The odor transduction process has a large time constant and is susceptible to various types of noise. Therefore, the olfactory code at the sensor/receptor level is in general a slow and highly variable indicator of the input odor in both natural and artificial situations. Insects overcome this problem by using a neuronal device in their Antennal Lobe (AL), which transforms the identity code of olfactory receptors to a spatio-temporal code. This transformation improves the decision of the Mushroom Bodies (MBs), the subsequent classifier, in both speed and accuracy.Here we propose a rate model based on two intrinsic mechanisms in the insect AL, namely integration and inhibition. Then we present a MB classifier model that resembles the sparse and random structure of insect MB. A local Hebbian learning procedure governs the plasticity in the model. These formulations not only help to understand the signal conditioning and classification methods of insect olfactory systems, but also can be leveraged in synthetic problems. Among them, we consider here the discrimination of odor mixtures from pure odors. We show on a set of records from metal-oxide gas sensors that the cascade of these two new models facilitates fast and accurate discrimination of even highly imbalanced mixtures from pure odors.

We address the problem of learning classifiers when observations have multiple views, some of which may not be observed for all examples. We assume the existence of view generating functions which may complete the missing views in an approximate way. This situation corresponds for example to learning text classifiers from multilingual collections where documents are not available in all languages. In that case, Machine Translation (MT) systems may be used to translate each document in the missing languages. We derive a generalization error bound for classifiers learned on examples with multiple artificially created views. Our result uncovers a trade-off between the size of the training set, the number of views, and the quality of the view generating functions. As a consequence, we identify situations where it is more interesting to use multiple views for learning instead of classical single view learning. An extension of this framework is a natural way to leverage unlabeled multi-view data in semi-supervised learning. Experimental results on a subset of the Reuters RCV1/RCV2 collections support our findings by showing that additional views obtained from MT may significantly improve the classification performance in the cases identified by our trade-off.

Subspace-based learning problems involve data whose elements are linear subspaces of a vector space. To handle such data structures, Grassmann kernels have been proposed and used previously. In this paper, we analyze the relationship between Grassmann kernels and probabilistic similarity measures. Firstly, we show that the KL distance in the limit yields the Projection kernel on the Grassmann manifold, whereas the Bhattacharyya kernel becomes trivial in the limit and is suboptimal for subspace-based problems. Secondly, based on our analysis of the KL distance, we propose extensions of the Projection kernel which can be extended to the set of affine as well as scaled subspaces. We demonstrate the advantages of these extended kernels for classification and recognition tasks with Support Vector Machines and Kernel Discriminant Analysis using synthetic and real image databases.

Speaker comparison, the process of finding the speaker similarity between two speech signals, occupies a central role in a variety of applications---speaker verification, clustering, and identification. Speaker comparison can be placed in a geometric framework by casting the problem as a model comparison process. For a given speech signal, feature vectors are produced and used to adapt a Gaussian mixture model (GMM). Speaker comparison can then be viewed as the process of compensating and finding metrics on the space of adapted models. We propose a framework, inner product discriminant functions (IPDFs), which extends many common techniques for speaker comparison: support vector machines, joint factor analysis, and linear scoring. The framework uses inner products between the parameter vectors of GMM models motivated by several statistical methods. Compensation of nuisances is performed via linear transforms on GMM parameter vectors. Using the IPDF framework, we show that many current techniques are simple variations of each other. We demonstrate, on a 2006 NIST speaker recognition evaluation task, new scoring methods using IPDFs which produce excellent error rates and require significantly less computation than current techniques.

The learning of appropriate distance metrics is a critical problem in classification. In this work, we propose a boosting-based technique, termed BoostMetric, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used to enforce this constraint, but does not scale well. BoostMetric is instead based on a key observation that any positive semidefinite matrix can be decomposed into a linear positive combination of trace-one rank-one matrices. BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting method is easy to implement, does not require tuning, and can accommodate various types of constraints. Experiments on various datasets show that the proposed algorithm compares favorably to those state-of-the-art methods in terms of classification accuracy and running time.

We consider the problem of binary classification where the classifier may abstain instead of classifying each observation. The Bayes decision rule for this setup, known as Chow's rule, is defined by two thresholds on posterior probabilities. From simple desiderata, namely the consistency and the sparsity of the classifier, we derive the double hinge loss function that focuses on estimating conditional probabilities only in the vicinity of the threshold points of the optimal decision rule. We show that, for suitable kernel machines, our approach is universally consistent. We cast the problem of minimizing the double hinge loss as a quadratic program akin to the standard SVM optimization problem and propose an active set method to solve it efficiently. We finally provide preliminary experimental results illustrating the interest of our constructive approach to devising loss functions.

We propose a multiple incremental decremental algorithm of Support Vector Machine (SVM). Conventional single cremental decremental SVM can update the trained model efficiently when single data point is added to or removed from the training set. When we add and/or remove multiple data points, this algorithm is time-consuming because we need to repeatedly apply it to each data point. The roposed algorithm is computationally more efficient when multiple data points are added and/or removed simultaneously. The single incremental decremental algorithm is built on an optimization technique called parametric programming. We extend the idea and introduce multi-parametric programming for developing the proposed algorithm. Experimental results on synthetic and real data sets indicate that the proposed algorithm can significantly reduce the computational cost of multiple incremental decremental operation. Our approach is especially useful for online SVM learning in which we need to remove old data points and add new data points in a short amount of time.

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.