Feature Extraction for Incomplete Data Via Low-Rank Tensor Decomposition With Feature Regularization
Feature Extraction for Incomplete Data Via Low-Rank Tensor Decomposition With Feature Regularization
复制标题
通过低秩张量分解和特征正则化对不完整数据进行特征提取
DOI：
10.1109/tnnls.2018.2873655
复制
发表时间：
2019-06
期刊：
影响因子：
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通讯作者：
Haiping Lu
中科院分区：
文献类型：
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作者：
Qiquan Shi;Yiu-Ming Cheung;Qibin Zhao;Haiping Lu
多维数据（即，张量）在实践中是常见的。从不完备张量中提取特征是机器学习、模式识别和计算机视觉等领域中的一个重要而又具有挑战性的问题。虽然缺失项可以通过张量补全技术来恢复，但这些补全方法只关注缺失数据的估计，而没有有效的特征提取。据我们所知，从不完全张量中提取特征的问题在文献中还没有得到很好的探讨。因此，在本文中，我们在无监督学习环境中解决了这个问题。具体地说，我们将低秩张量分解与特征方差最大化（TDVM）结合在一个统一的框架中。基于正交Tucker分解和CP分解，将Tucker模型的核张量作为特征，将CP模型的权向量作为特征，设计了两种TDVM方法TDVM-Tucker和TDVM-CP来学习低维特征。TDVM通过最大化特征方差来探索数据样本之间的关系，同时通过低秩Tucker/CP逼近估计缺失项，从而直接从观测项中提取信息特征。此外，我们还将特征正则化与低秩张量近似相结合，建立了一个通用模型，从而推广了所提出的方法.此外，我们将交替方向乘子法和块坐标下降法相结合，提出了一种联合优化方法来求解所提出的方法。最后，在一个新设计的多块缺失环境下，对六个真实图像和视频数据集进行了实验评估.在人脸识别、对象/动作分类和人脸/步态聚类中对提取的特征进行评估。实验结果表明，所提出的方法相比，国家的最先进的方法具有上级的性能。
Multidimensional data (i.e., tensors) with missing entries are common in practice. Extracting features from incomplete tensors is an important yet challenging problem in many fields such as machine learning, pattern recognition, and computer vision. Although the missing entries can be recovered by tensor completion techniques, these completion methods focus only on missing data estimation instead of effective feature extraction. To the best of our knowledge, the problem of feature extraction from incomplete tensors has yet to be well explored in the literature. In this paper, we therefore tackle this problem within the unsupervised learning environment. Specifically, we incorporate low-rank tensor decomposition with feature variance maximization (TDVM) in a unified framework. Based on orthogonal Tucker and CP decompositions, we design two TDVM methods, TDVM-Tucker and TDVM-CP, to learn low-dimensional features viewing the core tensors of the Tucker model as features and viewing the weight vectors of the CP model as features. TDVM explores the relationship among data samples via maximizing feature variance and simultaneously estimates the missing entries via low-rank Tucker/CP approximation, leading to informative features extracted directly from observed entries. Furthermore, we generalize the proposed methods by formulating a general model that incorporates feature regularization into low-rank tensor approximation. In addition, we develop a joint optimization scheme to solve the proposed methods by integrating the alternating direction method of multipliers with the block coordinate descent method. Finally, we evaluate our methods on six real-world image and video data sets under a newly designed multiblock missing setting. The extracted features are evaluated in face recognition, object/action classification, and face/gait clustering. Experimental results demonstrate the superior performance of the proposed methods compared with the state-of-the-art approaches.