We shed light on the discrimination between patterns belonging to two different classes by casting this decoding problem into a generalized prototype framework. The discrimination process is then separated into two stages: a projection stage that reduces the dimensionality of the data by projecting it on a line and a threshold stage where the distributions of the projected patterns of both classes are separated. For this, we extend the popular mean-of-class prototype classification using algorithms from machine learning that satisfy a set of invariance properties. We report a simple yet general approach to express different types of linear classification algorithms in an identical and easy-to-visualize formal framework using generalized prototypes where these prototypes are used to express the normal vector and offset of the hyperplane. We investigate non-margin classifiers such as the classical prototype classifier, the Fisher classifier, and the relevance vector machine. We then study hard and soft margin classifiers such as the support vector machine and a boosted version of the prototype classifier. Subsequently, we relate mean-of-class prototype classification to other classification algorithms by showing that the prototype classifier is a limit of any soft margin classifier and that boosting a prototype classifier yields the support vector machine. While giving novel insights into classification per se by presenting a common and unified formalism, our generalized prototype framework also provides an efficient visualization and a principled comparison of machine learning classification.

We attempt to shed light on the algorithms humans use to classify images of human faces according to their gender. For this, a novel methodology combining human psychophysics and machine learning is introduced. We proceed as follows. First, we apply principal component analysis (PCA) on the pixel information of the face stimuli. We then obtain a data set composed of these PCA eigenvectors combined with the subjects' gender estimates of the corresponding stimuli. Second, we model the gender classification process on this data set using a separating hyperplane (SH) between both classes. This SH is computed using algorithms from machine learning: the support vector machine (SVM), the relevance vector machine, the prototype classifier, and the K-means classifier. The classification behavior of humans and machines is then analyzed in three steps. First, the classification errors of humans and machines are compared for the various classifiers, and we also assess how well machines can recreate the subjects' internal decision boundary by studying the training errors of the machines. Second, we study the correlations between the rank-order of the subjects' responses to each stimulus-the gender estimate with its reaction time and confidence rating-and the rank-order of the distance of these stimuli to the SH. Finally, we attempt to compare the metric of the representations used by humans and machines for classification by relating the subjects' gender estimate of each stimulus and the distance of this stimulus to the SH. While we show that the classification error alone is not a sufficient selection criterion between the different algorithms humans might use to classify face stimuli, the distance of these stimuli to the SH is shown to capture essentials of the internal decision space of humans. Furthermore, algorithms such as the prototype classifier using stimuli in the center of the classes are shown to be less adapted to model human classification behavior than algorithms such as the SVM based on stimuli close to the boundary between the classes.

We study gender discrimination of human faces using a combination of psychophysical classification and discrimination experiments together with methods from machine learning. We reduce the dimensionality of a set of face images using principal component analysis, and then train a set of linear classifiers on this reduced representation (linear support vec- tor machines (SVMs), relevance vector machines (RVMs), Fisher linear discriminant (FLD), and prototype (prot) classifiers) using human clas- sification data. Because we combine a linear preprocessor with linear classifiers, the entire system acts as a linear classifier, allowing us to visu- alise the decision-image corresponding to the normal vector of the separ- ating hyperplanes (SH) of each classifier. We predict that the female-to- maleness transition along the normal vector for classifiers closely mim- icking human classification (SVM and RVM [1]) should be faster than the transition along any other direction. A psychophysical discrimina- tion experiment using the decision images as stimuli is consistent with this prediction.

Recent developments in computer vision have shown that local features can provide efficient representations suitable for robust object recognition. Support vector machines have been established as powerful learning algorithms with good generalization capabilities. We combine these two approaches and propose a general kernel method for recognition with local features. We show that the proposed kernel satisfies the Mercer condition and that it is, suitable for many established local feature frameworks. Large-scale recognition results are presented on three different databases, which demonstrate that SVMs with the proposed kernel perform better than standard matching techniques on local features. In addition, experiments on noisy and occluded images show that local feature representations significantly outperform global approaches.

We attempt to understand visual classification in humans using both psy- chophysical and machine learning techniques. Frontal views of human faces were used for a gender classification task. Human subjects classi- fied the faces and their gender judgment, reaction time and confidence rating were recorded. Several hyperplane learning algorithms were used on the same classification task using the Principal Components of the texture and shape representation of the faces. The classification perfor- mance of the learning algorithms was estimated using the face database with the true gender of the faces as labels, and also with the gender es- timated by the subjects. We then correlated the human responses to the distance of the stimuli to the separating hyperplane of the learning algo- rithms. Our results suggest that human classification can be modeled by some hyperplane algorithms in the feature space we used. For classifica- tion, the brain needs more processing for stimuli close to that hyperplane than for those further away.

This paper discusses classification using support vector machines in a normalized feature space. We consider both normalization in input space and in feature space. Exploiting the fact that in this setting all points lie on the surface of a unit hypersphere we replace the optimal separating hyperplane by one that is symmetric in its angles, leading to an improved estimator. Evaluation of these considerations is done in numerical experiments on two real-world datasets. The stability to noise of this offset correction is subsequently investigated as well as its optimality.