Tensor Learning in Multi-view Kernel PCA

Abstract

In many real-life applications data can be described through multiple representations, or views. Multi-view learning aims at combining the information from all views, in order to obtain a better performance. Most well-known multi-view methods optimize some form of correlation between two views, while in many applications there are three or more views available. This is usually tackled by optimizing the correlations pairwise. However, this ignores the higher-order correlations that could only be discovered when exploring all views simultaneously. This paper proposes novel multi-view Kernel PCA models. By introducing a model tensor, the proposed models aim to include the higher-order correlations between all views. The paper further explores the use of these models as multi-view dimensionality reduction techniques and shows experimental results on several real-life datasets. These experiments demonstrate the merit of the proposed methods.

Tensor-based restricted kernel machines for multi-view classification

“…The representation of the features is manipulated, however, such that only the lower-order (pairwise) interactions between the views are taken into account. Additionally, various multi-view dimensionality reduction methods [23,24] incorporate tensor learning to account for higher-order correlations. Furthermore, Blondel et al [25,26] present an efficient algorithm to train higher-order factorization machines (HOFM), which model higher-order interactions between features.…”

Latent Space Exploration Using Generative Kernel PCA

“…This connection between kernel PCA and RBMs was later used to explore a generative mechanism for the kernel PCA [9]. A tensor-based multi-view classification model was introduced in [13]. In [14], a multiview generative model called Generative RKM (Gen-RKM) is proposed which uses explicit featuremaps in a novel training procedure for joint feature-selection and subspace learning.…”

Robust Generative Restricted Kernel Machines Using Weighted Conjugate Feature Duality

“…[15] showed how kernel PCA fits into the RKM framework. A tensor-based multi-view classification model was developed in [16]. In [17], a multiview generative model called Generative RKM (Gen-RKM) is introduced which uses explicit feature-maps for joint feature-selection and subspace learning.…”