City block

To construct dissimilarity measures, one uses mismatches Here a + b is the Hamming (Manhattan, taxi-cab, city-block) distance, and a + h) is the Euclidean distance. 

Hamming, Manhattan, taxi-cab, city-block distance (a + fc) ... 

At the bar at Chino Latino, which looked about a city block long and was backlighted with yellow LED-like light, a young crowd in baseball caps and beautifully conditioned hair hoisted beer bottles and cocktail glasses and jammed themselves together happily like a child balling a piece of white bread. 

It can be shown [5] that the Hamming distance is a binary version of the city block distance (Section 30.2.3.2). 

For those variables that are measured on a scale of integer values consisting of more than two levels, one uses the Manhattan or city-block distance. This is also referred to as the L,-norm. It is given for variable j by ... 

Fig. 30.6. D - is the Euclidean distance between i and i dm and dm are the city-block distances between i and i for variables Xi and X2 respectively. The city-block distance is 4ri + dm-...

In the case of r = 2 we obtain the ordinary Euclidean distance of eq. (31.75), which is also called the L2-norm. In the case of r = 1 we derive the city-block distance (also called Hamming-, taxi- or Manhattan-distance), which is also referred to as... 

Non-linear PCA can be obtained in many different ways. Some methods make use of higher order terms of the data (e.g. squares, cross-products), non-linear transformations (e.g. logarithms), metrics that differ from the usual Euclidean one (e.g. city-block distance) or specialized applications of neural networks [50]. The objective of these methods is to increase the amount of variance in the data that is explained by the first two or three components of the analysis. We only provide a brief outline of the various approaches, with the exception of neural networks for which the reader is referred to Chapter 44. 

The same idea can be developed in the case of a non-Euclidean metric such as the city-block metric or L,-norm (Section 31.6.1). Here we find that the trajectories, traced out by the variable coefficient kj are curvilinear, rather than linear. Markers between equidistant values on the original scales of the columns of X are usually not equidistant on the corresponding curvilinear trajectories of the nonlinear biplot (Fig. 31.17b). Although the curvilinear trajectories intersect at the origin of space, the latter does not necessarily coincide with the centroid of the row-points of X. We briefly describe here the basic steps of the algorithm and we refer to the original work of Gower [53,54] for a formal proof. 

The Third Army had not fought on paper, they were short of file cabinets and folders. To salvage these, they tossed away vital Farben evidence. More than a hundred tons of records lay dispersed over an area larger than a city block when the Bernstein investigators came down from Berlin Northwest 7. 

The chemical constitution of a molecule or an ensemble of molecules (EM) of n atoms is representable by a symmetric n X n BE-matrix and corresponds accordingly to a point P in TR ( +D/a an n(n +1)/2 dimensional Euclidean space, the Dugundji space of the FIEM(A). The "city block distance of two points P i and P 2 is twice the number of electrons that are involved in the interconversion EMi EM2 of those EM that belong to the points Pi and P2. This chemical metric on the EM of an FIEM provides not only a formalism for constitutional chemistry, but also allows us to use the properties of Euclidean spaces in expressing the logical structure of the FIEM, and thus of constitutional chemistry 3e>32c>. 

Euclidean distance City block (Manhattan) distance Minkowski distance Correlation coefficient (cos a), similarity... 

FIGURE 2.10 Euclidean distance and city block distance (Manhattan distance) between objects represented by vectors or points xA and xB. The cosine of the angle between the object vectors is a similarity measure and corresponds to the correlation coefficient of the vector... 

The distance between object points is considered as an inverse similarity of the objects. This similarity depends on the variables used and on the distance measure applied. The distances between the objects can be collected in a distance matrk. Most used is the euclidean distance, which is the commonly used distance, extended to more than two or three dimensions. Other distance measures (city block distance, correlation coefficient) can be applied of special importance is the mahalanobis distance which considers the spatial distribution of the object points (the correlation between the variables). Based on the Mahalanobis distance, multivariate outliers can be identified. The Mahalanobis distance is based on the covariance matrix of X this matrix plays a central role in multivariate data analysis and should be estimated by appropriate methods—mostly robust methods are adequate. 

Euclidean distance, (Euclid), city block distance, d(city), or Mahalanobis distance, (Mahalanobis). 

Similarity and Distance. Two sequences of subgraphs m and n such as those in Table 1 have the property that there is a built-in one-to-one correspondence between the elements of one sequence (m,) and those of the other (/i,). Accordingly, it is straightforward to calculate various well-known (17) measures of the distance d between the sequences, e.g. Euclidean distance [2,( Wi city block distance... 

Bit vectors live in an -dimensional, discrete hypercubic space, where each vertex of the hypercube corresponds to a set. Figure 2 provides an example of sets with three elements. Distances between two bit vectors, vA and vB, measured in this space correspond to Hamming distances, which are based on the city-block Zj metric... 

Distances in these spaces should be based upon an Zj or city-block metric (see Eq. 2.18) and not the Z2 or Euclidean metric typically used in many applications. The reasons for this are the same as those discussed in Subheading 2.2.1. for binary vectors. Set-based similarity measures can be adapted from those based on bit vectors using an ansatz borrowed from fuzzy set theory (41,42). For example, the Tanimoto similarity coefficient becomes... 

Test Station, China Lake, Caiif (Refs 3 vapor clouds were once considered a way-out technique. A cloud of volatile fuel, mixed with air, is discharged and then detonated on a target, with the same violent expin that characterized grain-silo dust explns or blast, when a propane tank truck blows up. This kind of expln can level a city block. 

A firefighter is often required to assist civilians who seek travel directions or referral to city agencies and facilities. The accompanying map shows a section of the city where some public buildings are located. Each of the squares represents one city block. Street... 

Continuous or unbroken site or a set of buildings in adjacent city blocks. 

Level 2 changes consist of site changes within a contiguous campus, or between facilities in adjacent city blocks, where the same equipment, SOP s, environmen-tal conditions (e.g., temperature and humidity) and controls, and personnel common to both manufacturing sites are used, and where no changes are made to the manufacturing batch records, except for administrative information and the location of the facility. 

New and old building not on a contiguous site or not in adjacent city blocks. 

Different campus—one that is not on the same original contiguous site or where the facilities are not on adjacent city blocks. 

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