PCA using graph total variation

Abstract

Mining useful clusters from high dimensional data has received significant attention of the signal processing and machine learning community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the curse of dimensionality. However, often such methods are accompanied with problems such as high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix factorization methods) or susceptibility to gross corruptions in the data. In this paper we propose a convex, robust, scalable and efficient Principal Component Analysis (PCA) based method to approximate the low-rank representation of high dimensional datasets via a two-way graph regularization scheme. Compared to the exact recovery methods, our method is approximate, in that it enforces a piecewise constant assumption on the samples using a graph total variation and a piecewise smoothness assumption on the features using a graph Tikhonov regularization. Futhermore, it retrieves the low-rank representation in a time that is linear in the number of data samples. Clustering experiments on 3 benchmark datasets with different types of corruptions show that our proposed model outperforms 7 state-ofthe-art dimensionality reduction models.

Graph regularized implicit pose for 3D human action recognition

“…The proposed method improves over the baseline and shows that graph regularization helps improving recognition performance. Further, we can see that while adding standard PCA (reduced to 10 dimensions) helps due to the KNN classifier's sensitivity to high dimensionality, PCA-GTV is better due to the robustness against noise, which was previously demonstrated by Shahid et al [10].…”

“…We propose a framework that learns a linear subspace suitable for fast KNN-classifier recognition. Our approach uses the moving pose descriptor [15], and then performs dimensionality reduction with graph regularizers [10] for learning our subspace. An overview of the proposed system is shown in Fig.…”

“…For learning our representation space, we turn to the PCA-GTV framework [10], which is a dimensionality reduction method using graph regularizers. We create a data matrix M 2 R p⇥n by stacking all p-dimensional MP descriptors along the columns.…”

“…Tikhonov regularization ensures smoothness following the graph; computational efficiency is granted through a closed-form solution. Following this work, Shahid et al [10] created PCA-GTV, with added graph total variation (GTV) regularization, which demonstrated that the regularizer helps learning a subspace that is very robust against noise, and also more discriminative, as it has an automatic grouping effect [10].…”

“…We find a low-rank representation that allows data representation using only a few components. • GTV is quite robust against noise [10], which helps as the Kinect skeletons are often erroneous due to tracking failures. • Our enhanced method is just a matrix multiplication at test time, which keeps the running time of the action classification method low.…”