Signal Processing - January 2017 - 103
Example 5
DUCA Filtering for PPFR Application:
By applying SVM to the full-dimensional Yale data set, it yields a recognition accuracy of 82%. We have also
applied a utility-driven DUCA score,
i.e., -S B U (i, i) / ^Sr (i, i) + th, to select
the best 399 (of 4,096) Wavelet-transformed components. We have found
that the DUCA-filtered CP method actually offers a higher accuracy at 82.3%,
again via SVM. At the same time, it
also totally obfuscates the face images,
as exemplified by Figure 9(d). In short,
the DUCA-filtering feature selection is
promising for PPFR since it offers PP
compression without compromising the
FR accuracy.
4
4
2
2
0
0
-2
-2
-4
-4
-6
-6
-8 -6 -4 -2 0
2
(a)
4
6
8 10
In the kernel learning models [3], u (x)
and p (x) will be nonlinear functions
in general. As such, it can induce an
expanded solution space and thus further
improve the performance. It involves
a simple kernelization procedure to
extend from DCA to kernel DCA [6].
For example, the discriminant matrix
in (31) can be extended to the following
kernel-DCA discriminant matrix:
(39)
r and K B U denote the kernelized
where K
counterparts of Sr and S B U, respectively.
Again, applying eigen-space analysis to
this kernelized matrix will lead to the
optimal query solution in the kernel vector space.
For applications to CP problems,
a kernel-DUCA discriminant matrix
may be derived by substituting K B U by
K B U - K B P in (39). (Again, the principle eigen-subspace analysis would
yield the optimal queries.) However,
for such applications, the reduced dimension must be strictly lower than
the original dimension M, since the
CP encoding scheme must necessarily
be lossy.
Recently, there has been growing interest in multikernel research[3], where
a multikernel function is expressed as
linear combination of many kernels:
-8 -6 -4 -2 0
2
(b)
4
6
8 10
DCA
3
2
1
0
-1
-2
-3
-4
-5
2
1
0
-1
-2
-3
Extension to kernel
DCA and kernel DUCA
r 2 + tK
r ] -1 K B U
[K
PCA
4
-4
-5
-5 -4 -3 -2 -1 0 1
(c)
2 3 4
-6 -5 -4 -3 -2 -1 0 1 2 3 4
(d)
DUCA
3
2
3
2
1
0
1
0
-1
-2
-3
-4
-1
-2
-3
-4
-6 -5 -4 -3 -2 -1 0
(e)
1
2
3
-5 -4 -3 -2 -1 0
(f)
1
2
3
Figure 10. Visualization of a query, marked as H, mapped to the (a) and (b) optimal two-dimensional
PCA, (c) and (d), DCA, and (e) and (f) DUCA subspaces. The high/middle/low utility labels are marked
by + / ) / #, and the two privacy labels are marked by 3 / 4 . The results suggest that DUCA-subspace offers a promising approach to optimal utility-privacy tradeoff.
K (x, y) = / l c l K l (x, y). In this case,
the trace-norm of kernel-DCA discriminant matrix in (39) may be used as an effective evaluation criterion for finding the
optimal coefficients: {c l, l = 1, f, L}.
(Detail omitted.)
the privacy subspace, leading to a new
query: yv = vf T (vx + e), with colored noise
covariance / e = tS B p . This compels
the eigen-solution (37) to be modified as:
Tailor designed noise
for privacy preservation
Intuitively speaking, such a design
aims to dampen Eve's ability to intrude
privacy while leaving the utility gain
for Bob relatively unaffected.
L
Pursuant to (23), the privacy matrix S B p
may be learned from labeled training
data and the original data xv be purposefully perturbed by noise parallel to
IEEE Signal Processing Magazine
|
January 2017
|
eig (aS B U - bS B P, Sr + tS B P)
(continued on page 112)
103
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
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Signal Processing - January 2017 - Cover3
Signal Processing - January 2017 - Cover4
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