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Topic: Manhattan distance

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	Sensei's Library: Manhattan distance
		Manhattan distance is a measure of the distance between two vertices used in computer go.
		A "circle" is defined as the set of all points that have the same distance from a given point.
		Fhayashi: Presumably, the name reflects the fact that in modern urban cities with orthogonal streets, regardless of the straight-line distance between two points, the practical distance is the number of block-sides you must transit to get to your destination...
	senseis.xmp.net /?ManhattanDistance (208 words)

	Distance - Wikipedia, the free encyclopedia
		In the case of two locations on Earth, usually the distance along the surface is meant: either " as the crow flies " (along a great circle) or by road, railroad, etc. Distance is sometimes expressed in terms of the time to cover it, for example walking or by car.
		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 a 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 (551 words)

	Taxicab geometry - Wikipedia, the free encyclopedia
		Taxicab geometry, considered by Hermann Minkowski in the 19th century, is a form of geometry in which the usual metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the (absolute) differences of their coordinates.
		Notice that the Manhattan distance depends on the choice on the rotation of the coordinate system, but does not depend on the translation of the coordinate system or its reflection with resect to a coordinate axis.
		In chess, the distance between squares on the chessboard for rooks is measured in Manhattan distance; kings and queens use Chebyshev distance, and bishops use the Manhattan distance (between squares of the same color) on the chessboard rotated 45 degrees, i.e., with its diagonals as coordinate axes.
	en.wikipedia.org /wiki/Manhattan_distance (347 words)

	Distance
		In mathematics, a distance between two points P and Q in a metric space is d ( P, Q), where d is the distance function.
		The distance, d, between two points expressed in Cartesian coordinates equals the square root of the sum of the squares of the changes of each coordinate.
		He used four categories for informal space: the intimate distance for embracing or whispering (6-18 inches), the personal distance for conversations among good friends (1.5-4 feet), social distance for conversations among acquaintances (4-12 feet), and public distance used for public speaking (12 feet or more).
	www.brainyencyclopedia.com /encyclopedia/d/di/distance.html (708 words)

	Distance Summary
		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.
	www.bookrags.com /Distance (3719 words)

	Patent 5384722: Apparatus and method for determining the Manhattan distance between two points
		One application of this basic distance measure is in recognition routines and algorithms where a distance measure is used to quantify the difference between an unknown and a reference pattern, such that a determination can be made as to the identity of the unknown.
		Another distance measure is referred to as the Manhattan distance measure, or the "city block distance." The Manhattan distance is the distance between two points as measured by a path comprised of horizontal and vertical perpendicular paths and is illustrated in conjunction with FIG.
		When the instruction is the Manhattan distance instruction, an opcode of 1B Hex causes two of the operator units to be involved, namely the adder/subtractor 70b and the ALU operator 70c.
	www.freepatentsonline.com /5384722.html (11445 words)

	[No title] (Site not responding. Last check: 2007-09-11)
		The first one was used was to calculate the straight distance from the current node to the goal node and multiply it by 3 which is the distance by the diagonal move.
		Manhattan Distance - this is the sum of the number of moves that a particular tile must take to get to its desired position.
		Manhattan Heuristic This heuristic goes beyond the Misplaced Blank Heuristic,returning the sum of the Manhattan distances every tile is from its final resting place (rather than just the blank).
	www.cs.colostate.edu /~cs440/assignments/assignment2-readmes (14930 words)

	Features
		Manhattan distance is computed by taking the sum of the distances for each feature taken one at a time.
		While Euclidean gives you the shortest distance between two points "as the crow flies", Manhattan distance is like walking along city blocks in New York - the distance walked is the sum of the distances walked along streets and avenues separately.
		Hamming distance, like Manhattan distance, is the sum of the distances computed feature by feature, where the distance for each feature is restricted to be either zero or one.
	www.shepardsons.net /OptiPath/Documentation/Features.htm (1327 words)

	Effect of Distance Measure on k-NN (Site not responding. Last check: 2007-09-11)
		The goal of this exercise is to briefly examine the effect of the distance measure on the compuation time and classification accuracy of k-NN.
		I looked at the standard Euclidean distance (which is built into Weka, so I've been using it for most of the classifications), the Euclidean distance without the square root, and the Manhattan distance.
		Manhattan appears to tend to consistantly have the lowest standard deviation.
	www.music.mcgill.ca /~rebecca/thesis/distance/distance_measures1.htm (369 words)

	Mining Software Engineering Data: A Survey - 5.3 Clustering Techniques (Site not responding. Last check: 2007-09-11)
		The algorithm uses the distance measure to agglomerate single records in clusters and interactively group these clusters into higher level clusters until all the records are clustered together at the highest level cluster.
		The distance measure used to group clusters together is the minimum distance between the records of the lower level clusters.
		The Euclidean distance is calculated as the square root of the sum of the squared distances.
	www.dacs.dtic.mil /techs/datamining/Ctechniques.shtml (1094 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)

	[No title] (Site not responding. Last check: 2007-09-11)
		It has the property that distances along any line-of-sight will be accurate within a factor of 2/sqrt(2), and distances along the same line of sight will compare accurately.
		Where the manhattan distance is accurate within 2/sqrt(2), the Chebyshev distance is accurate within sqrt(2)/2.
		Typically you want to use the manhattan distance when it's important not to underestimate and the Chebyshev distance when it's important not to overestimate.
	library.simugraph.com /relview/docs/rpg/levelgeneration/distance_calculation.txt (486 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)

	MMU - Biol. Sic., MSc Multivariate Stastics: distance measures
		Although there are important differences between distances and similarities the two sets of measures are both referred to as distances in these notes.
		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)

	The Big Apple
		"Manhattan distance" is a mathematical term based on the grid system for Manhattan's street.
		284 The approximation for distance is sometimes called the 'Manhattan distance', because the distance between two points in New York City is best thought of as the distance along city streets at right angles to one another.
		For example, if [P] denotes Manhattan distance the unit circle is a square with corners on the x and y axes and with sides of (Euclidean) length 2 1/2(power - ed.).
	www.barrypopik.com /index.php/new_york_city/comments/manhattan_distance (376 words)

	Manhattan Networks (Site not responding. Last check: 2007-09-11)
		The problem of Manhattan Networks is extensively encountered in fields ranging from transportation, robotics, designing of printed circuit boards to layout of pipes and cables.
		Manhattan Networks are used to plan an optimum and efficient layout, reducing path lengths and conserving space.
		The efficient layout of aisles can reduce the space used, the distance and the time spent on movement of men and material from one work station to the next.
	www.utpadan.com /manhattan/manhattan.htm (705 words)

	Efficiently Implementing Dilate and Erode Image Functions
		In Manhattan, the distance between any two places is the number of blocks you have to walk to get there.
		The distance to the nearest pixel will be the minimum of the pixel to the left and the pixel to the right.
		The maximum Manhattan distance that a pixel can be away from a pixel that is "on" is the sum of the width and the height of the image.
	ostermiller.org /dilate_and_erode.html (1147 words)

	distance measures
		There are distances that are euclidean (can be measured with a 'ruler') and there are other distances based on similarity.
		However, if distance is measured in terms of the characteristics of a city York is closer to Canterbury.
		Distances that are not straight-line, but which obey certain rules.
	www.doe-mbi.ucla.edu /~parag/multivar/dist.htm (810 words)

	Manhattan (Site not responding. Last check: 2007-09-11)
		Manhattan distance is the "city block" distance function (metric) we usually use in computing distance traveling along streets and avenues between two points
		The alternatives to Manhattan distance are Euclidean distance and Hamming distance.
		If you choose to use different metrics for different features of your data, particularly if one feature uses Hamming distance, it may be advisable to normalize your data, particularly for features using Euclidean or Manhattan distance.
	www.shepardsons.net /OptiPath/Documentation/manhattan.htm (134 words)

	Francis Hwang: Defining distance
		The importance of distance breaks down most visibly in a place like New York, where dense transit networks and intense crowding conspire to create a physical environment in which normal strategies are irrelevant.
		Mapquest can recommend the shortest route by geographical distance, but if you hit a bad stretch of highway coming out of Manhattan on a Friday evening you could waste an hour in stop-and-go traffic, at which point driving a quarter-mile less in distance would be scant consolation.
		Of course, this means that Manhattan is proportionally bigger in the subway map than in real life, which could affect our psychological impression of Manhattan's importance, which could affect City Hall's funding priorities regarding the development of new subway lines...
	fhwang.net /blog/19.html (682 words)

	[No title] (Site not responding. Last check: 2007-09-11)
		A heuristic that is said to be “consistent” is one that never overestimates the distance to the goal.
		This heuristic, however, is dominated by the “Manhattan Distance” heuristic, which calculates necessary moves to goal without constraining moves to places that are empty.
		Searching using the addition of the Manhattan Distance and the number of blocks out of place as the heuristic would return very different answers, sometimes much faster and sometimes much slower than using the former alone, even on the same puzzle.
	www.rpi.edu /~gerstm/AIassn3.doc (488 words)

	Manhattan distance (Site not responding. Last check: 2007-09-11)
		Definition: The distance between two points measured along axes at right angles.
		Manhattan distance is often used in integrated circuits where wires only run parallel to the X or Y axis.
		distance, taxi cab metric, or city block distance.
	www.nist.gov /dads/HTML/manhattanDistance.html (124 words)

	AiLab.si
		For other measure of distance, a distance between unknown and known or between two unknown values is always 0.5.
		Manhattan distance between two examples is a sum of absolute values of distances between pairs of attributes, e.g.
		Euclidean distance is a square root of sum of squared per-attribute distances, i.e.
	www.ailab.si /orange/doc/reference/ExamplesDistance.htm (803 words)

	Crowne Plaza Manhattan. (Site not responding. Last check: 2007-09-11)
		Located in the heart of Manhattan; the Algonquin is the hotel preferred by those who best appreciate NY; a true landmark with a tradition of elegance that began a century ago.
		In the heart of Manhattan the 3 star Roosevelt Hotel NY is perfectly positioned where the business district meets the shopping and theatre districts.
		The hotel is within walking distance of many downtown attractions including the Hudson River Esplanade; The New York Stock Exchange; Pier 11 and the ferries to the Statue of Liberty and Ellis Islan This 2 star Grand Union Hotel is located in Midtown Manhattan.
	www.travel-days.com /NY/crowne-plaza-manhattan.htm (2190 words)

	Your Heading Goes Here
		The heuristic estimates the distance from a state to the solution.
		This computation of distance to be traveled (assuming a grid-like path), is sometimes referred to as 'Manhattan distance' (as opposed to an 'as the crow flies' distance).
		The sum of such distances added across all 15 blocks gives us an optimistic estimate of the total number of moves to get to the desired solution.
	goalseeker.sourceforge.net /Heuristic.htm (452 words)

	Worley (Site not responding. Last check: 2007-09-11)
		The basic idea of the function is to compute the distance from any render point on the surface of the object to some cell centers.
		It is called Manhattan because of the similarity of having to walk around blocks in streets when you want to go from one point to another in a city.
		C1, C2, C3 and C4 are respectively the distance from the render point to the nearest cell, to the second nearest cell, to the third nearest cell and to the fourth nearest cell.
	www.ypoart.com /Downloads/worley.htm (1396 words)

	Routing with SNACC
		The Manhattan distance between two points is the sum of the horizontal distance between two points and the vertical distance between two points.
		Thus, the Manhattan distance is equal to the minimum wire length necessary to connect the endpoints of a network routing along gridded channels.
		The Manhattan distance between the two endpoints of network A is 5, the sum of the horizontal distance between the endpoints (3) and the vertical distance between the endpoints (2).
	www.cs.utexas.edu /users/bogo/vlsi/node2.html (1297 words)

	Cluster Analysis
		However, the joining algorithm does not "care" whether the distances that are "fed" to it are actual real distances, or some other derived measure of distance that is more meaningful to the researcher; and it is up to the researcher to select the right method for his/her specific application.
		This method has certain advantages (e.g., the distance between any two objects is not affected by the addition of new objects to the analysis, which may be outliers).
		In this method, the distance between two clusters is calculated as the average distance between all pairs of objects in the two different clusters.
	www.statsoftinc.com /textbook/stcluan.html (3800 words)

	Improved Heterogeneous Distance Functions
		As discussed in the previous section, the Euclidean distance function is inappropriate for nominal attributes, and VDM is inappropriate for continuous attributes, so neither is sufficient on its own for use on a heterogeneous application, i.e., one with both nominal and continuous attributes.
		As discussed in Section 2.1, distances are often normalized by dividing the distance for each variable by the range of that attribute, so that the distance for each input variable is in the range 0..1.
		When computing the distance for each attribute, the normalized_diff function was used for linear attributes, and the normalized_vdm function N1, N2, or N3 was used (in each of the three respective experiments) for nominal attributes.
	axon.cs.byu.edu /~randy/jair/wilson3.html (1952 words)

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