Mixture of latent trait analyzers for model-based clustering of categorical data

Model-based clustering methods for continuous data are well established and commonly used in a wide range of applications. However, model-based clustering methods for categorical data are less standard. Latent class analysis is a commonly used method for model-based clustering of binary data and/or categorical data, but due to an assumed local independence structure there may not be a correspondence between the estimated latent classes and groups in the population of interest. The mixture of latent trait analyzers model extends latent class analysis by assuming a model for the categorical response variables that depends on both a categorical latent class and a continuous latent trait variable; the discrete latent class accommodates group structure and the continuous latent trait accommodates dependence within these groups. Fitting the mixture of latent trait analyzers model is potentially difficult because the likelihood function involves an integral that cannot be evaluated analytically. We develop a variational approach for fitting the mixture of latent trait models and this provides an efficient model fitting strategy. The mixture of latent trait analyzers model is demonstrated on the analysis of data from the National Long Term Care Survey (NLTCS) and voting in the U.S. Congress. The model is shown to yield intuitive clustering results and it gives a much better fit than either latent class analysis or latent trait analysis alone

Recognizing two handed gestures with generative, discriminative and ensemble methods via Fisher kernels

Abstract. Use of gestures extends Human Computer Interaction (HCI) possibilities in multimodal environments. However, the great variability in gestures, both in time, size, and position, as well as interpersonal differences, makes the recognition task difficult. With their power in modeling sequence data and processing variable length sequences, modeling hand gestures using Hidden Markov Models (HMM) is a natural extension. On the other hand, discriminative methods such as Support Vector Machines (SVM), compared to model based approaches such as HMMs, have flexible decision boundaries and better classification performance. By extracting features from gesture sequences via Fisher Kernels based on HMMs, classification can be done by a discriminative classifier. We compared the performance of this combined classifier with generative and discriminative classifiers on a small database of two handed gestures recorded with two cameras. We used Kalman tracking of hands from two cameras using center-of-mass and blob tracking. The results show that (i) blob tracking incorporates general hand shape with hand motion and performs better than simple center-of-mass tracking, and (ii) in a stereo camera setup, even if 3D reconstruction is not possible, combining 2D information from each camera at feature level decreases the error rates, (iii) Fisher Score methodology combines the powers of generative and discriminative approaches and increases the classification performance.

Discriminative vs. generative classifiers for cost sensitive learning

This paper experimentally compares the performance of discriminative and generative classifiers for cost sensitive learning. There is some evidence that learning a discriminative classifier is more effective for a traditional classification task. This paper explores the advantages, and disadvantages, of using a generative classifier when the misclassification costs, and class frequencies, are not fixed. The paper details experiments built around commonly used algorithms modified to be cost sensitive. This allows a clear comparison to the same algorithm used to produce a discriminative classifier. The paper compares the performance of these different variants over multiple data sets and for the full range of misclassification costs and class frequencies. It concludes that although some of these variants are better than a single discriminative classifier, the right choice of training set distribution plus careful calibration are needed to make them competitive with multiple discriminative classifiers.

On discriminative joint density modeling

Abstract. We study discriminative joint density models, that is, generative models for the joint density p(c, x) learned by maximizing a discriminative cost function, the conditional likelihood. We use the framework to derive generative models for generalized linear models, including logistic regression, linear discriminant analysis, and discriminative mixture of unigrams. The benefits of deriving the discriminative models from joint density models are that it is easy to extend the models and interpret the results, and missing data can be treated using justified standard methods.