A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham’s razor: “Entities should not be multiplied without neces sity. ” This principle enabled scientists to select the ”best” physical laws and theories to explain the workings of the Universe and continued to guide scienti?c research, leadingtobeautifulresultsliketheminimaldescriptionlength approachtostatistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts anddependonthelanguage“spoken”whenpresentingideasandresults. The?eldof sparse representations, that recently underwent a Big Bang like expansion, explic itly deals with the Yin Yang interplay between the parsimony of descriptions and the “language” or “dictionary” used in them, and it became an extremely exciting area of investigation. It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the ?rst guide book to Sparseland, and I am sure you’ll ?nd in it both familiar and new landscapes to see and admire, as well as ex cellent pointers that will help you ?nd further valuable treasures. Enjoy the journey to Sparseland! Haifa, Israel, December 2009 Alfred M. Bruckstein vii Preface This book was originally written to serve as the material for an advanced one semester (fourteen 2 hour lectures) graduate course for engineering students at the Technion, Israel.

A realistic and comprehensive review of joint approaches to machine learning and signal processing algorithms, with application to communications, multimedia, and biomedical engineering systems Digital Signal Processing with Kernel Methods reviews the milestones in the mixing of classical digital signal processing models and advanced kernel machines statistical learning tools. It explains the fundamental concepts from both fields of machine learning and signal processing so that readers can quickly get up to speed in order to begin developing the concepts and application software in their own research. Digital Signal Processing with Kernel Methods provides a comprehensive overview of kernel methods in signal processing, without restriction to any application field. It also offers example applications and detailed benchmarking experiments with real and synthetic datasets throughout. Readers can find further worked examples with Matlab source code on a website developed by the authors: http://github.com/DSPKM • Presents the necessary basic ideas from both digital signal processing and machine learning concepts • Reviews the state-of-the-art in SVM algorithms for classification and detection problems in the context of signal processing • Surveys advances in kernel signal processing beyond SVM algorithms to present other highly relevant kernel methods for digital signal processing An excellent book for signal processing researchers and practitioners, Digital Signal Processing with Kernel Methods will also appeal to those involved in machine learning and pattern recognition.

This book constitutes the thoroughly refereed post-proceedings of the 4th International Workshop on Semantics in Data and Knowledge Bases, SDKB 2010, held in Bordeaux, France in July 2010. The 6 revised full papers presented together with an introductory survey by the volume editors were carefully reviewed and selected during two rounds of revision and improvement. The papers reflect a variety of approaches to semantics in data and knowledge bases.

Deep learning has developed as a useful approach for data mining tasks such as unsupervised feature learning and representation. This is thanks to its ability to learn from examples with no prior guidance. Unsupervised learning is the process of discovering patterns and structures in unlabeled data without the use of any explicit labels or annotations. This type of learning does not require the data to be annotated or labelled. This is especially helpful in situations in which labelled data are few or nonexistent. Unsupervised feature learning and representation have seen widespread application of deep learning methods such as auto encoders and generative adversarial networks (GANs). These algorithms learn to describe the data in a hierarchical fashion, where higher-level characteristics are stacked upon lower-level ones, capturing increasingly complicated and abstract patterns as they progress. Neural networks are known as Auto encoders, and they are designed to reconstruct their input data from a compressed representation known as the latent space. The hidden layers of the network are able to learn to encode valuable characteristics that capture the underlying structure of the data when an auto encoder is trained on input that does not have labels attached to it. It is possible to use the reconstruction error as a measurement of how well the auto encoder has learned to represent the data. GANs are made up of two different types of networks: a generator network and a discriminator network. While the discriminator network is taught to differentiate between real and synthetic data, the generator network is taught to generate synthetic data samples that are an accurate representation of the real data. By going through an adversarial training process, both the generator and the discriminator are able to improve their skills. The generator is able to produce more realistic samples, and the discriminator is better able to tell the difference between real and fake samples. One meaningful representation of the data could be understood as being contained within the latent space of the generator. After the deep learning model has learned a reliable representation of the data, it can be put to use for a variety of data mining activities.

Connects fundamental mathematical theory with real-world problems, through efficient and scalable optimization algorithms.

Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or monograph has yet appeared on the subject. Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including: * Finite Frame Constructions; * Optimal Erasure Resilient Frames; * Quantization of Finite Frames; * Finite Frames and Compressed Sensing; * Group and Gabor Frames; * Fusion Frames. Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory. With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.