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Action classification
Common Subspace Projection
Feature
Extraction
Feature
Extraction
Feature
Extraction
. . .
Fig. 1. Overview of the proposed system. Features are extracted for each available
view. They are projected into a common subspace by Canonical Correlation Analysis.
This projection is the used for action classification.
3.1 Classical Definition
Canonical Correlation Analysis [6] allows measuring the linear relationship be-
tween a pair of multidimensional variables. Given two random variables x 1 and
x 2 of dimension d 1 and d 2 and zero mean, CCA finds a pair of linear transforma-
tions w 1 , w 2 , such that one component within each set of transformed variables
is correlated with a single component in the other set. The correlation between
the corresponding components is called canonical correlation, and there can be
at most d = min ( d 1 ,d 2 ) canonical correlations. The first canonical correlation
is defined as:
w 1 x 1 ·
w 2 x 2
ρ =max
w 1 ,w 2
2
2
w 1 x 1
w 2 x 2
w 1 x 1 x 2 w 2
w 1 x 1 x 1 w 1 w 2 x 2 x 2 w 2
where x 1 x 1 , x 2 x 2 and x 1 x 2 are respectively estimated as Σ 11 , Σ 22 and
Σ 12 , i.e, the different minors of the sample covariance matrix
=max
w 1 ,w 2
Σ = Σ 11
Σ 12
Σ 21
Σ 22
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