Principal component analysis is a widely used technique for dimensionality reduction, but is not based on a probability model. Many recently proposed dimension reduction methods are based on latent variable modelling with restrictive assumptions on the latent distribution. We present a semi-parametric latent variable model based technique for density modelling, dimensionality reduction and visualization. Unlike previous methods, we estimate the latent distribution non-parametrically. Using this estimated prior to reduce dimensions ensures that multi-modality is better preserved in the projected space. In addition, we allow the components of latent variable models to be drawn from the exponential family which makes the method suitable for special data types, for example binary or count data. We discuss connections to other probabilistic and non-probabilistic dimension reduction schemes based on gaussian and other exponential family distributions. Simulations on real valued, binary and count data show favorable comparison to other related schemes both in terms of separating different populations and generalization to unseen samples.

Papers presented at NIPS, the flagship meeting on neural computation, held in December 2004 in Vancouver.The annual Neural Information Processing Systems (NIPS) conference is the flagship meeting on neural computation. It draws a diverse group of attendees--physicists, neuroscientists, mathematicians, statisticians, and computer scientists. The presentations are interdisciplinary, with contributions in algorithms, learning theory, cognitive science, neuroscience, brain imaging, vision, speech and signal processing, reinforcement learning and control, emerging technologies, and applications. Only twenty-five percent of the papers submitted are accepted for presentation at NIPS, so the quality is exceptionally high. This volume contains the papers presented at the December, 2004 conference, held in Vancouver.

Clustering and Classification, Data Analysis, Data Handling and Business Intelligence are research areas at the intersection of statistics, mathematics, computer science and artificial intelligence. They cover general methods and techniques that can be applied to a vast set of applications such as in business and economics, marketing and finance, engineering, linguistics, archaeology, musicology, biology and medical science. This volume contains the revised versions of selected papers presented during the 11th Biennial IFCS Conference and 33rd Annual Conference of the German Classification Society (Gesellschaft für Klassifikation - GfKl). The conference was organized in cooperation with the International Federation of Classification Societies (IFCS), and was hosted by Dresden University of Technology, Germany, in March 2009.

This book constitutes the proceedings of the International Workshop on Clustering High-Dimensional Data, CHDD 2012, held in Naples, Italy, in May 2012. The 9 papers presented in this volume were carefully reviewed and selected from 15 submissions. They deal with the general subject and issues of high-dimensional data clustering; present examples of techniques used to find and investigate clusters in high dimensionality; and the most common approach to tackle dimensionality problems, namely, dimensionality reduction and its application in clustering.

This book constitutes the refereed proceedings of the 7th International Conference on Formal Concept Analysis, ICFCA 2009, held in Darmstadt, Germany, in May 2009. The 15 revised full papers presented were carefully reviewed and selected from 29 submissions for inclusion in the book. The papers comprise state of the art research and present new results in Formal Concept Analysis and related fields. These results range from theoretical novelties to advances in FCA-related algorithmic issues, as well as application domains of FCA such as data visualization, information retrieval, machine learning, data analysis and knowledge management.

Sparse models are particularly useful in scientific applications, such as biomarker discovery in genetic or neuroimaging data, where the interpretability of a predictive model is essential. Sparsity can also dramatically improve the cost efficiency of signal processing.Sparse Modeling: Theory, Algorithms, and Applications provides an introduction t

This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.