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ItemVoxel-based offsetting at high resolution with tunable speed and precision using hybrid dynamic trees(Georgia Institute of Technology, 2016-11-11) Hossain, Mohammad MoazzemIn the recent years, digital manufacturing has experienced the wave of rapid prototyping through the innovation and ubiquity in 3D printing technology. While such advancement liberates the constraints of shape selection in physical objects, 3D printing is yet to match the precision, robustness and vast applicability offered by the classical subtractive manufacturing process. To simplify the toolpath planning in conventional multi-axis CNC machining, recent researches have proposed adopting a voxel-based geometric modeling. Inherently, a voxel representation is amenable for parallel acceleration on modern ubiquitous GPU hardware. While there can be many different approaches to represent voxels, this work is based on a novel voxel data structure called hybrid dynamic tree (HDT) that combines dense grid and sparse octree in such a way that makes it both more compact (i.e., storage efficient) and better-suited to GPUs (i.e., computation effective) than state-of-the-art alternatives. This dissertation contributes in the following four aspects: First, we present a parallel method to construct the HDT representation on GPU for a CAD input modeled in a triangle mesh. In addition, to optimize the memory footprint in the HDT our research explores the theoretical storage analysis for different active node branchings in the Octree. Thus, we incorporate tunability into the HDT organization to study the complexity of memory footprint. The developed theoretical storage analysis is validated with rigorous experimentation that helps devising optimal parameter selections for storage-compact HDT representation. Next, the thesis presents a mathematical morphology based offsetting algorithm using the HDT voxel representation. At our target resolution of 4096 x 4096 x 4096, our goal is to compute large-scale offsets in minutes, match or beat the number of bits of the representation compared to state-of-the-art alternatives, and experimentally characterize any trade-offs among speed, storage, and precision. While using the HDT as the underlying data structure leads naturally to a storage-efficient representation, the challenge in developing a high-performance implementation of offset algorithm is choosing an optimal configuration of the HDT parameters.These parameters not only govern the memory footprint of the voxelized representation of the solid, but also control the parallel code execution efficiency on parallel computing units on GPU. Capability of fine-tuning of a data structure is crucial for understanding, and thereby optimizing, the developed computation-intensive algorithm that uses the HDT as the underlying voxel representation. Towards that end, this thesis explores different practical approaches to achieve high-performance voxel offsetting. First, we study the impact of the different HDT configurations on the voxel offsetting. Next, to devise a fast voxel offsetting we analyze the trade-offs between speed and accuracy through controllable size of the morphological filter. We study the impact of the decomposition of a large offset distance into a series of offsetting with smaller distances. To facilitate this trade-off analysis, we implement a GPU-accelerated error measurement technique. Finally, to enable even faster voxel offsetting, we present the principles of offloading the offset computation in the HDTs across a cluster of GPUs co-hosted on the same computing node. Our research studies the impact of different approaches for CUDA kernel execution controlled through either single or multiple independent CPU threads. In addition, we examine different load distribution policies that consider the computational disparity in the deployed GPUs. With more and more GPUs integrated on a single computing node, such exploration of algorithmic speedup through load-balanced implementation of voxel offsetting across multiple GPUs emphasizes the high scalability of the HDT's hybrid voxel representation.
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ItemProcess-structure linkages with materials knowledge systems(Georgia Institute of Technology, 2016-09-09) Brough, DavidThe search for optimal manufacturing process routes that results in the combination of desired properties for any application is a highly dimensional optimization problem due to the hierarchical nature of material structure. Yet, this problem is a key component to materials design. Customized materials data analytics provides a new avenue of research in the efforts to address the challenge described above, while accounting for the inherently stochastic nature of the available data. The analytics mine and curate transferable, high value, materials knowledge at multiple length and time scales. More specifically, this materials knowledge is cast in the form of Process-Structure-Property (PSP) linkages of interest to the design/manufacturing experts. The extension of the novel Materials Knowledge Systems (MKS) framework to Process-Structure linkages holds the exciting potential to development full PSP linkages that can be can be leveraged by experts in data science, manufacturing and materials science and engineering communities. PSP linkages are an essential component in the to realize a modern accelerated materials innovation ecosystem. This work describes the methodologies used to extend the MKS framework to Process-Structure linkages and demonstrates their utility.
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ItemModeling, learning, and inference of high-dimensional asynchronous event data(Georgia Institute of Technology, 2016-05-05) Du, NanThe increasing availability of temporal-spatial events produced from natural and social systems provides new opportunities and challenges for effective modeling the latent dynamics which inherently govern these seemly ``random'' data. In our work, we propose a unified probabilistic framework based on multivariate point processes to better predict `who will do what by when and where?' in the future. This framework comprises a systematic paradigm for modeling, learning, and making inference of large-scale asynchronous high-dimensional event data. With this common framework, we contribute in the following three aspects. Accurate Modeling: we first propose non-parametric and topic-modulated multivariate terminating point processes to capture continuous-time heterogeneous information diffusions. We then develop the low-rank Hawkes process to describe the recurrent temporal interactions among different types of entities. We also build a link between the recurrent neural network and the temporal point process to learn a general representation of the influence from the past event history. Finally, we establish a previously unexplored connection between Bayesian Nonparametrics and temporal point processes to jointly model the temporal data and other type of additional information. Efficient Learning: we develop a robust structure learning algorithm via group lasso, which is able to efficiently uncover sparse heterogeneous interdependent relations specified via vectorized parameters among the dimensions. We also propose an efficient nonnegative matrix rank minimization algorithm, which elegantly inherits the advantages from both the proximal methods and the conditional gradient methods to solve the matrix rank minimization problem under different constraints. Finally, in the data streaming setting, we develop a Bayesian inference algorithm for inferring latent variables and updating the respective model parameters based on both temporal and textual information, which achieves almost constant processing time per data sample. Scalable Inference: another important aspect of our research is to make future predictions by exploiting the learned models. Specifically, based on the terminating processes, we develop the first scalable influence estimation algorithm in continuous-time diffusion networks with provable performance guarantees. Based on the low-rank Hawkes processes, we develop the first time-sensitive recommendation algorithm, which not only can recommend the most relevant item specific to a given moment, but also can predict the next returning time for a user to a designated service. Finally, based on the recurrent point processes, we have derived an analytic solution to shape the overall network activities of users. We show that our method can provide fine-grained control over user activities in a time-sensitive fashion.
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ItemScalable and distributed constrained low rank approximations(Georgia Institute of Technology, 2016-04-15) Kannan, RamakrishnanLow rank approximation is the problem of finding two low rank factors W and H such that the rank(WH) << rank(A) and A ≈ WH. These low rank factors W and H can be constrained for meaningful physical interpretation and referred as Constrained Low Rank Approximation (CLRA). Like most of the constrained optimization problem, performing CLRA can be computationally expensive than its unconstrained counterpart. A widely used CLRA is the Non-negative Matrix Factorization (NMF) which enforces non-negativity constraints in each of its low rank factors W and H. In this thesis, I focus on scalable/distributed CLRA algorithms for constraints such as boundedness and non-negativity for large real world matrices that includes text, High Definition (HD) video, social networks and recommender systems. First, I begin with the Bounded Matrix Low Rank Approximation (BMA) which imposes a lower and an upper bound on every element of the lower rank matrix. BMA is more challenging than NMF as it imposes bounds on the product WH rather than on each of the low rank factors W and H. For very large input matrices, we extend our BMA algorithm to Block BMA that can scale to a large number of processors. In applications, such as HD video, where the input matrix to be factored is extremely large, distributed computation is inevitable and the network communication becomes a major performance bottleneck. Towards this end, we propose a novel distributed Communication Avoiding NMF (CANMF) algorithm that communicates only the right low rank factor to its neighboring machine. Finally, a general distributed HPC- NMF framework that uses HPC techniques in communication intensive NMF operations and suitable for broader class of NMF algorithms.
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ItemGraph-based algorithms and models for security, healthcare, and finance(Georgia Institute of Technology, 2016-04-15) Tamersoy, AcarGraphs (or networks) are now omnipresent, infusing into many aspects of society. This dissertation contributes unified graph-based algorithms and models to help solve large-scale societal problems affecting millions of individuals' daily lives, from cyber-attacks involving malware to tobacco and alcohol addiction. The main thrusts of our research are: (1) Propagation-based Graph Mining Algorithms: We develop graph mining algorithms to propagate information between the nodes to infer important details about the unknown nodes. We present three examples: AESOP (patented) unearths malware lurking in people's computers with 99.61% true positive rate at 0.01% false positive rate; our application of ADAGE on malware detection (patent-pending) enables to detect malware in a streaming setting; and EDOCS (patent-pending) flags comment spammers among 197 thousand users on a social media platform accurately and preemptively. (2) Graph-induced Behavior Characterization: We derive new insights and knowledge that characterize certain behavior from graphs using statistical and algorithmic techniques. We present two examples: a study on identifying attributes of smoking and drinking abstinence and relapse from an addiction cessation social media community; and an exploratory analysis of how company insiders trade. Our work has already made impact to society: deployed by Symantec, AESOP is protecting over 120 million people worldwide from malware; EDOCS has been deployed by Yahoo and it guards multiple online communities from comment spammers.
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ItemGraph analysis combining numerical, statistical, and streaming techniques(Georgia Institute of Technology, 2016-03-31) Fairbanks, James PaulGraph analysis uses graph data collected on a physical, biological, or social phenomena to shed light on the underlying dynamics and behavior of the agents in that system. Many fields contribute to this topic including graph theory, algorithms, statistics, machine learning, and linear algebra. This dissertation advances a novel framework for dynamic graph analysis that combines numerical, statistical, and streaming algorithms to provide deep understanding into evolving networks. For example, one can be interested in the changing influence structure over time. These disparate techniques each contribute a fragment to understanding the graph; however, their combination allows us to understand dynamic behavior and graph structure. Spectral partitioning methods rely on eigenvectors for solving data analysis problems such as clustering. Eigenvectors of large sparse systems must be approximated with iterative methods. This dissertation analyzes how data analysis accuracy depends on the numerical accuracy of the eigensolver. This leads to new bounds on the residual tolerance necessary to guarantee correct partitioning. We present a novel stopping criterion for spectral partitioning guaranteed to satisfy the Cheeger inequality along with an empirical study of the performance on real world networks such as web, social, and e-commerce networks. This work bridges the gap between numerical analysis and computational data analysis.