____ : ..... '"i-t.-

the algorithms under various conditions and settings. The total amount of code consists of about 25,000 lines and even includes a graphical routine based on the X Windows system. The code itself is reasonably well documented and thus is amenable to extension and further development by the interested reader. The datasets presented in the book are also included in the tar archive. So what is the use for 2D Object Detection and Recognition? The book seems to be intended primarily for those researchers in computer vision and related fields who would like to see the world though Amit’s eyes. The book requires some background knowledge of computer vision (not much, though) and is reasonably self-contained. It would also work very well in a more-advanced study group setting, where several students can work their way through the chapters, making extensive use of the available software. I congratulate Yali Amit on writing a very fine book based on his many years of research experience that led to excellent and novel contributions to the field. This book is an example of how to do things right: simply, efficiently, and correctly. I have no reservations at all in recommending the book highly to all readers interested in the field of computer vision and/or (really) applied statistics.

Advanced Calculus with Applications in Statistics

In this manuscript, we derive a non-parametric version of the Fisher kernel. We obtain this original result from the Non-negative Matrix Factorization with the Kullback-Leibler divergence. By imposing suitable normalization conditions on the obtained factorization, it can be assimilated to a mixture of densities, with no assumptions on the distribution of the parameters. The equivalence between the Kullback-Leibler divergence and the log-likelihood leads to kernelization by simply taking partial derivatives. The estimates provided by this kernel, retain the consistency of the Fisher kernel.

A Non-parametric Fisher Kernel.

AbstractThe Fisher kernel has good statistical properties. However, from a practical point of view, the necessary distributional assumptions complicate the applicability. We approach the solution to this problem with the NMF (Non-negative Matrix Factorization) methods, which with adequate normalization conditions, provide stochastic matrices. Using the Bregman divergence as the objective function, formally equivalent solutions appear for the specific forms of the functionals involved. We show that simply by taking these results and plug-in into the general expression of the NMF kernel, obtained with purely algebraic techniques, without any assumptions about the distribution of the parameters, the properties of the Fisher kernel hold, and it is a convenient procedure to use this kernel the situations in which they are needed we derive the expression of the information matrix of Fisher. In this work, we have limited the study to the Gaussian metrics, KL (Kullback-Leibler), and I-divergence.KeywordsFisher kernelNon-parametricBregman divergenceNon-negative Matrix Factorization 

Generalized Fisher Kernel with Bregman Divergence

The Probabilistic Latent Semantic Analysis has been related with the Singular Value Decomposition. Several problems occur when this comparative is done. Data class restrictions and the existence of several local optima mask the relation, being a formal analogy without any real significance. Moreover, the computational difficulty in terms of time and memory limits the technique applicability. In this work, we use the Nonnegative Matrix Factorization with the Kullback–Leibler divergence to prove, when the number of model components is enough and a limit condition is reached, that the Singular Value Decomposition and the Probabilistic Latent Semantic Analysis empirical distributions are arbitrary close. Under such conditions, the Nonnegative Matrix Factorization and the Probabilistic Latent Semantic Analysis equality is obtained. With this result, the Singular Value Decomposition of every nonnegative entries matrix converges to the general case Probabilistic Latent Semantic Analysis results and constitutes the unique probabilistic image. Moreover, a faster algorithm for the Probabilistic Latent Semantic Analysis is provided.

Pau Figuera Vinué

Papers

On the Probabilistic Latent Semantic Analysis Generalization as the Singular Value Decomposition Probabilistic Image