Cross-entropy is similar to KL divergence, but they serve different purposes: cross-entropy is typically used in machine learning to evaluate the performance of a model where the objective is to minimize the error between the predicted probability distribution and true distribution, whereas KL is mo...
the probability of facing up is 1/2, and the probability of standing up is 0. According to the information entropy H (X) formula, adding the result with a probability of occurrence of 0 will not affect the measurement of uncertainty. ...
Shannon’s entropy quantified the unpredictability of information, enabling engineers to calculate the efficiency of data transmission and compression. His formula established entropy as a universal metric for measuring uncertainty, linking it to probability distributions and creating a foundation for modern ...
Let's explore cross-entropy functions in detail and discuss their applications in machine learning, particularly for classification issues.
This study presents the concept of a computationally efficient machine learning (ML) model for diagnosing and monitoring Parkinson’s disease (PD) using rest-state EEG signals (rs-EEG) from 20 PD subjects and 20 normal control (NC) subjects at a sampling rate of 128 Hz. Based on the compar...
I found this helpful in trying to memorize the formula. A uniform distribution would also be the maximum entropy distribution that event could possibly come from given its probability…though you can’t reference entropy without first explaining information 🙂 Anyway the mid part of this article ...
The formula is depicted as: $$\begin{aligned}dom_{j} ( { \oslash }_{i} ,\oslash_{k} ) = \left\{ {\begin{array}{*{20}c} {\sqrt {\frac{{w_{{jr}} d_{H} (q_{{ij}} ,q_{{kj}} )}}{{\sum\limits_{{j = 1}}^{n} {w_{{jr}} } }},} } & {{\text{if }...
The Eq. (5) demonstrate the normalization formula, which is performed for each attribute individually and n is the number of attributes. $$X_{norm} = \frac{x\left( i \right) - \min \left( i \right)}{{\max \left( i \right) - \min \left( i \right)}},i = 1, \ldots ,n...
An equation was proposed to assess the connectivity of nodes in the directed graph via probability values calculated from the Shannon entropy formula. A direct proof of calculation based on the proposed mathematical formula was presented using e-DRW with gene expression data. Based on the results,...
In this paper, we shall firstly study the topological entropy of monotone and competitive dynamical systems and provide an entropy formula, which says that the topological entropy of such a system is the supremum of the topological entropy on all invariant and unordered Lipschitz submanifolds with co...