Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some type of dissimilarity measure. In this paper we derive analytic expressions for four stochastic distances between relaxed scaled complex Wishart distributions in their most general form and in important particular cases. Using these distances, inequalities are obtained which lead to new ways of deriving the Bartlett and revised Wishart distances. The expressiveness of the four analytic distances is assessed with respect to the variation of parameters. Such distances are then used for deriving new tests statistics, which are proved to have asymptotic chi-square distribution. Adopting the test size as a comparison criterion, a sensitivity study is performed by means of Monte Carlo experiments suggesting that the Bhattacharyya statistic outperforms all the others. The power of the tests is also assessed. Applications to actual data illustrate the discrimination and homogeneity identification capabilities of these distances.Comment: Accepted for publication in the IEEE Transactions on Geoscience and Remote Sensing journa

A hierarchy of recurrent networks for speech recognition

Generative models for sequential data based on directed graphs of Restricted Boltzmann Machines (RBMs) are able to accurately model high dimensional sequences as recently shown. In these models, temporal dependencies in the input are discovered by either buffering previous visible variables or by recurrent connections of the hidden variables. Here we propose a modification of these models, the Temporal Reservoir Machine (TRM). It utilizes a recurrent artificial neural network (ANN) for integrating information from the input over time. This information is then fed into a RBM at each time step. To avoid difficulties of recurrent network learning, the ANN remains untrained and hence can be thought of as a random feature extractor. Using the architecture of multi-layer RBMs (Deep Belief Networks), the TRMs can be used as a building block for complex hierarchical models. This approach unifies RBM-based approaches for sequential data modeling and the Echo State Network, a powerful approach for black-box system identification. The TRM is tested on a spoken digits task under noisy conditions, and competitive performances compared to previous models are observed

Disturbance Grassmann Kernels for Subspace-Based Learning

In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. To handle this kind of data, Grassmann kernels were proposed to measure the space structure and used with classifiers, e.g., Support Vector Machines (SVMs). However, the existing discriminative algorithms mostly ignore the instability of subspaces, which would cause the classifiers misled by disturbed instances. Thus we propose considering all potential disturbance of subspaces in learning processes to obtain more robust classifiers. Firstly, we derive the dual optimization of linear classifiers with disturbance subject to a known distribution, resulting in a new kernel, Disturbance Grassmann (DG) kernel. Secondly, we research into two kinds of disturbance, relevant to the subspace matrix and singular values of bases, with which we extend the Projection kernel on Grassmann manifolds to two new kernels. Experiments on action data indicate that the proposed kernels perform better compared to state-of-the-art subspace-based methods, even in a worse environment.Comment: This paper include 3 figures, 10 pages, and has been accpeted to SIGKDD'1

A Scale Mixture Perspective of Multiplicative Noise in Neural Networks

Corrupting the input and hidden layers of deep neural networks (DNNs) with multiplicative noise, often drawn from the Bernoulli distribution (or 'dropout'), provides regularization that has significantly contributed to deep learning's success. However, understanding how multiplicative corruptions prevent overfitting has been difficult due to the complexity of a DNN's functional form. In this paper, we show that when a Gaussian prior is placed on a DNN's weights, applying multiplicative noise induces a Gaussian scale mixture, which can be reparameterized to circumvent the problematic likelihood function. Analysis can then proceed by using a type-II maximum likelihood procedure to derive a closed-form expression revealing how regularization evolves as a function of the network's weights. Results show that multiplicative noise forces weights to become either sparse or invariant to rescaling. We find our analysis has implications for model compression as it naturally reveals a weight pruning rule that starkly contrasts with the commonly used signal-to-noise ratio (SNR). While the SNR prunes weights with large variances, seeing them as noisy, our approach recognizes their robustness and retains them. We empirically demonstrate our approach has a strong advantage over the SNR heuristic and is competitive to retraining with soft targets produced from a teacher model

A Detailed Investigation into Low-Level Feature Detection in Spectrogram Images

Being the first stage of analysis within an image, low-level feature detection is a crucial step in the image analysis process and, as such, deserves suitable attention. This paper presents a systematic investigation into low-level feature detection in spectrogram images. The result of which is the identification of frequency tracks. Analysis of the literature identifies different strategies for accomplishing low-level feature detection. Nevertheless, the advantages and disadvantages of each are not explicitly investigated. Three model-based detection strategies are outlined, each extracting an increasing amount of information from the spectrogram, and, through ROC analysis, it is shown that at increasing levels of extraction the detection rates increase. Nevertheless, further investigation suggests that model-based detection has a limitation—it is not computationally feasible to fully evaluate the model of even a simple sinusoidal track. Therefore, alternative approaches, such as dimensionality reduction, are investigated to reduce the complex search space. It is shown that, if carefully selected, these techniques can approach the detection rates of model-based strategies that perform the same level of information extraction. The implementations used to derive the results presented within this paper are available online from http://stdetect.googlecode.com