We describe an algorithm for learning bilinear SVMs. Bilinear classifiers are a discriminative variant of bilinear models, which capture the dependence of data on multiple factors. Such models are particularly appropriate for visual data that is better represented as a matrix or tensor, rather than a vector. Matrix encodings allow for more natural regularization through rank restriction. For example, a rank-one scanning-window classifier yields a separable filter. Low-rank models have fewer parameters and so are easier to regularize and faster to score at run-time. We learn low-rank models with bilinear classifiers. We also use bilinear classifiers for transfer learning by sharing linear factors between different classification tasks. Bilinear classifiers are trained with biconvex programs. Such programs are optimized with coordinate descent, where each coordinate step requires solving a convex program - in our case, we use a standard off-the-shelf SVM solver. We demonstrate bilinear SVMs on difficult problems of people detection in video sequences and action classification of video sequences, achieving state-of-the-art results in both.

Learning distance functions with side information plays a key role in many machine learning and data mining applications. Conventional approaches often assume a Mahalanobis distance function. These approaches are limited in two aspects: (i) they are computationally expensive (even infeasible) for high dimensional data because the size of the metric is in the square of dimensionality; (ii) they assume a fixed metric for the entire input space and therefore are unable to handle heterogeneous data. In this paper, we propose a novel scheme that learns nonlinear Bregman distance functions from side information using a non-parametric approach that is similar to support vector machines. The proposed scheme avoids the assumption of fixed metric because its local distance metric is implicitly derived from the Hessian matrix of a convex function that is used to generate the Bregman distance function. We present an efficient learning algorithm for the proposed scheme for distance function learning. The extensive experiments with semi-supervised clustering show the proposed technique (i) outperforms the state-of-the-art approaches for distance function learning, and (ii) is computationally efficient for high dimensional data.

In classification problems, Support Vector Machines maximize the margin of separation between two classes. While the paradigm has been successful, the solution obtained by SVMs is dominated by the directions with large data spread and biased to separate the classes by cutting along large spread directions. This article proposes a novel formulation to overcome such sensitivity and maximizes the margin relative to the spread of the data. The proposed formulation can be efficiently solved and experiments on digit datasets show drastic performance improvements over SVMs.

The cluster assumption is exploited by most semi-supervised learning (SSL) methods. However, if the unlabeled data is merely weakly related to the target classes, it becomes questionable whether driving the decision boundary to the low density regions of the unlabeled data will help the classification. In such case, the cluster assumption may not be valid; and consequently how to leverage this type of unlabeled data to enhance the classification accuracy becomes a challenge. We introduce Semi-supervised Learning with Weakly-Related Unlabeled Data" (SSLW), an inductive method that builds upon the maximum-margin approach, towards a better usage of weakly-related unlabeled information. Although the SSLW could improve a wide range of classification tasks, in this paper, we focus on text categorization with a small training pool. The key assumption behind this work is that, even with different topics, the word usage patterns across different corpora tends to be consistent. To this end, SSLW estimates the optimal word-correlation matrix that is consistent with both the co-occurrence information derived from the weakly-related unlabeled documents and the labeled documents. For empirical evaluation, we present a direct comparison with a number of state-of-the-art methods for inductive semi-supervised learning and text categorization; and we show that SSLW results in a significant improvement in categorization accuracy, equipped with a small training set and an unlabeled resource that is weakly related to the test beds."

Much recent work in bioinformatics has focused on the inference of various types of biological networks, representing gene regulation, metabolic processes, protein-protein interactions, etc. A common setting involves inferring network edges in a supervised fashion from a set of high-confidence edges, possibly characterized by multiple, heterogeneous data sets (protein sequence, gene expression, etc.). Here, we distinguish between two modes of inference in this setting: direct inference based upon similarities between nodes joined by an edge, and indirect inference based upon similarities between one pair of nodes and another pair of nodes. We propose a supervised approach for the direct case by translating it into a distance metric learning problem. A relaxation of the resulting convex optimization problem leads to the support vector machine (SVM) algorithm with a particular kernel for pairs, which we call the metric learning pairwise kernel (MLPK). We demonstrate, using several real biological networks, that this direct approach often improves upon the state-of-the-art SVM for indirect inference with the tensor product pairwise kernel.

Predictive learning has traditionally been a standard indu ctive learning, where different sub-problem formulations have been identified. One of the most re presentative is classification, consisting on the estimation of a mapping from the feature sp ace into a finite class space. Depending on the cardinality of the finite class space we are l eft with binary or multiclass classification problems. Finally, the presence or absence o r a "natural" order among classes will separate nominal from ordinal problems. Although two-class and nominal classification problems hav e been dissected in the literature, the ordinal sibling has not yet received a lot of attention, e ven with many learning problems involving classifying examples into classes which have a na tural order. Scenarios in which it is natural to rank instances occur in many fields, such as info rmation retrieval, collaborative filtering, econometric modeling and natural sciences. Conventional methods for nominal classes or for regression problems could be employed to solve ordinal data problems; however, the use of techniques designed specifically for ordered classes yields simpler classifiers, making it easier to inte rpret the factors that are being used to discriminate among classes, and generalises better. Alt hough the ordinal formulation seems conceptually simpler than nominal, some technical di fficulties to incorporate in the algorithms this piece of additional information - the order - may explain the widespread use of conventional methods to tackle the ordinal data problem. This dissertation addresses this void by proposing a nonpar ametric procedure for the classification of ordinal data based on the extension of the original dataset with additional variables, reducing the classification task to the well-known two-clas s problem.

This paper presents a novel approach for using clickthrough data to learn ranked retrieval functions for web search results. We observe that users searching the web often perform a sequence, or chain, of queries with a similar information need. Using query chains, we generate new types of preference judgments from search engine logs, thus taking advantage of user intelligence in reformulating queries. To validate our method we perform a controlled user study comparing generated preference judgments to explicit relevance judgments. We also implemented a real-world search engine to test our approach, using a modified ranking SVM to learn an improved ranking function from preference data. Our results demonstrate significant improvements in the ranking given by the search engine. The learned rankings outperform both a static ranking function, as well as one trained without considering query chains.

Experimental physics, along with many other fields in applied and basic research, uses experiments, physical tests, and observations to gain insight into various phenomena and to validate hypotheses and models. Shock p hysics is a field that explores the response of materials to the extremes of p ressure, deformation, and temperature which are present when shock waves interact with those materials [17]. High explosive (HE) or propellant guns are often used to generate these strong shock waves. Many different diagnostic ap proaches have been used to probe these phenomena [8]. Because of the energetic nature of the shock wave drive, often a large amount of experimental equipment is destroyed during the test.

This paper deals with the problem of classifying signals. The new method for building so called local classifiers and local features is presented. The method is a combination of the lifting scheme and the support vector machines. Its main aim is to produce effective and yet comprehensible classifiers that would help in understanding processes hidden behind classified signals. To illustrate the method we present the results obtained on an artificial and a real dataset.

From a geometric perspective most nonlinear binary classification algorithms, including state of the art versions of Support Vector Machine (SVM) and Radial Basis Function Network (RBFN) classifiers, and are based on the idea of reconstructing indicator functions. We propose instead to use reconstruction of the signed distance function (SDF) as a basis for binary classification. We discuss properties of the signed distance function that can be exploited in classification algorithms. We develop simple versions of such classifiers and test them on several linear and nonlinear problems. On linear tests accuracy of the new algorithm exceeds that of standard SVM methods, with an average of 50% fewer misclassifications. Performance of the new methods also matches or exceeds that of standard methods on several nonlinear problems including classification of benchmark diagnostic micro-array data sets.