Online Matrix Completion and Online Robust PCA

This work studies two interrelated problems - online robust PCA (RPCA) and online low-rank matrix completion (MC). In recent work by Cand\`{e}s et al., RPCA has been defined as a problem of separating a low-rank matrix (true data), $L:=[\ell_1, \ell_2, \dots \ell_{t}, \dots , \ell_{t_{\max}}]$ and a sparse matrix (outliers), $S:=[x_1, x_2, \dots x_{t}, \dots, x_{t_{\max}}]$ from their sum, $M:=L+S$. Our work uses this definition of RPCA. An important application where both these problems occur is in video analytics in trying to separate sparse foregrounds (e.g., moving objects) and slowly changing backgrounds. While there has been a large amount of recent work on both developing and analyzing batch RPCA and batch MC algorithms, the online problem is largely open. In this work, we develop a practical modification of our recently proposed algorithm to solve both the online RPCA and online MC problems. The main contribution of this work is that we obtain correctness results for the proposed algorithms under mild assumptions. The assumptions that we need are: (a) a good estimate of the initial subspace is available (easy to obtain using a short sequence of background-only frames in video surveillance); (b) the $\ell_t$'s obey a `slow subspace change' assumption; (c) the basis vectors for the subspace from which $\ell_t$ is generated are dense (non-sparse); (d) the support of $x_t$ changes by at least a certain amount at least every so often; and (e) algorithm parameters are appropriately setComment: Presented at ISIT (IEEE Intnl. Symp. on Information Theory), 2015. Submitted to IEEE Transactions on Information Theory. This version: changes are in blue; the main changes are just to explain the model assumptions better (added based on ISIT reviewers' comments

Design and implementation of NoC routers and their application to Prdt-based NoC\u27s

With a communication-centric design style, Networks-on-Chips (NoCs) emerges as a new paradigm of Systems-on-Chips (SoCs) to overcome the limitations of bus-based communication infrastructure. An important problem in the design of NoCs is the router design, which has great impact on the cost and performance of a NoC system. This thesis is focused on the design and implementation of an optimized parameterized router which can be applied in mesh/torus-based and Perfect Recursive Diagonal Torus (PRDT)-based NoCs; In specific, the router design includes the design and implementation of two routing algorithms (vector routing and circular coded vector routing), the wormhole switching scheme, the scheduling scheme, buffering strategy, and flow control scheme. Correspondingly, the following components are designed and implemented: input controller, output controller, crossbar switch, and scheduler. Verilog HDL codes are generated and synthesized on ASIC platforms. Most components are designed in parameterized way. Performance evaluation of each component of the router in terms of timing, area, and power consumption is conducted. The efficiency of the two routing algorithms and tradeoff between computational time (tsetup) and area are analyzed; To reduce the area cost of the router design, the two major components, the crossbar switch and the scheduler, are optimized. Particularly, for crossbar switch, a comparative study of two crossbar designs is performed with the aid of Magic Layout editor, Synopsys CosmosSE and Awaves; Based on the router design, the PRDT network composed of 4x4 routers is designed and synthesized on ASIC platforms

A foundation for machine learning in design

This paper presents a formalism for considering the issues of learning in design. A foundation for machine learning in design (MLinD) is defined so as to provide answers to basic questions on learning in design, such as, "What types of knowledge can be learnt?", "How does learning occur?", and "When does learning occur?". Five main elements of MLinD are presented as the input knowledge, knowledge transformers, output knowledge, goals/reasons for learning, and learning triggers. Using this foundation, published systems in MLinD were reviewed. The systematic review presents a basis for validating the presented foundation. The paper concludes that there is considerable work to be carried out in order to fully formalize the foundation of MLinD

Incorporating molecular data in fungal systematics: a guide for aspiring researchers

The last twenty years have witnessed molecular data emerge as a primary research instrument in most branches of mycology. Fungal systematics, taxonomy, and ecology have all seen tremendous progress and have undergone rapid, far-reaching changes as disciplines in the wake of continual improvement in DNA sequencing technology. A taxonomic study that draws from molecular data involves a long series of steps, ranging from taxon sampling through the various laboratory procedures and data analysis to the publication process. All steps are important and influence the results and the way they are perceived by the scientific community. The present paper provides a reflective overview of all major steps in such a project with the purpose to assist research students about to begin their first study using DNA-based methods. We also take the opportunity to discuss the role of taxonomy in biology and the life sciences in general in the light of molecular data. While the best way to learn molecular methods is to work side by side with someone experienced, we hope that the present paper will serve to lower the learning threshold for the reader.Comment: Submitted to Current Research in Environmental and Applied Mycology - comments most welcom

2D and 3D surface image processing algorithms and their applications

This doctoral dissertation work aims to develop algorithms for 2D image segmentation application of solar filament disappearance detection, 3D mesh simplification, and 3D image warping in pre-surgery simulation. Filament area detection in solar images is an image segmentation problem. A thresholding and region growing combined method is proposed and applied in this application. Based on the filament area detection results, filament disappearances are reported in real time. The solar images in 1999 are processed with this proposed system and three statistical results of filaments are presented. 3D images can be obtained by passive and active range sensing. An image registration process finds the transformation between each pair of range views. To model an object, a common reference frame in which all views can be transformed must be defined. After the registration, the range views should be integrated into a non-redundant model. Optimization is necessary to obtain a complete 3D model. One single surface representation can better fit to the data. It may be further simplified for rendering, storing and transmitting efficiently, or the representation can be converted to some other formats. This work proposes an efficient algorithm for solving the mesh simplification problem, approximating an arbitrary mesh by a simplified mesh. The algorithm uses Root Mean Square distance error metric to decide the facet curvature. Two vertices of one edge and the surrounding vertices decide the average plane. The simplification results are excellent and the computation speed is fast. The algorithm is compared with six other major simplification algorithms. Image morphing is used for all methods that gradually and continuously deform a source image into a target image, while producing the in-between models. Image warping is a continuous deformation of a: graphical object. A morphing process is usually composed of warping and interpolation. This work develops a direct-manipulation-of-free-form-deformation-based method and application for pre-surgical planning. The developed user interface provides a friendly interactive tool in the plastic surgery. Nose augmentation surgery is presented as an example. Displacement vector and lattices resulting in different resolution are used to obtain various deformation results. During the deformation, the volume change of the model is also considered based on a simplified skin-muscle model