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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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