自适应权重的迭代群稀疏人脸识别：提升鲁棒性和结构信息
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更新于2024-07-15
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立即下载 本文主要探讨了自适应权重学习在迭代再约束群稀疏人脸识别（Iterative Re-Constrained Group Sparse Face Recognition, IRGSC）中的应用。作者们， Jianwei Zheng、Ping Yang、Shengyong Chen（IEEE高级会员）、Guojiang Shen 和 Wanliang Wang，针对面部识别问题提出了一个创新的方法，即基于群稀疏表示分类（Group Sparse Representation Classification, GSRC）的框架。
在GSRC方法中，关键在于采用了加权特征和协同的组结构，旨在编码更多的结构性信息以及区分度信息。这与基于回归的传统方法相比，能更有效地捕捉和利用数据的局部结构和特征的有效性。通过这种方式，IRGSC将局部性结构整合到L2范数和p-norm正则化中，形成了一种统一的优化模型。
该研究的一大亮点是引入了自适应权重学习。这些权重能够动态地适应数据特性，从而更好地适应不同特征的重要性，提升了模型的鲁棒性和准确性。这种方法允许在保持群体结构的同时，灵活地调整各个特征的贡献，增强了分类器的性能。
此外，文中还提出了一种高效的算法来优化所提出的优化目标，并进行了理论上的收敛性证明。这意味着在实际应用中，即使面对复杂和变化多样的数据，IRGSC算法也能保证有效的求解过程和良好的性能表现。
这篇研究论文在人脸识别领域具有重要的理论价值和实践意义，它不仅提升了人脸识别的精度，还展示了自适应权重学习如何与群稀疏策略结合，形成了一种强大而灵活的面部识别解决方案，对于处理大规模和高维度的数据集具有显著的优势。
ZHENG et al.: ITERATIVE RE-CONSTRAINED GROUP SPARSE FACE RECOGNITION WITH ADAPTIVE WEIGHTS LEARNING 2411
where σ is the bandwidth parameter and η
ij
denotes the
distance between y and x
ij
. Clearly, the larger the η
ij
is,
the smaller the weight coefficient is. In (5), when p is assigned
as 1 or 2, the corresponding weighted classifier is WSRC [18]
and WCRC [19], respectively.
Similar to WSRC and WCRC, LGSR [20] combines the
reconstruction error with data locality constrained group
sparsity regularizer. However, the locality constraint regu-
larized term disrupts the group structure of sparse solution.
WGSC [21] imposes not only locality constraints on group
sparsity to exclude the training samples which are far away
from the test sample, but also considers the similarity between
the test sample and each class. Accordingly, the weight coef-
ficients of WGSC is formulated as η = r d,whered is
computed same as (6), and r is used to assess the relative
importance of all the reference classes. Inspired by LRC [9],
r is computed as
r
i
=y − X
i
θ
∗
i
2
2
, θ
∗
i
= arg min y − X
i
θ
i
2
2
. (7)
C. Robust Regression Type Classifier
Although the diversity of norm constrained regularization,
the aforementioned classifiers all employ the l
2
-norm to
characterize the reconstruction residual. Considering the fact
that the l
2
-norm is sensitive to large outliers, RSRC [5]
adopts l
1
-norm into SRC for prompting the residual estimation
to be more robust. Similarly, RCRC [23] characterizes the
representation fidelity of CRC with l
1
-norm for robustness to
corruptions/occlusions. That is to say, the value of q in (4) is
set to be 1. From the perspective of maximum likelihood esti-
mation, the l
2
-norm and l
1
-norm are based on the hypothesis
that the error residuals are independent identically distributed
with Gaussian distribution or Laplacian distribution. RRC [28]
models sparse coding as a robust regression problem and
adopts an adaptive distribution to characterize the noises.
Specifically, RRC uses the following criteria
min
θ
s (y − Xθ )
2
2
+ λθ
p
p
, (8)
where p can be 1 or 2 (termed as RRCL1 or RRCL2, respec-
tively). Rewrite X as X =[z
1
; z
2
; ...; z
m
],wherez
i
∈ R
n
is
the ith row of X,andlete = y− Xθ =[e
1
; e
2
; ...; e
n
],where
e
i
= y
i
− z
i
θ, i = 1, 2,...,m. The feature weight s in (8) is
set to be the following logistic function
s
i
=
exp (−μe
2
i
+ μδ)
1 + exp (−μe
2
i
+ μδ)
, (9)
where μ and δ are positive scalars. Parameter μ manipulates
the decreasing rate from 1 to 0, and parameter δ determines
the location of demarcation point. With the help of s, RRC
prefers to assign larger weights to inliers and smaller weights
to outliers; that is, it has higher capability to classify inliers
and outliers.
III. I
TERATIVE RE-CONSTRAINED GROUP
SPARSE CLASSIFICATION
In addition to encompassing most popular regression type
classification algorithms, the criteria (3) can also serve as a
Fig. 1. The residual distributions of occluded face image by competing
methods. (a) Clean image. (b) Occluded query image. (c) and (d) Distributions
of coding residuals in linear and log domains.
general framework under which new algorithms for classifica-
tion to be derived. The mentioned works in Section 2 only
employ limited advantages to their models. For example,
SRC just emphasizes that strong sparsity will bring about
strong discriminant power. RRC assigns different weights
to different features according to their coding residuals, but
without consideration of locality. Following the intuition
that group sparsity, distance locality, and weighted features
explicitly encourages a better representation-type classifier,
we incorporate all these advantages into the objective function.
Correspondingly, our preliminary objective is
min
θ
s (y − Xθ)
2
2
+ λ
c
i=1
η
i
θ
i
p
2
, (10)
which consists of two parts: s(y−Xθ ) is the reconstruction
error with integration of feature weights s, and the second part
represents the weighted l
2, p
mixed norm based regularizer on
the coefficient θ ,wherep > 0.
A. Adaptive Feature Weights Learning
As indicated by [25], different s leads to different classifiers.
When s is set to be 1 constantly, it corresponds to the l
2
-norm
fidelity as in CRC; when set as s
i
= 1/|e
i
|, it turns to the
l
1
-norm fidelity as in SRC; when set to a logistic function
as Eq.(9), it becomes RRC. However, all these functions
fundamentally have certain limits. The l
2
-norm fidelity treats
all features equally, no matter whether they are outlier or not.
The l
1
-norm fidelity assigns infinity to features when the
residual approaches to zero, making the coding unstable. The
logistic weight function has two tunable parameters need to be
set manually, which costs a lot of time. Moreover, the essential
relationship between the logistic function and the real weights
has not been theoretically revealed.
In this paper, we expect s to be more flexible, which
is adaptive to the query y so that the classifier is more
robust to mixed types of noises. We first use an example
to illustrate different distributions of residual e by different
models. Fig.1(a) is a clean face sample from the AR database,
while Fig.1(b) presents the real disguised query face image y
with scarf. The distributions of e by using Gaussian (SRC),
Laplacian (RSRC), and the logistic function (RRC) are plotted
in Fig.1(c). Fig.1(d) further illustrates the distributions in log
domain for better observation of the tails. It has been reported
repeatedly that the empirical distribution of e has a strong
peak at zero but with a long tail, which is mostly caused by
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