A Connection Between GRBF and MLP

Both multilayer perceptrons (MLP) and Generalized Radial Basis Functions (GRBF) have good approximation properties, theoretically and experimentally. Are they related? The main point of this paper is to show that for normalized inputs, multilayer perceptron networks are radial function networks (albeit with a non-standard radial function). This provides an interpretation of the weights w as centers t of the radial function network, and therefore as equivalent to templates. This insight may be useful for practical applications, including better initialization procedures for MLP. In the remainder of the paper, we discuss the relation between the radial functions that correspond to the sigmoid for normalized inputs and well-behaved radial basis functions, such as the Gaussian. In particular, we observe that the radial function associated with the sigmoid is an activation function that is good approximation to Gaussian basis functions for a range of values of the bias parameter. The implication is that a MLP network can always simulate a Gaussian GRBF network (with the same number of units but less parameters); the converse is true only for certain values of the bias parameter. Numerical experiments indicate that this constraint is not always satisfied in practice by MLP networks trained with backpropagation. Multiscale GRBF networks, on the other hand, can approximate MLP networks with a similar number of parameters.

A Trainable Object Detection System: Car Detection in Static Images

This paper describes a general, trainable architecture for object detection that has previously been applied to face and peoplesdetection with a new application to car detection in static images. Our technique is a learning based approach that uses a set of labeled training data from which an implicit model of an object class -- here, cars -- is learned. Instead of pixel representations that may be noisy and therefore not provide a compact representation for learning, our training images are transformed from pixel space to that of Haar wavelets that respond to local, oriented, multiscale intensity differences. These feature vectors are then used to train a support vector machine classifier. The detection of cars in images is an important step in applications such as traffic monitoring, driver assistance systems, and surveillance, among others. We show several examples of car detection on out-of-sample images and show an ROC curve that highlights the performance of our system.

Sparse Correlation Kernel Analysis and Reconstruction

This paper presents a new paradigm for signal reconstruction and superresolution, Correlation Kernel Analysis (CKA), that is based on the selection of a sparse set of bases from a large dictionary of class- specific basis functions. The basis functions that we use are the correlation functions of the class of signals we are analyzing. To choose the appropriate features from this large dictionary, we use Support Vector Machine (SVM) regression and compare this to traditional Principal Component Analysis (PCA) for the tasks of signal reconstruction, superresolution, and compression. The testbed we use in this paper is a set of images of pedestrians. This paper also presents results of experiments in which we use a dictionary of multiscale basis functions and then use Basis Pursuit De-Noising to obtain a sparse, multiscale approximation of a signal. The results are analyzed and we conclude that 1) when used with a sparse representation technique, the correlation function is an effective kernel for image reconstruction and superresolution, 2) for image compression, PCA and SVM have different tradeoffs, depending on the particular metric that is used to evaluate the results, 3) in sparse representation techniques, L_1 is not a good proxy for the true measure of sparsity, L_0, and 4) the L_epsilon norm may be a better error metric for image reconstruction and compression than the L_2 norm, though the exact psychophysical metric should take into account high order structure in images.