Signal Processing - January 2017 - 100
DCA
PCA
Random
14
10
5
2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Face
Recognition Performance (Yale)
4,096
2,000
1,000
Accuracy
PPFR simulation results
Dimension (Log Scale)
Figure 6. The FR accuracies on the Yale data
set, with respect to different reduced-dimensions via DCA, PCA, and random projection.
(Figure courtesy of T. Chanyaswad.)
eig ^ Sr , S W U + tI h,
(34)
where S W U denotes the within-(utility)class scatter matrix. This variant is
an extension of Fisher's LDA and is
indeed a very close sibling of the DIMtype DCA. To prove that the Fishertype DCA is exactly the same as the
DIM-type DCAs, when t = 0, we
let {m i, v i} and {mli , vli} respectively
denote the eigenvalues/eigenvectors
for DIM-DCA [see (32)] and FisherDCA [see (34)]. It can then be shown
that vli = v i and mli = (1 - m i) -1 . The
latter guarantees " mli , and {m i} to be
sorted in the same order, thus verifying the equivalence.
Apply PCA and DCA to the Yale data
set for PP face recognition (FR) (PPFR)
applications, we have the following
observations:
■■ PCA/DCA Classification Ac -
curacies. There are only L - 1
meaningful eigenvectors, because
rank ^S B U h # L - 1. Note also that
usually L % M, it implies that the
DCA eigen-components can enjoy a
win-win advantage in improving privacy without sacrificing utility.
- First, the L - 1 principal components can capture key features
fully adequate for very high performance, as evidenced by the
performance curves shown in
Figure 6. Note that DCA far outperforms PCA and random projection in terms of FR accuracies.
- The DCA dimension reduction
results in removal of a large proportion of components, making it
an effective compression tool for
privacy preservation.
■■ Data Visualization by PCA/DCA
Projection. The high-dimensional
Yale data set may be visualized by
means of two-dimensional PCA or
DCA subspace projection. Figure 7(a) displays the PCA visualization, showing that many classes are
nonseparable by PCA. In contrast,
the DCA visualization in Figure 7(b)
shows very well separated classes.
In fact, many data points from the
same class align almost perfectly,
sometimes making the whole class
of data projected to a single point.
Privacy-driven desensitized
DCA via ridge DCA (RDCA)
In the previous section, the utility-driven learning algorithms are good for scenarios where the intended utility is well
defined but the privacy policy is still
open. Conversely, there are other scenarios where the intended utility is yet
to be determined but the privacy policy
is already pre-defined. This calls for a
DCA variant tailored designed for the
extraction of desensitized components.
To this end, we further incorporate
another ridge parameter tl to regulate
the (privacy) signal matrix S B P, resulting in the following privacy-driven
learning algorithm [7].
Algorithm 2: Privacy-driven
ridge DCA algorithm
Find the projection
W RDCA ! 0 M # m:
W RDCA =
argmax
{W: W T 6 Sr + tI @W = I}
tr ^W T 6S B P - tl I@ Wh .
where S B P denotes the between(privacy)-class scatter matrix and tl
is a small positive value. The optimal
RDCA solution can be derived from
the m eigenvectors corresponding to the
Lth, f, (L + m - 1) th eigenvalues of
eig ^S B P - tl I , Sr + tIh .
100
DCA 2
P (v i) . -
0
-100
Equation (36) assures that the desensitized components can be orderly
extracted according to their eigenvalues, just like PCA. This is why RDCA
is sometimes referred to as desensitized
DCA or, more simply, desensitized PCA.
Let us highlight some key properties of
RDCA's eigen-components:
■■ Signal-Subspace Components, i.e.,
when i 1 L: The first L - 1 eigencomponents are potentially most
400
300
200
100
0
-100
-200
4,000
2,000
-200
0
- t, for i $ L. (36)
4
DCA 1
(b)
Figure 7. The high-dimensional Yale data set may be visualized by means of two-dimensional (a) PCA
or (b) DCA subspace projection. Each mark represents a data point, and data points in the same class
share the same shape and color. (Figure courtesy of T. Chanyaswad.)
100
tl
mi
-50
-150
PCA 1
(a)
(35)
The component powers are closely related to their corresponding eigenvalues:
DCA-Subspace Visualization
50
-2,000
4,000
3,000
2,000
1,000
0
-1,000
-2,000
-3,000
-4,000
-4,000
PCA 2
PCA-Subspace Visualization
mat r ix
IEEE Signal Processing Magazine
|
January 2017
|
Table of Contents for the Digital Edition of Signal Processing - January 2017
Signal Processing - January 2017 - Cover1
Signal Processing - January 2017 - Cover2
Signal Processing - January 2017 - 1
Signal Processing - January 2017 - 2
Signal Processing - January 2017 - 3
Signal Processing - January 2017 - 4
Signal Processing - January 2017 - 5
Signal Processing - January 2017 - 6
Signal Processing - January 2017 - 7
Signal Processing - January 2017 - 8
Signal Processing - January 2017 - 9
Signal Processing - January 2017 - 10
Signal Processing - January 2017 - 11
Signal Processing - January 2017 - 12
Signal Processing - January 2017 - 13
Signal Processing - January 2017 - 14
Signal Processing - January 2017 - 15
Signal Processing - January 2017 - 16
Signal Processing - January 2017 - 17
Signal Processing - January 2017 - 18
Signal Processing - January 2017 - 19
Signal Processing - January 2017 - 20
Signal Processing - January 2017 - 21
Signal Processing - January 2017 - 22
Signal Processing - January 2017 - 23
Signal Processing - January 2017 - 24
Signal Processing - January 2017 - 25
Signal Processing - January 2017 - 26
Signal Processing - January 2017 - 27
Signal Processing - January 2017 - 28
Signal Processing - January 2017 - 29
Signal Processing - January 2017 - 30
Signal Processing - January 2017 - 31
Signal Processing - January 2017 - 32
Signal Processing - January 2017 - 33
Signal Processing - January 2017 - 34
Signal Processing - January 2017 - 35
Signal Processing - January 2017 - 36
Signal Processing - January 2017 - 37
Signal Processing - January 2017 - 38
Signal Processing - January 2017 - 39
Signal Processing - January 2017 - 40
Signal Processing - January 2017 - 41
Signal Processing - January 2017 - 42
Signal Processing - January 2017 - 43
Signal Processing - January 2017 - 44
Signal Processing - January 2017 - 45
Signal Processing - January 2017 - 46
Signal Processing - January 2017 - 47
Signal Processing - January 2017 - 48
Signal Processing - January 2017 - 49
Signal Processing - January 2017 - 50
Signal Processing - January 2017 - 51
Signal Processing - January 2017 - 52
Signal Processing - January 2017 - 53
Signal Processing - January 2017 - 54
Signal Processing - January 2017 - 55
Signal Processing - January 2017 - 56
Signal Processing - January 2017 - 57
Signal Processing - January 2017 - 58
Signal Processing - January 2017 - 59
Signal Processing - January 2017 - 60
Signal Processing - January 2017 - 61
Signal Processing - January 2017 - 62
Signal Processing - January 2017 - 63
Signal Processing - January 2017 - 64
Signal Processing - January 2017 - 65
Signal Processing - January 2017 - 66
Signal Processing - January 2017 - 67
Signal Processing - January 2017 - 68
Signal Processing - January 2017 - 69
Signal Processing - January 2017 - 70
Signal Processing - January 2017 - 71
Signal Processing - January 2017 - 72
Signal Processing - January 2017 - 73
Signal Processing - January 2017 - 74
Signal Processing - January 2017 - 75
Signal Processing - January 2017 - 76
Signal Processing - January 2017 - 77
Signal Processing - January 2017 - 78
Signal Processing - January 2017 - 79
Signal Processing - January 2017 - 80
Signal Processing - January 2017 - 81
Signal Processing - January 2017 - 82
Signal Processing - January 2017 - 83
Signal Processing - January 2017 - 84
Signal Processing - January 2017 - 85
Signal Processing - January 2017 - 86
Signal Processing - January 2017 - 87
Signal Processing - January 2017 - 88
Signal Processing - January 2017 - 89
Signal Processing - January 2017 - 90
Signal Processing - January 2017 - 91
Signal Processing - January 2017 - 92
Signal Processing - January 2017 - 93
Signal Processing - January 2017 - 94
Signal Processing - January 2017 - 95
Signal Processing - January 2017 - 96
Signal Processing - January 2017 - 97
Signal Processing - January 2017 - 98
Signal Processing - January 2017 - 99
Signal Processing - January 2017 - 100
Signal Processing - January 2017 - 101
Signal Processing - January 2017 - 102
Signal Processing - January 2017 - 103
Signal Processing - January 2017 - 104
Signal Processing - January 2017 - 105
Signal Processing - January 2017 - 106
Signal Processing - January 2017 - 107
Signal Processing - January 2017 - 108
Signal Processing - January 2017 - 109
Signal Processing - January 2017 - 110
Signal Processing - January 2017 - 111
Signal Processing - January 2017 - 112
Signal Processing - January 2017 - 113
Signal Processing - January 2017 - 114
Signal Processing - January 2017 - 115
Signal Processing - January 2017 - 116
Signal Processing - January 2017 - Cover3
Signal Processing - January 2017 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201809
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201807
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201805
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201803
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_201801
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0917
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0717
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0517
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0317
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0117
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0916
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0716
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0516
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0316
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0116
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0915
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0715
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0515
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0315
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0115
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0914
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0714
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0514
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0314
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0114
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0913
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0713
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0513
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0313
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0113
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0912
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0712
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0512
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0312
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0112
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0911
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0711
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0511
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0311
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0111
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0910
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0710
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0510
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0310
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0110
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0909
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0709
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0509
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0309
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0109
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_1108
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0908
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0708
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0508
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0308
https://www.nxtbook.com/nxtbooks/ieee/signalprocessing_0108
https://www.nxtbookmedia.com