The last few years have witnessed a tremendous growth of the demand for wireless services and a significant increase of the number of mobile subscribers. A recent data traffic forecast from Cisco reported that the global mobile data traffic reached 1.2 zettabytes per year in 2016, and the global IP traffic will increase nearly threefold over the next 5 years. Based on these predictions, a 127-fold increase of the IP traffic is expected from 2005 to 2021. It is also anticipated that the mobile data traffic will reach 3.3 zettabytes per year by 2021, and that the number of mobile-connected devices will reach 3.5 per capita.
With such demands for higher data rates and for better quality of service (QoS), fifth generation (5G) standardization initiatives, whose initial phase was specified in June 2018 under the umbrella of Long Term Evolution (LTE) Release 15, have been under vibrant investigation. In particular, the International Telecommunication Union (ITU) has identified three usage scenarios (service categories) for 5G wireless networks: (i) enhanced mobile broadband (eMBB), (ii) ultra-reliable and low latency communications (uRLLC), and (iii) massive machine type communications (mMTC). The vast variety of applications for beyond 5G wireless networks has motivated the necessity of novel and more flexible physical layer (PHY) technologies, which are capable of providing higher spectral and energy efficiencies, as well as reduced transceiver implementations.
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Subspace learning theory for dimensionality reduction was initiated with the Principal Component Analysis (PCA) formulation proposed by Pearson in 1901. PCA was first widely used for data analysis in the field of psychometrics and chemometrics but today it is often the first step in more various types of exploratory data analysis, predictive modeling, classification and clustering problems. It finds modern applications in signal processing, biomedical imaging, computer vision, process fault detection, recommendation system design and many more domains. Since one century, numerous other subspace learning models, either reconstructive and discriminative, were developed over time in literature to address dimensionality reduction while keeping the relevant information in a different manner from PCA. However, PCA can also be viewed as a soft clustering method that seeks to find clusters in different subspaces within a dataset, and numerous clustering methods are based on dimensionality reduction. These methods are called subspace clustering methods that are extension of traditional PCA based clustering, and divide data points belonging to the union of subspaces (UoS) into the respective subspaces. In several modern applications, the main limitation of the subspace learning and clustering models are their sensitivity to outliers. Thus, further developments concern robust subspace learning which refers to the problem of subspace learning in the presence of outliers. In fact, even the classical subspace learning problem with speed or memory constraints is not a solved problem. These issues have become practically important for modern datasets because of the following reasons:
Thus, the special issue on Robust Subspace Learning and Tracking published in IEEE Journal of Selected Topics in Signal Processing in December 2018 group recent works in robust subspace learning and clustering related to theory, algorithms and applications for signal processing and computer vision applications. Several papers concern algorithms to address robustness of subspace learning against different kinds of outliers.
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