
	Where results make sense

Topic: Euclidean distance

Related Topics

Distance

Chebyshev distance

Mahalanobis distance

Metric space

Euclidean space

Normed vector space

Distance measuring equipment

Covariance matrix

Random vector

Cartesian coordinate system

Euclidean geometry

Probability distribution

BBC Sports Personality of the Year

World Values Survey

Industrial robot

	Distance - Wikipedia, the free encyclopedia
		One might attempt to define the distance between two non-empty subsets of a given set as the infimum of the distances between any two of their respective points, which would agree with the every-day use of the word.
		Distance is a scalar quantity, containing only a magnitude, whereas displacement is an equivalent vector quantity containing both magnitude and direction.
		The distance covered by a vehicle (often recorded by an odometer), person, animal, object, etc. should be distinguished from the distance from starting point to end point, even if latter is taken to mean e.g.
	en.wikipedia.org /wiki/Distance (963 words)

	Euclidean distance - Wikipedia, the free encyclopedia
		In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" distance between the two points that one would measure with a ruler, which can be proven by repeated application of the Pythagorean theorem.
		Also note that when comparing distances (for which is greatest, not for the actual difference), it isn't necessary to take the square root at all.
		As noted in the 2D approximation section, when comparing distances (for which is greatest, not for the actual difference), it isn't necessary to take the square root at all.
	en.wikipedia.org /wiki/Euclidean_distance (542 words)

	:: Ecological Distance :: (Site not responding. Last check: 2007-10-21)
		This is a result from the fact that the Hellinger distance uses a division by the total abundance of a community (it is based on proportional abundance which is equal in community 1 and 2 as both their species have half the total abundance).
		The transformation method is especially useful for cluster algorithms or ordination methods that are based on the Euclidean distance, but that do not use a distance matrix as input or during calculations.
		Distance matrices where cells indicate the ecological distance among the objects (communities, sites) corresponding to each row and column can be used as input in a number of clustering or ordination methods (see examples).
	www.worldagroforestry.org /sites/rsu/resources/biodiversity/analysistypes/ecologicaldistance.asp (1205 words)

	Measures of Similarity and Distance (Site not responding. Last check: 2007-10-21)
		In other words, euclidean distance is the square root of the sum of squared differences between corresponding elements of the two vectors.
		Euclidean distance is only appropriate for data measured on the same scale.
		Euclidean distance is most often used to compare profiles of respondents across variables.
	www.analytictech.com /mb813/handouts/distance_and_correlation.htm (881 words)

	PlanetMath: Euclidean distance
		This distance induces a metric (and therefore a topology) on
		The resulting (topological and vectorial) space is known as Euclidean space.
		This is version 10 of Euclidean distance, born on 2002-01-05, modified 2005-03-04.
	planetmath.org /encyclopedia/EuclideanDistance.html (203 words)

	MMU - Biol. Sic., MSc Multivariate Stastics: distance measures (Site not responding. Last check: 2007-10-21)
		There are distances that are euclidean (can be measured with a 'ruler') and there are other distances, often based on similarity, that are non-Eucliean.
		For example, in terms of road distance (a euclidean distance) York is closer to Manchester than it is Canterbury.
		In the bivariate case the minimum distance is the hypotenuse of a triangle formed from the points.
	obelia.jde.aca.mmu.ac.uk /multivar/dist.htm (917 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 Euclidean distance is simply the square root of the squared differences between corresponding elements of the rows (or columns).
	www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/matrdist.htm (601 words)

	Improved Heterogeneous Distance Functions
		For datasets with no nominal attributes, Euclidean and HVDM are equivalent, and all the distance functions perform about the same on average except for DVDM, which averages about 4% less than the others, indicating the detrimental effects of discretization.
		Euclidean and HOEM have similar definitions for applications without any nominal attributes, except that Euclidean is normalized by standard deviation while HOEM is normalized by the range of each attribute.
		For datasets with both nominal and continuous attributes, HVDM is slightly higher than Euclidean distance on these datasets, which is in turn slightly higher than HOEM, indicating that the overlap metric may not be much of an improvement on heterogeneous databases.
	axon.cs.byu.edu /~randy/jair/wilson6.html (1432 words)

	Improved Heterogeneous Distance Functions
		A variety of distance functions are available for such uses, including the Minkowsky (Batchelor, 1978), Mahalanobis (Nadler and Smith, 1993), Camberra, Chebychev, Quadratic, Correlation, and Chi-square distance metrics (Michalski, Stepp and Diday, 1981; Diday, 1974); the Context-Similarity measure (Biberman, 1994); the Contrast Model (Tversky, 1977); hyperrectangle distance functions (Salzberg, 1991; Domingos, 1995) and others.
		The Euclidean and Manhattan distance functions are equivalent to the Minkowskian r-distance function (Batchelor, 1978) with r = 2 and 1, respectively.
		For the purposes of comparison during testing, we define a heterogeneous distance function that is similar to that used by IB1, IB2 and IB3 (Aha, Kibler and Albert, 1991; Aha, 1992) as well as that used by Giraud-Carrier and Martinez (1995).
	axon.cs.byu.edu /~randy/jair/wilson2.html (1867 words)

	References on Euclidean Distance Transforms
		A distance map is an image where the value of each pixel is the distance from this pixel to the nearest pixel belonging to a given set or object.
		In Chapter 7, the 3D Euclidean DT is applied to the registration of MR images of the brain where the matching criterion is the distance between the surfaces of similar objects (skin, cortex, ventricular system,...) in both images.
		The distance transform is an operation that converts an image consisting of fl and white pixels to an image where each pixel has a value or coordinate that represents the distance or location to the nearest fl pixel.
	www.lems.brown.edu /vision/people/leymarie/Refs/CompVision/DT/EDT.html (2076 words)

	Euclidean Distance
		Euclidean Distance is the most common use of distance.
		Euclidean distance or simply 'distance' examines the root of square differences between coordinates of a pair of objects.
		Euclidean distance is a special case of Minkowski distance with
	people.revoledu.com /kardi/tutorial/Similarity/EuclideanDistance.html (77 words)

	Objects distant and near
		You may or may not remember that the most customary notion of the distance is somehow related to the Pythagorean Theorem.
		Distance, the metric function, is the mathematical abstraction of measurement.
		Thus it's clear that once several distance functions have been defined on the same set the expression "the distance between two points" becomes ambiguous.
	www.cut-the-knot.org /do_you_know/far_near.shtml (785 words)

	Mathematics for Elementary Teachers Chapter 1 -- Projects
		Taxicab distance is the distance between two points traveled by taxicabs along roads arranged in a grid.
		Alice agrees that the sum of the distances should be a minimum, but she is adamant that they both have exactly the same distance to walk to work.
		Write a definition of the distance from a point A to a line L that is equally useful in both Pythagorean and taxicab geometry.
	cwx.prenhall.com /bookbind/pubbooks/esm_masingila_mathelem_1/chapter1/custom1/deluxe-content.html (1191 words)

	Cluster 3.0 for Windows, Mac OS X, Linux, Unix
		The harmonically summed Euclidean distance is a variation of the Euclidean distance, where the terms for the different dimensions are summed inversely (similar to the harmonic mean):
		The city-block distance, alternatively known as the Manhattan distance, is related to the Euclidean distance.
		This is equal to the distance you would have to walk between two points in a city, where you have to walk along city blocks.
	bioinfo.tau.ac.il /man/cluster/html/Distance.html (849 words)

	Distance Tutorial
		Once the ranks are normalized, the distance can be computed as quantitative variables.
		To deal with pure rank data, you may use other distance such as Spearman Distance, Kendall Distance, Cayley Distance, and Hamming Distance for ordinal variables, Ulam Distance, and Chebyshev /Maximum Distance for ordinal variable.
		The Euclidean distance between park A and park B is
	people.revoledu.com /kardi/tutorial/Similarity/Normalized-Rank.html (307 words)

	- Thermo Electron Corporation - 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 (1582 words)

	General Distances
		City Block Distance is akin to the walking distance between two points in a city like New York's Manhatten district, where each component is the number of blocks in the directions North-South and East-West.
		In hierarchcical cluster analysis and k-means analysis, it is necessary to compute the distance between a case and a cluster, or between two clusters.
		The chosen criterion function, including Euclidean Sum of Squares, can then be optimized in terms of the sum of the distance components across all variables k, thereby allowing for mixed data types most generally in cluster analysis.
	www.clustan.com /general_distances.html (1000 words)

	A Comparative Study of Text-Independent Speaker Identification using Statistical Features
		Regarding the distance measure, four variations according to different usage of the covariance matrix [10] are studied.
		A match occurs if a test vector is labelled to the right speaker: for distance measures, it means the intra-speaker distance is smaller than all the inter-speaker ones; while for probability density estimation, it means the intra-speaker probability is larger than the inter-speaker ones.
		Distance measure is one of the classification methods, it is based on the assumption that the underlying probability has a Gaussian distribution.
	www.journal.au.edu /ijcem/jan98/article5.html (2306 words)

	[No title]
		Euclidean Distance measures the length of a straight line between two cases.
		The squared Euclidean measure should be used when the CENTROID, MEDIAN, or WARD cluster method is requested. For Ward’s method, the dissimilarity between cluster A and cluster B is represented by the “loss of information” from joining the two clusters with this loss of information being measured by the increase in error sum of squares.
		Distance or similarity measures are generated by the Proximities procedure.
	www.people.vcu.edu /~randrews/mgmt643/cluster_analysis.doc (1810 words)

	Distance estimation in minimal virtual enviroments
		Euclidean judgements were found to become more accurate with extended navigational experience though the accuracy of route distances judgements was unchanged.
		Yet results from this study have demonstrated that route judgements are systematically inaccurate (increasingly so as the distance to estimate increase) and vary as a function of the distance to judge while the Euclidean judgements are relatively accurate independent of the distance to judge.
		Figure 3 is a graph of the line of best fit plotting the errors made in judging route distances against the actual route distance for the one period of exploration condition (as the graph for the three periods of exploration is almost identical it has been omitted).
	www.ee.surrey.ac.uk /Personal/R.Bowden/publications/vrsig97old/proceed/030/30.htm (2586 words)

	Morphology - Distance Transform
		There is a dual to the distance transform described above which produces the distance transform for the background region rather than the foreground region.
		There are several different sorts of distance transform, depending upon which distance metric is being used to determine the distance between pixels.
		The distance transform is very closely linked to both the medial axis transform and to skeletonization.
	homepages.inf.ed.ac.uk /rbf/HIPR2/distance.htm (906 words)

	MORPH_DISTANCE
		The distance map is useful for a variety of morphological operations: thinning, erosion and dilation by discs of radius r, and granulometry.
		Each neighbor is assigned a distance corresponding to the number of pixels to be visited when travelling from the current pixel to the neighbor.
		Each neighbor is assigned an approximate Euclidean distance, where the distances along the diagonals and the center row and column are correct, but for speed the off-diagonal elements are approximated by adding together the distances after the square root.
	idlastro.gsfc.nasa.gov /idl_html_help/MORPH_DISTANCE.html (327 words)

	Data Mining Developers - EUCLIDEAN DISTANCE IN K-MEANS CLUSTERING : DATA MINING TUTORIAL
		The Euclidean distance between two points/objects/items in a dataset, defined by point X and point Y is defined by Equation 1A below.
		Equation 1A defines the Euclidean distance between two rows of data or two points/items/objects in a dataset/database or in space, where each datapoint has N attributes or N Fields (an attribute or field is a characteristic of the item, e.g.
		Find the Euclidean distance between two datapoints named John and Henry in a dataset of people, where each person is defined by 3 attributes or fields; Age, Height, Weight.
	www.kdkeys.net /forums/3993/ShowPost.aspx (290 words)

	[No title]
		Euclidean geometry measures distance "as the crow flies", but this rarely constitutes a good model for real-life situations, particularly in cities, where one is only concerned with the distance their car will need to travel, and cars certainly don't fly (yet).
		As a less serious application, taxicab distance is the right model of distance for some games played on a square grid and where only vertical and horizontal moves are allowed.
		As Eugene F. Krause writes in the introduction of his book (see bibliography), "To fully appreciate Euclidean geometry, one needs to have some contact with a non-Euclidean geometry." Taxicab geometry has the advantage of being fairly intuitive compared to some other non-euclidean geometries, and it requires less mathematical background.
	www.cs.mcgill.ca /~ptesso/cs644/why.html (228 words)

	mmdist
		The distances available are based on the Euclidean metrics and on metrics generated by a a regular graph, that is characterized by a connectivity rule defined by the structuring element
		To generate useful Distance transforms, the structuring elements must be symmetric and have the origin included.
		The Euclidean distance transform is rounded to the nearest integer, since it is represented as an unsigned integer image.
	www.mmorph.com /pymorph/morph/morph/mmdist.html (156 words)

	[No title]
		Sketch the Euclidean distance from A (2,3) to the given B. Sketch the taxicab distance from A (2,3) to the given B. Find the Euclidean distance and taxicab distance from (2,3) to the following points.
		Find as many geoboard pegs as possible that are at a Euclidean distance 5 from (5,5) Find as many geoboard pegs as possible that are at a taxicab distance 5 from (5,5).
		In Euclidean geometry, for three points A, B, and C we always have EMBED Equation.3 This is called the triangle inequality.
	www.kctm.org /taxicab.doc (749 words)

	taxicab homework key (Site not responding. Last check: 2007-10-21)
		The taxicab distance is usually longer than the Euclidean distance.
		The taxicab distance can be equal to the Euclidean distance only when P and Q are on the same horizontal or vertical line.
		No: For example, B and H are the same Euclidean distance from A, but they are different taxicab distances from A. No: For example, F and G are the same taxicab distance from A, but they are different Euclidean distances from A. Circles
	www.austincc.edu /herbling/taxi-key.html (147 words)

	Computing Proximities
		Just by examining the proximities we can determine interesting details, such as the fact that donkey and zebra are quite similar, with a squared distance value of 0.186, whereas donkey and seal are the two most dissimilar cases, with a squared distance of 8.731.
		Of course it's not very practicable to examine all 288 proximities by inspecting the proximity matrix for 25 cases; and it certainly would not be practicable with 10,000 cases.
		Binary Euclidean Distance (B+C)/M is a dissimilarity coefficient and the other two are similarity coefficients.
	www.clustan.com /computing_proximities.html (588 words)

Try your search on: Qwika (all wikis)