Weitao Wan, Jiansheng Chen, Tianpeng Li, Yiqing Huang, Jingqi Tian, Cheng Yu. The definition can be derived from a set of axioms establishing that entropy should be a measure of how informative the average outcome of a variable is. Information Entropy Based Feature Pooling for Convolutional Neural Networks. Entropy has relevance to other areas of mathematics such as combinatorics and machine learning. The analogy results when the values of the random variable designate energies of microstates, so Gibbs formula for the entropy is formally identical to Shannon's formula. Shannon strengthened this result considerably for noisy channels in his noisy-channel coding theorem.Įntropy in information theory is directly analogous to the entropy in statistical thermodynamics. Shannon considered various ways to encode, compress, and transmit messages from a data source, and proved in his famous source coding theorem that the entropy represents an absolute mathematical limit on how well data from the source can be losslessly compressed onto a perfectly noiseless channel. The 'fundamental problem of communication' – as expressed by Shannon – is for the receiver to be able to identify what data was generated by the source, based on the signal it receives through the channel. Shannon's theory defines a data communication system composed of three elements: a source of data, a communication channel, and a receiver.

The concept of information entropy was introduced by Claude Shannon in his 1948 paper ' A Mathematical Theory of Communication', and is also referred to as Shannon entropy. Generally, information entropy is the average amount of information conveyed by an event, when considering all possible outcomes. Because of its dependence on ergodic theorems, however, it can also be viewed as a branch of ergodic theory, the theory of invariant transformations and transformations related to invariant transformations. Information theory can be viewed as simply a branch of applied probability theory. Two bits of entropy: In the case of two fair coin tosses, the information entropy in bits is the base-2 logarithm of the number of possible outcomes with two coins there are four possible outcomes, and two bits of entropy. (1), the classical Shannon entropy, whose quantum version, the Von Neumann entropy, S Tr ( log ), is probably more familiar to subatomic physicists. the entropy or self information in a process. An equivalent definition of entropy is the expected value of the self-information of a variable. Base 2 gives the unit of bits (or ' shannons'), while base e gives 'natural units' nat, and base 10 gives units of 'dits', 'bans', or ' hartleys'. By the way, the new 2D entropy measure predicts an (intuitively pleasing) entropy of 8 bits per pixel for the random image and 0. Where Σ, the logarithm, varies for different applications. The final computed Shannon information-entropy is rotation independent and corresponds precisely with the number of bits required to encode the image in a non-redundant gradient representation.

Information entropy