We propose one-class support measure machines (OCSMMs) for group anomaly detection which aims at recognizing anomalous aggregate behaviors of data points. The OCSMMs generalize well-known one-class support vector machines (OCSVMs) to a space of probability measures. By formulating the problem as quantile estimation on distributions, we can establish an interesting connection to the OCSVMs and variable kernel density estimators (VKDEs) over the input space on which the distributions are defined, bridging the gap between large-margin methods and kernel density estimators. In particular, we show that various types of VKDEs can be considered as solutions to a class of regularization problems studied in this paper. Experiments on Sloan Digital Sky Survey dataset and High Energy Particle Physics dataset demonstrate the benefits of the proposed framework in real-world applications.

Linear classifiers separate the data with a hyperplane. In this paper we focus on the novel method of construction of multithreshold linear classifier, which separates the data with multiple parallel hyperplanes. Proposed model is based on the information theory concepts -- namely Renyi's quadratic entropy and Cauchy-Schwarz divergence. We begin with some general properties, including data scale invariance. Then we prove that our method is a multithreshold large margin classifier, which shows the analogy to the SVM, while in the same time works with much broader class of hypotheses. What is also interesting, proposed method is aimed at the maximization of the balanced quality measure (such as Matthew's Correlation Coefficient) as opposed to very common maximization of the accuracy. This feature comes directly from the optimization problem statement and is further confirmed by the experiments on the UCI datasets. It appears, that our Multithreshold Entropy Linear Classifier (MELC) obtaines similar or higher scores than the ones given by SVM on both synthetic and real data. We show how proposed approach can be benefitial for the cheminformatics in the task of ligands activity prediction, where despite better classification results, MELC gives some additional insight into the data structure (classes of underrepresented chemical compunds).

Patients with diabetes must continually monitor their blood glucose levels and adjust insulin doses, striving to keep blood glucose levels as close to normal as possible. Blood glucose levels that deviate from the normal range can lead to serious short-term and long-term complications. An automatic prediction model that warned people of imminent changes in their blood glucose levels would enable them to take preventive action. In this paper, we describe a solution that uses a generic physiological model of blood glucose dynamics to generate informative features for a Support Vector Regression model that is trained on patient specific data. The new model outperforms diabetes experts at predicting blood glucose levels and could be used to anticipate almost a quarter of hypoglycemic events 30 minutes in advance. Although the corresponding precision is currently just 42%, most false alarms are in near-hypoglycemic regions and therefore patients responding to these hypoglycemia alerts would not be harmed by intervention.

Resting state functional magnetic resonance imaging (rsfMRI) is a powerful tool for investigating intrinsic and spontaneous brain activity. The application of univariate and multivariate methods such as multi voxel pattern analysis has been instrumental in localizing neural correlates to various cognitive states and psychiatric disease. However, many existing methods of rsfMRI analysis are insufficient for investigating the true mechanism of brain activity since they make implicit assumptions that are agnostic of the temporal and spatial dynamics of brain activity. The proposed method aims to create a superior feature space for representing brain activity using k-means and to create interpretable generalizations on these features for studying group differences using support vector machine classifiers.​

The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for complex-valued data and considers two cases: a) the complex data are split into their real and imaginary parts and a typical real kernel is employed to map the complex data to a complexified feature space and b) a pure complex kernel is used to directly map the data to the induced complex feature space. The recently developed Wirtinger's calculus on complex reproducing kernel Hilbert spaces (RKHS) is employed in order to compute the Lagrangian and derive the dual optimization problem. As one of our major results, we prove that any complex SVM/SVR task is equivalent with solving two real SVM/SVR tasks exploiting a specific real kernel which is generated by the chosen complex kernel. In particular, the case of pure complex kernels leads to the generation of new kernels, which have not been considered before. In the classification case, the proposed framework inherently splits the complex space into four parts. This leads naturally in solving the four class-task (quaternary classification), instead of the typical two classes of the real SVM. In turn, this rationale can be used in a multiclass problem as a split-class scenario based on four classes, as opposed to the one-versus-all method; this can lead to significant computational savings. Experiments demonstrate the effectiveness of the proposed framework for regression and classification tasks that involve complex data.

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.

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.

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.

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.