Scalable Algorithms for Tractable Schatten Quasi-Norm Minimization

The Schatten-p quasi-norm $(0<p<1)$ is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schatten-p quasi-norm minimization algorithms involve singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each iteration, and thus may become very slow and impractical for large-scale problems. In this paper, we first define two tractable Schatten quasi-norms, i.e., the Frobenius/nuclear hybrid and bi-nuclear quasi-norms, and then prove that they are in essence the Schatten-2/3 and 1/2 quasi-norms, respectively, which lead to the design of very efficient algorithms that only need to update two much smaller factor matrices. We also design two efficient proximal alternating linearized minimization algorithms for solving representative matrix completion problems. Finally, we provide the global convergence and performance guarantees for our algorithms, which have better convergence properties than existing algorithms. Experimental results on synthetic and real-world data show that our algorithms are more accurate than the state-of-the-art methods, and are orders of magnitude faster.Comment: 16 pages, 5 figures, Appears in Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI), Phoenix, Arizona, USA, pp. 2016--2022, 201

Hybrid MIMO Architectures for Millimeter Wave Communications: Phase Shifters or Switches?

Hybrid analog/digital MIMO architectures were recently proposed as an alternative for fully-digitalprecoding in millimeter wave (mmWave) wireless communication systems. This is motivated by the possible reduction in the number of RF chains and analog-to-digital converters. In these architectures, the analog processing network is usually based on variable phase shifters. In this paper, we propose hybrid architectures based on switching networks to reduce the complexity and the power consumption of the structures based on phase shifters. We define a power consumption model and use it to evaluate the energy efficiency of both structures. To estimate the complete MIMO channel, we propose an open loop compressive channel estimation technique which is independent of the hardware used in the analog processing stage. We analyze the performance of the new estimation algorithm for hybrid architectures based on phase shifters and switches. Using the estimated, we develop two algorithms for the design of the hybrid combiner based on switches and analyze the achieved spectral efficiency. Finally, we study the trade-offs between power consumption, hardware complexity, and spectral efficiency for hybrid architectures based on phase shifting networks and switching networks. Numerical results show that architectures based on switches obtain equal or better channel estimation performance to that obtained using phase shifters, while reducing hardware complexity and power consumption. For equal power consumption, all the hybrid architectures provide similar spectral efficiencies.Comment: Submitted to IEEE Acces

Robust Orthogonal Complement Principal Component Analysis

Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the original observation space but can seriously affect the principal subspace estimation. Based on a mathematical formulation of such transformed outliers, a novel robust orthogonal complement principal component analysis (ROC-PCA) is proposed. The framework combines the popular sparsity-enforcing and low rank regularization techniques to deal with row-wise outliers as well as element-wise outliers. A non-asymptotic oracle inequality guarantees the accuracy and high breakdown performance of ROC-PCA in finite samples. To tackle the computational challenges, an efficient algorithm is developed on the basis of Stiefel manifold optimization and iterative thresholding. Furthermore, a batch variant is proposed to significantly reduce the cost in ultra high dimensions. The paper also points out a pitfall of a common practice of SVD reduction in robust PCA. Experiments show the effectiveness and efficiency of ROC-PCA in both synthetic and real data

Adaptive Online Sequential ELM for Concept Drift Tackling

A machine learning method needs to adapt to over time changes in the environment. Such changes are known as concept drift. In this paper, we propose concept drift tackling method as an enhancement of Online Sequential Extreme Learning Machine (OS-ELM) and Constructive Enhancement OS-ELM (CEOS-ELM) by adding adaptive capability for classification and regression problem. The scheme is named as adaptive OS-ELM (AOS-ELM). It is a single classifier scheme that works well to handle real drift, virtual drift, and hybrid drift. The AOS-ELM also works well for sudden drift and recurrent context change type. The scheme is a simple unified method implemented in simple lines of code. We evaluated AOS-ELM on regression and classification problem by using concept drift public data set (SEA and STAGGER) and other public data sets such as MNIST, USPS, and IDS. Experiments show that our method gives higher kappa value compared to the multiclassifier ELM ensemble. Even though AOS-ELM in practice does not need hidden nodes increase, we address some issues related to the increasing of the hidden nodes such as error condition and rank values. We propose taking the rank of the pseudoinverse matrix as an indicator parameter to detect underfitting condition.Comment: Hindawi Publishing. Computational Intelligence and Neuroscience Volume 2016 (2016), Article ID 8091267, 17 pages Received 29 January 2016, Accepted 17 May 2016. Special Issue on "Advances in Neural Networks and Hybrid-Metaheuristics: Theory, Algorithms, and Novel Engineering Applications". Academic Editor: Stefan Hauf