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Partial multi-view clustering has attracted various attentions from diverse fields. Most existing methods adopt separate steps to obtain unified representations and extract clustering indicators. This separate manner prevents two learning processes to negotiate to achieve optimal performance. In this paper, we propose the Joint Representation Learning and Clustering (JRLC) framework to address this issue. The JRLC framework employs representation matrices to extract view-specific clustering information directly from the presence of partial similarity matrices, and rotates them to learn a common probability label matrix simultaneously, which connects representation learning and clustering seamlessly to achieve better clustering performance. Under the guidance of JRLC framework, several new incomplete multi-view clustering methods can be developed by extending existing single-view graph-based representation learning methods. For illustration, within the framework, we propose two specific methods, JRLC with spectral embedding (JRLC-SE) and JRLC via integrating nonnegative embedding and spectral embedding (JRLC-NS). Two iterative algorithms with guaranteed convergence are designed to solve the resultant optimization problems of JRLC-SE and JRLC-NS. Experimental results on various datasets and news topic clustering application demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

High-dimensional non-Gaussian data are ubiquitous in many real applications. Face recognition is a typical example of such scenarios. The sampled face images of each person in the original data space are more closely located to each other than to those of the same individuals due to the changes of various conditions like illumination, pose variation, and facial expression. They are often non-Gaussian and differentiating the importance of each data point has been recognized as an effective approach to process the high-dimensional non-Gaussian data. In this paper, to embed non-Gaussian data well, we propose a novel unified framework named adaptive discriminative analysis (ADA), which combines the sample’s importance measurement and subspace learning in a unified framework. Therefore, our ADA can preserve the within-class local structure and learn the discriminative transformation functions simultaneously by minimizing the distances of the projected samples within the same classes while maximizing the between-class separability. Meanwhile, an efficient method is developed to solve our formulated problem. Comprehensive analyses, including convergence behavior and parameter determination, together with the relationship to other related approaches, are as well presented. Systematical experiments are conducted to understand the work of our proposed ADA. Promising experimental results on various types of real-world benchmark data sets are provided to examine the effectiveness of our algorithm. Furthermore, we have also evaluated our method in face recognition. They all validate the effectiveness of our method on processing the high-dimensional non-Gaussian data. [ABSTRACT FROM AUTHOR]

The genome-wide association study (GWAS) is a popular approach to identify disease-associated genetic factors for Alzhemer's Disease (AD). However, it remains challenging because of the small number of samples, very high feature dimensionality and complex structures. To accurately identify genetic risk factors for AD, we propose a novel method based on an in-depth exploration of the hierarchical structure among the features and the commonality across related tasks. Specifically, we first extract and encode the tree hierarchy among features; then, we integrate the tree structures with multi-task feature learning (MTFL) to learn the shared features—that are predictive of AD—among related tasks simultaneously. Thus, we can unify the strength of both the prior structure information and MTFL to boost the prediction performance. However, due to the highly complex regularizer that encodes the tree structure and the extremely high feature dimensionality, the learning process can be computationally prohibitive. To address this, we further develop a novel safe screening rule to quickly identify and remove the irrelevant features before training. Experiment results demonstrate that the proposed approach significantly outperforms the state-of-the-art in detecting genetic risk factors of AD and the speedup gained by the proposed screening can be several orders of magnitude. [ABSTRACT FROM AUTHOR]