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By Неизв.

ISBN-10: 1681081113

ISBN-13: 9781681081113

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Extra resources for Advances in Face Image Analysis: Theory and Applications

Example text

Yn]T be a one-dimensional map of X. Under a linear projection yT = pT X, each data point xi in the input space Rm is mapped into yi= pT xi in the real line. Here, p Rm is a projection axis. Let Y Rd×n be the data projections into a d dimensional space. Locality Preserving Projection LPP aims to preserve the local structure of the data by keeping two sample points close in the projection space when they are similar in the original space. The reasonable criterion of LPP is to optimize the following objective function under some constraints: (1) where W is the affinity matrix associated with the data.

In the projection space, a constraint matrix U is used to keep the samples with a same label in one point. The definition of U is as follows: (15) where the i-th row of J is a indictor vector of xi: (16) where j = 1,. , c. An auxiliary vector z is adopted to implement the constraint: (17) with the above constraint, it is clearly to see that if xi and xj share the same label, then yi= yj. With simple algebraic formulation, we have: (18) and (19) where the affinity matrix W is simply calculated as in Eq.

Let Y Rd×n be the data projections into a d dimensional space. Locality Preserving Projection LPP aims to preserve the local structure of the data by keeping two sample points close in the projection space when they are similar in the original space. The reasonable criterion of LPP is to optimize the following objective function under some constraints: (1) where W is the affinity matrix associated with the data. The way to define W can be alterable. One simple definition is as follows: (2) where δk( xi) means a set of the k neighbors of xi .

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Advances in Face Image Analysis: Theory and Applications by Неизв.


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