Information theoretic learning itl is a framework where information theory descriptors based on nonparametric estimator of r. Introduction during the last decade, research on mercer kernelbased learning algorithms has flourished 1, 2. A pdf estimation methods and experimental evaluation of itl descriptors. Quantifying bursting neuron activity from calcium signals. Proposed model is based on the information theory concepts namely renyi s quadratic entropy and cauchyschwarz divergence.
Learning from examples with information theoretic criteria. The renyi entropy and information converge to the shannon entropy for q 1. The ones marked may be different from the article in the profile. Renyis entropy and kernel perspectives information science and statistics book online at best prices in india on. Based on a series of scalar descriptors that summarizes in a relevant way all the information contained in the data distribution, the algorithms and clustering evaluation functions cef are capable of capturing the structure of the data beyond. If youre looking for a free download links of information theoretic learning.
Use features like bookmarks, note taking and highlighting while reading information theoretic learning. Entropies quantify the diversity, uncertainty, or randomness of a system. Itl is a framework where the conventional concepts of second order statistics covariance, l2 distances, correlation functions are substituted by scalars and functions with information theoretic underpinnings, respectively entropy, mutual information and correntropy. Information plane analysis of deep neural networks via matrix. Multivariate shannons entropy for adaptive iir filtering. The standard approach relies on the kernel trick to perform pairwise evaluations of a kernel function, leading to scalability issues for large datasets due to its linear and superlinear growth with respect to the training data. Information theoretic security foundations and trendsr in. The most commonly used information theoretic measure is entropy which measures the amount of information contained in a statistical distribution.
In contrast, the matrixbased renyis entropy shown in equation 2 have the same functional form of the statistical quantity in a reproducing kernel hilbert space rkhs. In this paper, information entropy is introduced in the field of control performance assessment cpa. Recently, the concept of an information plane began to shed light on the analysis of multilayer perceptrons mlps. Based on this index, the cascade system, the nonphase system, the traditional pid control system and the predictive control system, etc. From the point of view of estimation, renyis entropy is very appealing since it. School of mathematics and statistics, wuhan university, wuhan 430072, p. It was used in the siso system first, and then was extended to the mimo system. Information theoretic learning renyis entropy and kernel. Pdf algorithms for entropy and correntropy adaptation with applications to linear. Clustering using renyis entropy kent state university. We propose a kernel function estimation strategy to support machine learning tasks by analyzing the input samples using renyis information metrics. We provided an indepth insight into stacked autoencoders saes using a novel matrixbased renyi s \\alpha entropy functional, enabling. Renyis entropy and kernel perspectives find, read and cite all the research you need on. Information theoretic security foundations and trendsr in communications and information fetrio35.
For a random variable x with probability density function pdf fx in a. Unsupervised kernel function building using maximization. Renyis entropy and kernel perspectives springer, new york, ny, usa, 2010. Entropy free fulltext minimuminformationentropybased. However, information theoretic approaches often impose unrealistic parametric assumptions about the data distributions in order to evaluate the information theoretic metric 12. In this paper, we derive a recursive formula to estimate renyis. Renyis entropy and kernel perspectives information science and statistics kindle edition by principe, jose c download it once and read it on your kindle device, pc, phones or tablets.
Regularization schemes for minimum error entropy principle. On the parallel efficiency and scalability of the correntropy. On connections between renyi entropy principal component. Specifically, we aim to identify a reproducing kernel hilbert space spanning the most widely the information force among data points by the maximization of the information potential variability. Renyis entropy and kernel perspectives information science and statistics. Renyis entropy and its applications to adaptive system training. Proposed model is based on the information theory concepts namely renyis quadratic entropy and cauchyschwarz divergence. Information theoretic learning renyis entropy and kernel perspectives.
Principe and others published information theoretic learning. We provided an indepth insight into stacked autoencoders saes using a novel matrixbased renyis. This work addresses two main issues of the standard kernel entropy component analysis keca algorithm. Singletrial effective brain connectivity patterns enhance discriminability of mental imagery tasks. Information theoretic learning renyi s entropy and kernel perspectives. A novel algorithm based on renyi s quadratic entropy is used to train, directly from a data set, linear or nonlinear mappers for entropy maximization or minimization. Renyi s entropy and kernel perspectives information science and statistics book online at best prices in india on. An alternative approach is the information filtering that implies the propagation of the information matrix rather than processing p kk. A datadriven measure of effective connectivity based on. An information theoretic description of learning processes was given in, where learning is defined as a process in which the systems subjective entropy or, equivalently, its missing information decreases in time. Multivariate shannons entropy for adaptive iir filtering via kernel density estimators. Information theory, machine learning, and reproducing kernel hilbert spaces.
Tracking the entropy of a signal with stepwise timevarying pdf 86. Unsupervised kernel function building using maximization of. Renyis entropy and kernel perspectives information science and statistics pdf, epub, docx and torrent then this site is not for you. Understanding convolutional neural networks with information. Renyis entropy and kernel perspectives information science and. Understanding convolutional neural network training with. Principe is an american bioengineer, focusing in adaptive signal processing, kernel learning, information theoretic learning, neural networks, brain machine interfaces and cognitive architectures, currently distinguished professor of electrical and biomedical engineering and bellsouth professor at university of florida.
Information plane analysis of deep neural networks via. In this paper we propose a simple and intuitive clustering algorithm. When the probability distribution of x is estimated from a finite set of n measured data, x i i 1 n, by a gaussian kernel, g. In this paper, we first define the matrixbased renyis. Kernel entropy component analysis keca 1, 2 was recently proposed as a general informationtheoretic method for feature extraction and dimensionality reduction in pattern analysis and machine intelligence. Renyis entropy and kernel perspectives information. This is possible because of a nonparametric estimator of renyis quadratic entropy that is only a function of pairwise differences between samples. We focus on quadratic renyis entropy and connected cauchyschwarz divergence. Using information theoretic concepts to understand and explore the inner organization of deep neural networks dnns remains a big challenge. This paper discusses a framework for learning based on information theoretic criteria. A number of entropy estimatorsare available in the literature. Sequential maximum correntropy kalman filtering kulikova. Oct 16, 2014 where p k is defined from the probability distribution of random variable x and. Principe is an american bioengineer, focusing in adaptive signal processing, kernel learning, information theoretic learning, neural networks, brain machine interfaces and cognitive architectures, currently distinguished professor of electrical and biomedical engineering and bellsouth professor at university of florida references.
Online minimum error entropy algorithm with unbounded. System upgrade on feb 12th during this period, ecommerce and registration of new users may not be available for up to 12 hours. We begin with some general properties, including data scale invariance. Fast estimation of information theoretic learning descriptors.
Method to reconstruct neuronal action potential train from twophoton calcium imaging. Representative cross information potential clustering. We want also to stress that the argument of the log, which is the 2. We provided an indepth insight into stacked autoencoders saes using a novel matrixbased renyis \alphaentropy functional, enabling. In this paper we propose a simple and intuitive clustering algorithm firmly rooted in information theory, utilizing renyis entropy as our similarity metric. For the unknown time delay case, the minimum information entropy mie benchmark is presented, and a miebased performance index is defined.
Keca roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of by variance as in kernel principal components analysis. We provide an intriguing analogy between the computation and an information potential measuring the interactions among the data samples. I introduction one of the fundamental problems of our technology driven society is the huge amounts of data that are being generated by every segment of the society from factories, services, medicine and individulas alike fig 1. Kernel methods form a theoreticallygrounded, powerful and versatile framework to solve nonlinear problems in signal processing and machine learning. A novel algorithm based on renyis quadratic entropy is used to train, directly from a data set, linear or nonlinear mappers for entropy maximization or minimization. On estimation of a probability density function and mode. One of the information theoretic concepts which has been found very effective in machine learning is the entropy measure. The book compares the performance of itl algorithms with the second order counterparts in. In the course of these studies, we discovered that the main idea enabling a synergistic view as well as algorithmic implementations, does not involve the conventional central moments of the data mean and covariance. This cited by count includes citations to the following articles in scholar.