Eigenfaces vs. Fisherfaces: recognition using class specific linear projection

1997 ◽  
Vol 19 (7) ◽  
pp. 711-720 ◽  
Author(s):  
P.N. Belhumeur ◽  
J.P. Hespanha ◽  
D.J. Kriegman
Keyword(s):  
Linear Projection

scholarly journals Auerbach Bases and Minimal Volume Sufficient Enlargements

2011 ◽  
Vol 54 (4) ◽  
pp. 726-738
Author(s):  
M. I. Ostrovskii
Keyword(s):  
Linear Space ◽  
Isometric Embedding ◽  
Normed Linear Space ◽  
Convex Set ◽  
Linear Projection ◽  
Minimal Volume ◽  
Finite Dimensional ◽  
Dimensional Normed Space ◽  
Closed Convex Set

AbstractLet BY denote the unit ball of a normed linear space Y. A symmetric, bounded, closed, convex set A in a finite dimensional normed linear space X is called a sufficient enlargement for X if, for an arbitrary isometric embedding of X into a Banach space Y, there exists a linear projection P: Y → X such that P(BY ) ⊂ A. Each finite dimensional normed space has a minimal-volume sufficient enlargement that is a parallelepiped; some spaces have “exotic” minimal-volume sufficient enlargements. The main result of the paper is a characterization of spaces having “exotic” minimal-volume sufficient enlargements in terms of Auerbach bases.

Discriminant Criteria for Pattern Classification

2011 ◽  
pp. 30-57
Author(s):  
David Zhang ◽  
Fengxi Song ◽  
Yong Xu ◽  
Zhizhen Liang
Keyword(s):  
Feature Extraction ◽  
Pattern Classification ◽  
The Other ◽  
Linear Projection ◽  
Linear Discriminant ◽  
Large Margin ◽  
The Third ◽  
Fisher Discriminant ◽  
Squared Error ◽  
Fisher Discriminant Criterion

As mentioned in Chapter II, there are two kinds of LDA approaches: classification- oriented LDA and feature extraction-oriented LDA. In most chapters of this session of the book, we focus our attention on the feature extraction aspect of LDA for SSS problems. On the other hand,, with this chapter we present our studies on the pattern classification aspect of LDA for SSS problems. In this chapter, we present three novel classification-oriented linear discriminant criteria. The first one is large margin linear projection (LMLP) which makes full use of the characteristic of the SSS problems. The second one is the minimum norm minimum squared-error criterion which is a modification of the minimum squared-error discriminant criterion. The third one is the maximum scatter difference which is a modification of the Fisher discriminant criterion.

A characterization of M-Summands

1974 ◽  
Vol 76 (1) ◽  
pp. 157-159 ◽  
Author(s):  
Richard Evans
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Closed Subspace ◽  
Structure Theory ◽  
Linear Projection ◽  
Image Position

In the structure theory of Banach spaces as developed in (1), an important role is played by subspaces which are the ranges of projections having norm properties akin to those of the classical Banach spaces. A linear projection e on a Banach space V is called an M-projection ifand an L-projection if, insteadA closed subspace J of V is called an M-Summand if it is the range of an M-projection and an M-Ideal if J0 is the range of an L-projection in V′. Every M-Summand is an M-Ideal but the reverse is false.

Bringing Chaos to Order: Historical Memory and the Manipulation of History

2008 ◽  
Vol 15 (3-4) ◽  
pp. 280-303 ◽  
Author(s):  
Richard Ascough
Keyword(s):  
Historical Memory ◽  
Modern Science ◽  
Scientific Models ◽  
Social Scientists ◽  
Linear Projection ◽  
Classical Studies ◽  
Non Linear ◽  
Historical Investigation ◽  
Roman Antiquity

AbstractIn modern approaches to biblical and classical studies enlightenment scientific models have dominated historical investigation. As such, the notion of memories and traditions, even when they are assumed to be invented, are presented as reflecting a linear projection of history, with singular causes of change. Modern science, however, has moved beyond the Newtonian view of mechanics that undergirds such a view and is working with models of chaos and complexity. Social scientists and humanists are lagging behind and are only now beginning to understand the implications for their disciplines. This paper adds another voice to the small but growing cadre of promoters of a non-linear notion of historiography by noting its implications for a project of redescribing Graeco-Roman antiquity.

On Some Classes of Primary Banach Spaces

1977 ◽  
Vol 29 (4) ◽  
pp. 856-873 ◽  
Author(s):  
P. G. Casazza ◽  
C. A. Kottman ◽  
Bor-Luh Lin
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Bounded Linear ◽  
Linear Projection

A Banach spaceXis calledprimary(respectively,prime)if for every (bounded linear) projectionPonXeitherPXor (I—P)X(respectively,PXwith dimPX =∞ ) is isomorphic toX.It is well-known that C0andlp, 1 ≦p≦ ∞ [8;14] are prime. However, it is unknown whether there are other prime Banach spaces. For a discussion on prime and primary Banach spaces, we refer the reader to [9].

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