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Topic: Mahalanobis distance

Related Topics

Distance

Covariance matrix

Chebyshev distance

Euclidean distance

Taxicab geometry

Random vector

Power set

Correlation

Manhattan distance

Levenshtein distance

Distance measuring equipment

Hamming distance

Fisher transformation

Lebesgue measure

Probability distribution

	Mahalanobis distance - Wikipedia, the free encyclopedia
		The Mahalanobis distance is simply the distance of the test point from the center of mass divided by the width of the ellipsoid in the direction of the test point.
		The Mahalanobis distance of a data point from the centroid of a multivariate data set is (N − 1) times the leverage of that data point, where N is the number of data points in the set.
		A point that has a greater Mahalanobis distance from the rest of the sample population of points is said to have higher leverage since it has a greater influence on the slope or coefficients of the regression equation.
	en.wikipedia.org /wiki/Mahalanobis_distance (736 words)

	Thermo Scientific - Algorithms - Discriminant Analysis, Mahalanobis Distance
		The Mahalanobis distance is a very useful way of determining the "similarity" of a set of values from an "unknown: sample to a set of values measured from a collection of "known" samples.
		In addition, since the Mahalanobis distance is measured in terms of standard deviations from the mean of the training samples, the reported matching values give a statistical measure of how well the spectrum of the unknown sample matches (or does not match) the original training spectra.
		The Mahalanobis distance constructs a space that weights the variation in the sample along the axis of elongation less than in the shorter axis of the group ellipse.
	www.thermo.com /com/cda/resources/resources_detail/1,2166,13324,00.html (1588 words)

	Jenness Enterprises - ArcView Extensions; Mahalanobis Description
		Mahalanobis distances provide a powerful method of measuring how similar some set of conditions is to an ideal set of conditions, and can be very useful for identifying which regions in a landscape are most similar to some “ideal” landscape.
		Using Mahalanobis distances, we can quantitatively describe the entire landscape in terms of how similar it is to the ideal elevation, slope and vegetation density of that animal.
		Moreover, Mahalanobis distances are based on both the mean and variance of the predictor variables, plus the covariance matrix of all the variables, and therefore take advantage of the covariance among variables.
	www.jennessent.com /arcview/mahalanobis_description.htm (910 words)

	Matrix Distance
		Given an nxp data matrix X, we compute a distance matrix D. For row distances, the D(ij) element of the distance matrix is the distance between row i and row j, which results in a nxn D matrix.
		For column distances, the D(ij) element of the distance matrix is the distance between column i and column j, which results in a pxp D matrix.
		The Minkowsky distance is the pth root of the sum of the absolute differences to the pth power between corresponding elements of the rows (or columns).
	www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/matrdist.htm (601 words)

	Jenness Enterprises - ArcView Extensions; Mahalanobis Chi-Square Tools
		When the predictor variables used to generate the mean vector and covariance matrix are normally distributed, then Mahalanobis distances are distributed approximately according to a Chi-square distribution with n-1 degrees of freedom.
		In such cases it may be useful to convert the Mahalanobis distance grid into a grid of p-values.
		The p-value for each cell reflects the probability of seeing a Mahalanobis value as large or larger than the actual Mahalanobis value for that cell, assuming the vector of predictor values that produced that Mahalanobis value was sampled from a population with an ideal mean (i.e.
	www.jennessent.com /arcview/mahalanobis_grids_chi_square.htm (443 words)

	Prasanta Chandra Mahalanobis - Wikipedia, the free encyclopedia
		Prasanta Chandra Mahalanobis (Bangla: প্রশান্ত চন্দ্র মহলানবিস) (June 29, 1893–June 28, 1972) was an Indian scientist and applied statistician.
		He is best known for the Mahalanobis distance, a statistical measure.
		His name is also associated with the scale free multivariate distance measure, the Mahalanobis distance.
	en.wikipedia.org /wiki/Prasanta_Chandra_Mahalanobis (548 words)

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