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The formula for the Euclidean Distance (ED) between samples i and h across p dimensions is: [latex]ED = \sqrt{\sum_{j=1}^p(a_{hj} - a_{ij})^2}[/latex] Here is a dataset reporting the presence or absence of each of five species (variables) on three plots:
In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points.
To introduce the distance matrix as a method of summarizing a set of pairwise distances. To understand how distance measures use matrix algebra to provide a link between raw data, data adjustments, and techniques to test for statistical differences, identify groups, and visualize patterns.
We review the statistical properties of distances that are often used in scientific work, present their properties, and show how they compare to each other. We discuss an approximation framework for model-based inference using statistical distances.
There is of course overlap between these contexts and so there are distances that are useful in both, but they are motivated by slightly di erent considerations. 1 The Fundamental Statistical Distances There are four notions of distance that have an elevated status in statistical theory. Let P;Q be two probability measures with densities pand q. 1.
normal distribution. This is the only distance measure in the statistical literature that takes into account the probabilistic information of the data. In this thesis we address the study of different distance measures that share a fundamental characteristic: all the proposed distances incorporate probabilistic information.
1:4 A. Jaroszewicz, M. Roytman There has been much argument to the usefulness of Lp metrics where p 2 in high dimensional data. According to Beyer, et. al. [1], the ratio of Lp (for p 2) distances between the closest neighbor and the furthest neighbor to a given point approaches 1 as the dimensionality of the data grows large.
