深度学习中适应性特征投影与分布对齐的不完全多视图聚类

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"这篇文献是'Adaptive Feature Projection With Distribution Alignment for Deep Incomplete Multi-View Clustering'，发表在2023年的IEEETRANSACTIONS ON IMAGE PROCESSING期刊上，由Jie Xu, Chao Li, Liang Peng等人撰写。该研究主要关注深度不完全多视图聚类问题，特别是如何处理缺失数据和不同视图间的特征分布差异。" 深度不完全多视图聚类（IMVC）分析是一种在多视图数据中存在缺失数据情况下的研究领域，其目标是通过整合多个视角的信息来提升聚类效果。然而，当前的IMVC方法存在两个主要问题： 1. 传统方法倾向于专注于缺失数据的填充或恢复，但这些方法可能由于未知的标签信息导致填充值的准确性不足。文献指出，这种方法忽略了填充值可能存在的误差。 2. 多视图的共同特征通常是在数据补全后学习的，这可能导致忽略完整数据与不完整数据之间的特征分布不一致问题，从而影响聚类质量。针对以上问题，论文提出了一种无需数据填充的深度IMVC方法，并在特征学习中引入了分布对齐策略。具体来说，该方法利用自动编码器为每个视图学习特征，并采用自适应特征投影技术。这样可以避免直接进行数据补全，减少因不确定性导致的错误，并同时考虑了不同视图间特征分布的对齐，以减少由于数据不完整性引入的偏差。通过这种方式，提出的模型能够更好地捕获各视图之间的共享信息，同时减少由不准确的数据恢复带来的影响。这种方法有望在处理缺失数据时提高多视图聚类的准确性和鲁棒性，尤其适用于那些数据缺失情况严重或者难以精确填充的场景。这篇论文贡献了一种创新的无数据补全策略，通过分布对齐优化深度学习在不完全多视图聚类中的应用，对于处理具有缺失数据的复杂数据集提供了新的解决思路。

1356 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 32, 2023

subspace clustering method based on the latent representations

learned by autoencoders. Li et al. [42] incorporated the

adversarial training [43] with autoencoders in a uniﬁed multi-

view clustering framework. Fan et al. [44] introduced graph

autoencoders with graph constraints for multi-view clustering.

Yin et al. [45] proposed variational autoencoder based multi-

view clustering, where the shared features were learned with a

mixture of Gaussian distributions. Xu et al. [46] pointed out

to learn disentangled multi-view representations for clustering

with common and peculiar variables in variational autoen-

coders. Different from using the reconstruction objectives of

autoencoders, some works (e.g., [47], [48], [49]) proposed to

penalize the representation space with regularization constrains

for deep multi-view clustering. For example, Zhou et al. [47]

utilized encoder networks to extract informative features and

leveraged Gaussian kernel matrices to avoid the feature degen-

eration.

However, the real-word multi-view data always contain

missing data in some views, resulting in the inapplicability

of existing multi-view clustering methods. Therefore, deep

incomplete multi-view clustering is an important topic which

has attracted researchers’ attention in recent years.

B. Incomplete Multi-View Clustering

Incomplete multi-view clustering (IMVC) is also called par-

tial multi-view clustering in the literature. Traditional IMVC

methods utilize classic machine learning techniques such as

non-negative matrix factorization, kernel trick, graph learning,

and tensor techniques. Li et al. [22] proposed the non-negative

matrix factorization based method to handle incomplete multi-

view data. Hu et al. [26] incorporated weighted and regular-

ized matrix factorization in an online IMVC framework. The

recent matrix factorization based method [50] employed the

cosine similarity to preserve the manifold structures. Matrix

factorization based IMVC usually recovers the non-negative

matrix for the missing data with the available data. Similarly,

kernel based IMVC usually imputes the kernel matrix of

incomplete multi-view data by utilizing that of complete

multi-view data. For example, Guo et al. [23] presented a

kernel similarity based method with an anchor strategy for

partial multi-view clustering. Liu et al. [24] proposed multi-

ple kernel IMVC method, which completed each incomplete

base matrix of incomplete views with the learned consensus

matrix. The graph based IMVC is able to leverage graph

structure information to improve the recognition ability for

cluster patterns. For instance, the literature [31] established

graph regularization to achieve the consistency between the

available data and the imputed values for missing data. The

recent graph based method [51] considered the instance-to-

anchor and instance-to-instance similarities for spectral clus-

tering. Fang et al. [52] leveraged the biological evolution

theory to handle the unbalanced incompleteness in IMVC.

Recent works of tensor based IMVC (e.g., [27], [28], [29])

usually introduce low-rank tensor constraints to characterize

the high-order correlation and the inner structure among

multiple views. In recent years, deep learning based IMVC

has been attracting increasing attention. One of the natural

motivations is that the generative adversarial net (GAN [43])

can be applied to generate data for incomplete multi-view

data [33], [37]. Besides, Wen et al. [35] proposed a cognitive

deep incomplete multi-view clustering network, where the

nearest neighbor graph was constructed and the missing data

was ﬁlled by average values. Wei et al. [34] utilized shared

subspace representations to reconstruct the missing data via

a decoder of individual view. Recent work [36] stacked dual

prediction networks on autoencoders to perform data recovery

for incomplete data. Xu et al. [53] proposed to mine the non-

linear cluster complementarity among the incomplete multi-

view data. Tang et al. [54] proposed to dynamically impute

missing views with the learned semantic neighbors.

Most of the traditional and deep IMVC methods han-

dle incomplete multi-view data with imputation/recovery/

inference strategies. However, the inaccurate imputation values

for missing data will negatively affect the performance. This

issue is likely to occur when the number of missing data

is large. Additionally, previous IMVC methods usually learn

the common representations from the complete multi-view

data and generalize them to incomplete multi-view data. This

process might cause the distribution discrepancy between the

complete data and incomplete data. In this paper, we propose

an imputation-free deep IMVC method by considering dis-

tribution alignment in feature learning to address the above

issues.

III. METHOD

Notations: In this paper, {X

∈ R

N ×D

}

v=1

represents a

multi-view data set with V views, where D

is the dimen-

sionality of samples in the v-th view and N is the number

of samples. Moreover, we employ an indicator matrix A ∈

{0, 1}

N ×V

, where a

∈ A, a

= 0 denotes that the data of the

i-th sample in the v-th view is missing, and a

= 1 represents

that data is not missing. Denoting the complete data of all

views as {X

}

v=1

and the incomplete data of individual view

as X

, respectively, for each x

, if there exists

v=1

= V ,

then x

∈ X

; otherwise, x

∈ X

. Therefore, [X

; X

] ∈

×D

and the missing data result in N

≤ N . Table I lists

the deﬁned notations and descriptions.

A. Motivation and Framework

Deep autoencoder has been widely applied in IMVC meth-

ods due to its ability of learning clustering-friendly fea-

tures [33], [35], [36]. Concretely, these methods optimize the

reconstruction loss L

R EC

of all views by

R EC

v=1

R EC

v=1



− D

))



, (1)

where E

and D

denote the encoder and decoder net-

works of the v-th view, respectively. The encoder network

converts the raw data [X

; X

] into the view-speciﬁc features

; Z

] ∈ R

×L

to learn underlying characteristics, i.e.,

; Z

] = E

([X

; X

]). (2)

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