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Freedman–Diaconis rule. In statistics, the Freedman–Diaconis rule can be used to select the width of the bins to be used in a histogram. [1] It is named after David A. Freedman and Persi Diaconis. For a set of empirical measurements sampled from some probability distribution, the Freedman–Diaconis rule is designed approximately minimize ...
Histogram. A histogram is a visual representation of the distribution of quantitative data. The term was first introduced by Karl Pearson. [1] To construct a histogram, the first step is to "bin" (or "bucket") the range of values— divide the entire range of values into a series of intervals—and then count how many values fall into each ...
For digital images, a color histogram represents the number of pixels that have colors in each of a fixed list of color ranges, that span the image's color space, the set of all possible colors. The color histogram can be built for any kind of color space, although the term is more often used for three-dimensional spaces such as RGB or HSV.
Entropy estimation. In various science/engineering applications, such as independent component analysis, [1] image analysis, [2] genetic analysis, [3] speech recognition, [4] manifold learning, [5] and time delay estimation [6] it is useful to estimate the differential entropy of a system or process, given some observations.
Sum ← Sum + x. SumSq ← SumSq + x × x. Var = (SumSq − (Sum × Sum) / n) / (n − 1) This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to ...
Earth mover's distance. In computer science, the earth mover's distance (EMD) [1] is a measure of dissimilarity between two frequency distributions, densities, or measures, over a metric space D. Informally, if the distributions are interpreted as two different ways of piling up earth (dirt) over D, the EMD captures the minimum cost of building ...
Histogram matching. In image processing, histogram matching or histogram specification is the transformation of an image so that its histogram matches a specified histogram. [1] The well-known histogram equalization method is a special case in which the specified histogram is uniformly distributed. [2]
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made ...