sparse dictionary-based representation and recognition of...
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Sparse Dictionary-based
Representation and Recognition
of Action Attributes
Qiang Qiu, Zhuolin Jiang, Rama Chellappa
Center for Automation Research,
Institute for Advanced Computer Studies
University of Maryland, College Park
qiu@cs.umd.edu, {zhuolin, rama}@umiacs.umd.edu
Action Feature Representation
2
Shape
Motion
HOG
Action Sparse Representation
3
=
0 0 0.64 0.53 -0.40 0.35 0 0 0
0.43 0.63 0 0 -0.33 0 -0.36 0 0
= 0.43 × + 0.63 × - 0.33 × - 0.36 ×
= 0.64× + 0.53× - 0.40 × +0.35 ×
Action Dictionary
Sparse code
K-SVD
4
=
Y
y2 d1 d2 d3 …
0 0 0.64 0.53 -0.40 0.35 0 0 0
0.43 0.63 0 0 -0.33 0 -0.36 0 0
x1 x2
y1
D
X
K-SVD [1]
Input: signals Y, dictionary size, sparisty T
Output: dictionary D, sparse codes X
arg min |Y- DX|2 s.t. i , |xi|0 ≤ T D,X
Input signals Dictionary
Sparse codes
[1] M. Aharon and M. Elad and A. Bruckstein, K-SVD: An Algorithm for Designing
Overcomplete Dictionries for Sparse Representation, IEEE Trans. on Signal Process, 2006
5
Compact Discriminative and
Dictionary.
Learn a
Objective
Probabilistic Model for Sparse
Representation
A Gaussian Process
Dictionary Class Distribution
6
7
= 0.43 0.63 0 0 -0.33 0 -0.36 0 0 0 0 0 0
0 0 0.64 0.53 -0.40 0.35 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 -0.28 0.698 0.37 0.25 0
0 0 0 0 -0.42 0 0 0 0 0.42 0.47 0 0.32
y2 y1 y4 y3
l1 l1 l2 l2
d1 d2 d3 …
x1 x2 x3 x4
xd1
l1 l1 l2 l2
More Views of Sparse Representation
8
y2 y1 y4 y3
l1 l1 l2 l2
xd1 0.43 0 0 0
x1 x2 x3 x4
0.63 0 0 0
0 0.64 0 0
0 0.53 0 0
-0.33 -0.40 0 -0.42
… …
xd2
xd3
xd4
xd5
l1 l1 l2 l2
d1
d2
d3
d4
d5
A Gaussian Process
• Covariance function entry: K(i,j) = cov(xdi, xdj)
• P(Xd*|XD*) is a Gaussian with a closed-form conditional variance
A Gaussian Process
9
y2 y1 y4 y3
l1 l1 l2 l2
xd1 0.43 0 0 0
x1 x2 x3 x4
0.63 0 0 0
0 0.64 0 0
0 0.53 0 0
-0.33 -0.40 0 -0.42
… …
xd2
xd3
xd4
xd5
l1 l1 l2 l2
d1
d2
d3
d4
d5
Dictionary Class Distribution
• P(L|di), L [1, M]
• aggregate |xdi| based on class labels to obtain a M sized vector
• P(L=l1|d5) = (0.33+0.40)/(0.33+0.40+0.42) = 0.6348
• P(L=l2|d5) = (0+0.42)/(0.33+0.40+0.42) = 0.37
Dictionary Class Distribution
Dictionary Learning Approaches
Maximization of Joint Entropy (ME)
Maximization of Mutual Information (MMI)
Unsupervised Learning (MMI-1)
Supervised Learning (MMI-2)
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11
Maximization of Joint Entropy (ME)
- Initialize dictionary using k-SVD
Do =
- Start with D* = - Untill |D*|=k, iteratively choose d* from Do\D*,
d* = arg max H(d|D*)
Where
-A good approximation to ME criteria
arg max H(D)
d
D
ME dictionary
12
Maximization of Mutual Information
for Unsupervised Learning (MMI-1)
- Initialize dictionary using k-SVD
Do =
- Start with D* = - Untill |D*|=k, iteratively choose d* from Do\D*,
d* = arg max H(d|D*) - H(d|Do\(D* d))
-A near-optimal approximation to MMI criteria
arg max I(D; Do\D)
Within (1-1/e) of the optimum
d
D
MMI dictionary
13
Dictionary Class Distribution
• P(L|di), L [1, M]
• aggregate|xdi|based on class labels to obtain a M sized vector
• P(l1|d5) = (0.33+0.40)/(0.33+0.40+0.42) = 0.6348
• P(l2|d5) = (0+0.42)/(0.33+0.40+0.42) = 0.37
• P(Ld) = P(L|d) • P(LD) = P(L|D) , where
y2 y1 y4 y3
l1 l1 l2 l2
xd1 0.43 0 0 0
x1 x2 x3 x4
0.63 0 0 0
0 0.64 0 0
0 0.53 0 0
-0.33 -0.40 0 -0.42
… …
xd2
xd3
xd4
xd5
l1 l1 l2 l2
d1
d2
d3
d4
d5
Revisit
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Maximization of Mutual Information
for Supervised Learning (MMI-2)
- Initialize dictionary using k-SVD
Do =
- Start with D* = - Untill |D*|=k, iteratively choose d* from Do\D*,
d d* = arg max [H(d|D*) - H(d|Do\(D* d))]
+ λ[H(Ld|LD*) – H(Ld|LDo\(D* d))]
- MMI-1 is a special case of MMI-2 with λ=0.
Other learning methods
K-means
Liu-shah [1]
15
where
[1] J. Liu and M. Shah, Learning Human Actions via Information Maximization, CVPR 2008
Purity and Compactness
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Representation Consistency
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Keck gesture dataset
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Recognition Accuracy
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The recognition accuracy using initial dictionary Do: (a) 0.23 (b) 0.42 (c) 0.71
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