Face image clustering method and system based on localized simple multiple kernel k-means
A face image clustering method and system based on a localized simple multiple kernel k-means is provided. The face image clustering method based on localized simple multiple kernel k-means includes the following steps: S1, acquiring face images, and preprocessing the acquired face images to obtain an average kernel matrix for each view; S2, calculating n (τ×n)-nearest neighbor matrices according to the obtained average kernel matrices; S3, calculating a localized kernel matrix for each view according to the nearest neighbor matrices; S4, constructing a localized simple multiple kernel k-means clustering objective function according to the calculated localized kernel matrix for each view; S5, solving a minimum of the constructed objective function by adopting a reduced gradient descent method to obtain an optimal clustering partition matrix; and S6, performing k-means clustering on the obtained clustering partition matrix to achieve clustering.
1 . A face image clustering method based on localized simple multiple kernel k-means, comprising the following steps:
S1, acquiring face images, and preprocessing the face images to obtain an average kernel matrix for each view;
S2, calculating n (τ×n)-nearest neighbor matrices according to the average kernel matrices;
S3, calculating a localized kernel matrix for each view according to the nearest neighbor matrices;
S4, constructing a localized simple multiple kernel k-means clustering objective function according to the localized kernel matrix for each view;
S5, solving a minimum of the localized simple multiple kernel k-means clustering objective function by adopting a reduced gradient descent method to obtain an optimal clustering partition matrix; and
S6, performing k-means clustering on the optimal clustering partition matrix to achieve clustering.
2 . The face image clustering method based on localized simple multiple kernel k-means according to claim 1 , wherein calculating the localized kernel matrix of each view in S3 is expressed as:
K
¯
p
=
(
∑
i
=
1
n
A
(
i
)
)
⊗
K
p
wherein K p represents the localized kernel matrix of each view; A (i) represents the n (τ×n)-nearest neighbor matrices; K p represents a p-th given kernel matrix; n represents a number of samples; ⊗ represents a multiplication of elements.
3 . The face image clustering method based on localized simple multiple kernel k-means according to claim 2 , wherein the simple multiple kernel k-means clustering objective function in S4 is expressed as:
min
γ
∈
Δ
max
H
∈
ℝ
n
×
k
Tr
(
K
γ
HH
⊤
)
s
.
t
.
H
⊤
H
=
I
k
.
wherein γ represents a coefficient vector; H represents a partition matrix; H T represents a permutation of a commutation matrix; K γ represents a combined kernel matrix of K p generated by γ; I k represents a k-order identity matrix.
4 . The face image clustering method based on localized simple multiple kernel k-means according to claim 3 , wherein the localized simple multiple kernel k-means clustering objective function in S4 is expressed as:
min
γ
∈
Δ
max
H
∈
ℝ
n
×
k
TR
(
H
⊤
∑
i
=
1
n
(
A
(
i
)
K
γ
A
(
i
)
)
H
)
s
.
t
.
H
⊤
H
=
I
k
,
wherein
Δ
=
{
γ
∈
ℝ
m
❘
∑
p
=
1
m
γ
p
=
1
,
γ
p
≥
0
,
∀
p
}
,
R m represents an m-dimensional real number vector space; γ p represents a p-th component of γ.
5 . The face image clustering method based on localized simple multiple kernel k-means according to claim 4 , wherein solving the minimum of the localized simple multiple kernel k-means clustering objective function in S5 comprises:
simplifying the localized simple multiple kernel k-means clustering objective function into a simple multiple kernel k-means clustering objective function:
∑
i
=
1
n
=
Tr
(
H
⊤
(
A
(
i
)
K
γ
A
(
i
)
)
H
)
=
∑
i
=
1
n
〈
A
(
i
)
⊗
K
γ
,
A
(
i
)
⊗
(
HH
⊤
)
〉
F
=
∑
i
=
1
n
〈
A
(
i
)
⊗
K
γ
,
HH
⊤
〉
F
=
〈
(
∑
i
=
1
n
A
(
i
)
)
⊗
K
γ
,
HH
⊤
〉
F
=
∑
p
=
1
m
γ
p
2
〈
(
∑
i
=
1
n
A
(
i
)
)
⊗
K
p
,
HH
⊤
〉
F
=
∑
p
=
1
m
γ
p
2
〈
K
~
p
,
HH
⊤
〉
F
=
Tr
(
H
⊤
K
~
γ
H
)
,
wherein ⊗ represents the multiplication of elements;
K
~
p
=
(
∑
i
=
1
n
A
(
i
)
)
⊗
K
p
represents a standardized kernel matrix;
when all elements of A (i) are set to 1, the simple multiple kernel k-means clustering objective function is expressed as:
min
γ
∈
Δ
𝒥
(
γ
)
wherein
𝒥
(
γ
)
=
{
max
H
Tr
(
H
⊤
K
~
γ
H
)
,
s
.
t
.
H
⊤
H
=
I
k
.
}
,
representing an optimum function.
6 . The face image clustering method based on localized simple multiple kernel k-means according to claim 5 , wherein solving the minimum of the localized simple multiple kernel k-means clustering objective function by adopting the reduced gradient descent method in S5 comprises:
calculating the localized simple multiple kernel k-means clustering objective function by the reduced gradient descent method as:
[
▽𝒥
(
γ
)
]
p
=
∂
𝒥
(
γ
)
∂
γ
p
-
∂
𝒥
(
γ
)
∂
γ
u
∀
p
≠
u
[
▽𝒥
(
γ
)
]
u
=
∑
p
=
1
,
p
≠
u
m
(
∂
𝒥
(
γ
)
∂
γ
u
-
∂
𝒥
(
γ
)
∂
γ
p
)
wherein
∂
𝒥
(
γ
)
∂
γ
p
=
2
γ
p
Tr
(
H
*
⊤
K
~
p
H
*
)
H
*
=
{
arg
max
H
Tr
(
H
⊤
K
~
γ
H
)
s
.
t
.
H
⊤
H
=
I
k
}
;
u is set as a number indicating a largest component of vector γ, and a positive constraint of γ is expressed as:
d
p
=
{
0
if
γ
p
=
0
and
[
▽𝒥
(
γ
)
]
p
>
0
-
[
▽𝒥
(
γ
)
]
p
if
γ
p
=
0
and
p
≠
u
-
[
▽𝒥
(
γ
)
]
u
if
p
=
u
.
wherein d p represents a descending direction.