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Register a new userOn Optimizing Distributed Tucker Decomposition for Dense Tensors
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Added by
Venkatesan Chakaravarthy
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component analysis (PCA)and finds applications in diverse domains such as signal processing, computer vision and text analytics. Our objective is to develop an efficient distributed implementation for the case of dense tensors. The implementation is based on the HOOI (Higher Order Orthogonal Iterator) procedure, wherein the tensor-times-matrix product forms the core routine. Prior work have proposed heuristics for reducing the computational load and communication volume incurred by the routine. We study the two metrics in a formal and systematic manner, and design strategies that are optimal under the two fundamental metrics. Our experimental evaluation on a large benchmark of tensors shows that the optimal strategies provide significant reduction in load and volume compared to prior heuristics, and provide up to 7x speed-up in the overall running time.
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The Tucker decomposition generalizes the notion of Singular Value Decomposition (SVD) to tensors, the higher dimensional analogues of matrices. We study the problem of constructing the Tucker decomposition of sparse tensors on distributed memory systems via the HOOI procedure, a popular iterative method. The scheme used for distributing the input tensor among the processors (MPI ranks) critically influences the HOOI execution time. Prior work has proposed different distribution schemes: an offline scheme based on sophisticated hypergraph partitioning method and simple, lightweight alternatives that can be used real-time. While the hypergraph based scheme typically results in faster HOOI execution time, being complex, the time taken for determining the distribution is an order of magnitude higher than the execution time of a single HOOI iteration. Our main contribution is a lightweight distribution scheme, which achieves the best of both worlds. We show that the scheme is near-optimal on certain fundamental metrics associated with the HOOI procedure and as a result, near-optimal on the computational load (FLOPs). Though the scheme may incur higher communication volume, the computation time is the dominant factor and as the result, the scheme achieves better performance on the overall HOOI execution time. Our experimental evaluation on large real-life tensors (having up to 4 billion elements) shows that the scheme outperforms the prior schemes on the HOOI execution time by a factor of up to 3x. On the other hand, its distribution time is comparable to the prior lightweight schemes and is typically lesser than the execution time of a single HOOI iteration.
Recommendation systems, social network analysis, medical imaging, and data mining often involve processing sparse high-dimensional data. Such high-dimensional data are naturally represented as tensors, and they cannot be efficiently processed by conventional matrix or vector computations. Sparse Tucker decomposition is an important algorithm for compressing and analyzing these sparse high-dimensional data sets. When energy efficiency and data privacy are major concerns, hardware accelerators on resource-constraint platforms become crucial for the deployment of tensor algorithms. In this work, we propose a hybrid computing framework containing CPU and FPGA to accelerate sparse Tucker factorization. This algorithm has three main modules: tensor-times-matrix (TTM), Kronecker products, and QR decomposition with column pivoting (QRP). In addition, we accelerate the former two modules on a Xilinx FPGA and the latter one on a CPU. Our hybrid platform achieves $23.6 times sim 1091times$ speedup and over $93.519% sim 99.514 %$ energy savings compared with CPU on the synthetic and real-world datasets.
Distributed Stream Processing systems are becoming an increasingly essential part of Big Data processing platforms as users grow ever more reliant on their ability to provide fast access to new results. As such, making timely decisions based on these results is dependent on a systems ability to tolerate failure. Typically, these systems achieve fault tolerance and the ability to recover automatically from partial failures by implementing checkpoint and rollback recovery. However, owing to the statistical probability of partial failures occurring in these distributed environments and the variability of workloads upon which jobs are expected to operate, static configurations will often not meet Quality of Service constraints with low overhead. In this paper we present Khaos, a new approach which utilizes the parallel processing capabilities of virtual cloud automation technologies for the automatic runtime optimization of fault tolerance configurations in Distributed Stream Processing jobs. Our approach employs three subsequent phases which borrows from the principles of Chaos Engineering: establish the steady-state processing conditions, conduct experiments to better understand how the system performs under failure, and use this knowledge to continuously minimize Quality of Service violations. We implemented Khaos prototypically together with Apache Flink and demonstrate its usefulness experimentally.
This paper introduces RankMap, a platform-aware end-to-end framework for efficient execution of a broad class of iterative learning algorithms for massive and dense datasets. Our framework exploits data structure to factorize it into an ensemble of lower rank subspaces. The factorization creates sparse low-dimensional representations of the data, a property which is leveraged to devise effective mapping and scheduling of iterative learning algorithms on the distributed computing machines. We provide two APIs, one matrix-based and one graph-based, which facilitate automated adoption of the framework for performing several contemporary learning applications. To demonstrate the utility of RankMap, we solve sparse recovery and power iteration problems on various real-world datasets with up to 1.8 billion non-zeros. Our evaluations are performed on Amazon EC2 and IBM iDataPlex servers using up to 244 cores. The results demonstrate up to two orders of magnitude improvements in memory usage, execution speed, and bandwidth compared with the best reported prior work, while achieving the same level of learning accuracy.
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a low-rank approximation (in the form of a singular value decomposition) to an arbitrary matrix. Carefully honed algorithms yield results that are uniformly superior to those of the stock, deterministic implementations in Spark (the popular platform for distributed computation); in particular, whereas the stock software will without warning return left singular vectors that are far from numerically orthonormal, a significantly burnished randomized implementation generates left singular vectors that are numerically orthonormal to nearly the machine precision.
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