Hybrid manifold embedding

Adaptive Fusion of Heterogeneous Manifolds for Subspace Clustering

Multiview clustering (MVC) has recently received great interest due to its pleasing efficacy in combining the abundant and complementary information to improve clustering performance, which overcomes the drawbacks of view limitation existed in the standard single-view clustering. However, the existing MVC methods are mostly designed for vectorial data from linear spaces and, thus, are not suitable for multiple dimensional data with intrinsic nonlinear manifold structures, e.g., videos or image sets. Some works have introduced manifolds' representation methods of data into MVC and obtained considerable improvements, but how to fuse multiple manifolds efficiently for clustering is still a challenging problem. Particularly, for heterogeneous manifolds, it is an entirely new problem. In this article, we propose to represent the complicated multiviews' data as heterogeneous manifolds and a fusion framework of heterogeneous manifolds for clustering. Different from the empirical weighting methods, an adaptive fusion strategy is designed to weight the importance of different manifolds in a data-driven manner. In addition, the low-rank representation is generalized onto the fused heterogeneous manifolds to explore the low-dimensional subspace structures embedded in data for clustering. We assessed the proposed method on several public data sets, including human action video, facial image, and traffic scenario video. The experimental results show that our method obviously outperforms a number of state-of-the-art clustering methods.

Identifying Key Opinion Leaders in Social Media via Modality-Consistent Harmonized Discriminant Embedding

The digital age has empowered brands with new and more effective targeted marketing tools in the form of key opinion leaders (KOLs). Because of the KOLs' unique capability to draw specific types of audience and cultivate long-term relationship with them, correctly identifying the most suitable KOLs within a social network is of great importance, and sometimes could govern the success or failure of a brand's online marketing campaigns. However, given the high dimensionality of social media data, conducting effective KOL identification by means of data mining is especially challenging. Owing to the generally multiple modalities of the user profiles and user-generated content (UGC) over the social networks, we can approach the KOL identification process as a multimodal learning task, with KOLs as a rare yet far more important class over non-KOLs in our consideration. In this regard, learning the compact and informative representation from the high-dimensional multimodal space is crucial in KOL identification. To address this challenging problem, in this paper, we propose a novel subspace learning algorithm dubbed modality-consistent harmonized discriminant embedding (MCHDE) to uncover the low-dimensional discriminative representation from the social media data for identifying KOLs. Specifically, MCHDE aims to find a common subspace for multiple modalities, in which the local geometric structure, the harmonized discriminant information, and the modality consistency of the dataset could be preserved simultaneously. The above objective is then formulated as a generalized eigendecomposition problem and the closed-form solution is obtained. Experiments on both synthetic example and a real-world KOL dataset validate the effectiveness of the proposed method.

Dimensionality Reduction in Multiple Ordinal Regression

Supervised dimensionality reduction (DR) plays an important role in learning systems with high-dimensional data. It projects the data into a low-dimensional subspace and keeps the projected data distinguishable in different classes. In addition to preserving the discriminant information for binary or multiple classes, some real-world applications also require keeping the preference degrees of assigning the data to multiple aspects, e.g., to keep the different intensities for co-occurring facial expressions or the product ratings in different aspects. To address this issue, we propose a novel supervised DR method for DR in multiple ordinal regression (DRMOR), whose projected subspace preserves all the ordinal information in multiple aspects or labels. We formulate this problem as a joint optimization framework to simultaneously perform DR and ordinal regression. In contrast to most existing DR methods, which are conducted independently of the subsequent classification or ordinal regression, the proposed framework fully benefits from both of the procedures. We experimentally demonstrate that the proposed DRMOR method (DRMOR-M) well preserves the ordinal information from all the aspects or labels in the learned subspace. Moreover, DRMOR-M exhibits advantages compared with representative DR or ordinal regression algorithms on three standard data sets.