Robust Principal Component Analysis on Graphs

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first issue with a sparse penalty term. The second issue can be handled with the matrix factorization model, which is however non-convex. Besides, PCA based clustering can also be enhanced by using a graph of data similarity. In this article, we introduce a new model called "Robust PCA on Graphs" which incorporates spectral graph regularization into the Robust PCA framework. Our proposed model benefits from 1) the robustness of principal components to occlusions and missing values, 2) enhanced low-rank recovery, 3) improved clustering property due to the graph smoothness assumption on the low-rank matrix, and 4) convexity of the resulting optimization problem. Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with corruptions clearly reveal that our model outperforms 10 other state-of-the-art models in its clustering and low-rank recovery tasks

Deployment Strategies of Multiple Aerial BSs for User Coverage and Power Efficiency Maximization

Unmanned aerial vehicle (UAV) based aerial base stations (BSs) can provide rapid communication services to ground users and are thus promising for future communication systems. In this paper, we consider a scenario where no functional terrestrial BSs are available and the aim is deploying multiple aerial BSs to cover a maximum number of users within a certain target area. To this end, we first propose a naive successive deployment method, which converts the non-convex constraints in the involved optimization into a combination of linear constraints through geometrical relaxation. Then we investigate a deployment method based on K-means clustering. The method divides the target area into K convex subareas, where within each subarea, a mixed integer non-linear problem (MINLP) is solved. An iterative power efficient technique is further proposed to improve coverage probability with reduced power. Finally, we propose a robust technique for compensating the loss of coverage probability in the existence of inaccurate user location information (ULI). Our simulation results show that, the proposed techniques achieve an up to 30% higher coverage probability when users are not distributed uniformly. In addition, the proposed simultaneous deployment techniques, especially the one using iterative algorithm improve power-efficiency by up to 15% compared to the benchmark circle packing theory

Fast Robust PCA on Graphs

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition 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 three different problems: high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix factorization methods) and susceptibility to gross corruptions in the data. In this paper we propose a principal component analysis (PCA) based solution that overcomes these three issues and approximates a low-rank recovery method for high dimensional datasets. We target the low-rank recovery by enforcing two types of graph smoothness assumptions, one on the data samples and the other on the features by designing a convex optimization problem. The resulting algorithm is fast, efficient and scalable for huge datasets with O(nlog(n)) computational complexity in the number of data samples. It is also robust to gross corruptions in the dataset as well as to the model parameters. Clustering experiments on 7 benchmark datasets with different types of corruptions and background separation experiments on 3 video datasets show that our proposed model outperforms 10 state-of-the-art dimensionality reduction models. Our theoretical analysis proves that the proposed model is able to recover approximate low-rank representations with a bounded error for clusterable data