Manifold Alignment via Global and Local Structures Preserving PCA Framework

Abstract

Manifold alignment is very prevalent in machine learning for extracting common latent space from multiple datasets. These algorithms generally aim to achieve higher alignment accuracies by preserving the original structure while ensuring closeness between manifolds. This paper proposes a novel semi-supervised manifold alignment method that combines, in each manifold, both global and local linear reconstructions. We preserve a local structure through multiple manifold embedding methods. Moreover, we view manifold embedding methods as special forms of principal component analysis (PCA) and, thus, present a new penalty weight PCA approach to preserving a noise-free global structure. Finally, a closedform solution is presented in the manifold alignment. This method can concurrently match the pair-wise correspondence and preserve both the global and local structures of each dataset to obtain a latent lowdimensional space. The extensive experiments on manifold alignment prove that the proposed method achieves significantly better alignment results than the comparative methods.

Deep Multiview Learning From Sequentially Unaligned Data

“…These methods project data from two different but correlated manifolds to a subspace, simultaneously preserving the local structures and ensuring their closeness. A subgroup of this technique includes semisupervised methods [31]- [34] that utilize several sample-wise correspondences known in advance between the manifolds while learning a new subspace. In contrast, the second subgroup, which we focus on in this paper, contains unsupervised manifold alignment methods that do not require correspondences to be predetermined.…”

Research Hotspot Prediction and Regular Evolutionary Pattern Identification Based on NSFC Grants Using NMF and Semantic Retrieval

“…To evaluate the quality of the topic, we compare three methods (baseline) with our approach: PCA, SVD and LDA. Principal component analysis (PCA) [44] is a method for studying the main components of a document, which is often used for matrix dimensionality reduction. Singular value decomposition (SVD) [45] can obtain a low rank approximation matrix via matrix decomposition, which could be applied for signal denoising and big data mining.…”

Semi-Supervised Manifold Alignment Using Parallel Deep Autoencoders

“…We followed their example and used the same models to test our PDAE. To examine the robustness of the methods, the dataset generated from Model 21 was scaled by a factor of four because previous publications on manifold alignment did the same when testing the robustness of their methods [22,23,39,45,46]. Figure 3a shows the three-dimensional graphs of Models 1 and 21 where the x, y, and z coordinates of each model were the columns of the input data matrices X and Y, respectively.…”

“…Manifold alignment can also be used for data matching and information transfer between these datasets. There are several examples of application studies, for example, in face processing [14][15][16][17][18][19][20], graph matching [21,22], bioinformatics [23], and in image clustering and classification [24][25][26].…”