change of price using two ranking methods that require vector space features. We evaluate our rankings based on receiver operating characteristic curves and analyze the predictive power of our semantic features. For both learning tasks, the proposed semantic features provide superior results.