Parallel algorithms for tensor product-based inexact graph matching

Livi, Lorenzo; Rizzi, Antonello

doi:10.1109/ijcnn.2012.6252681

Cited by 13 publications

(10 citation statements)

References 24 publications

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“…We seek a pair of paths with matching labels on both nodes and edges, where one path goes from root to leaf in the pattern graph and the other path is in the state transition graph. The matching relation between labels that we define allows for non-exact matches; namely the symbol * is allowed to match both I and D. This is a type of approximate graph matching [24,25,26,27]. If such a pair exists, then the model is consistent with the data and cannot be rejected.…”

Section: Dsgrn Model Consistency With a Datasetmentioning

confidence: 99%

Using extremal events to characterize noisy time series

Berry¹,

Cummins²,

Nerem³

et al. 2020

J. Math. Biol.

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Experimental time series provide an informative window into the underlying dynamical system, and the timing of the extrema of a time series (or its derivative) contains information about its structure. However, the time series often contain significant measurement errors. We describe a method for characterizing a time series for any assumed level of measurement error ε by a sequence of intervals, each of which is guaranteed to contain an extremum for any function that ε-approximates the time series. Based on the merge tree of a continuous function, we define a new object called the normalized branch decomposition, which allows us to compute intervals for any level ε.We show that there is a well-defined total order on these intervals for a single time series, and that it is naturally extended to a partial order across a collection of time series comprising a dataset. We use the order of the extracted intervals in two applications. First, the partial order describing a single dataset can be used to pattern match against switching model output [1], which allows the rejection of a network model. Second, the comparison between graph distances of the partial orders of different datasets can be used to quantify similarity between biological replicates.

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Section: Dsgrn Model Consistency With a Datasetmentioning

confidence: 99%

Using extremal events to characterize noisy time series

Berry¹,

Cummins²,

Nerem³

et al. 2020

J. Math. Biol.

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show abstract

“…In DS-G-454, instead, we process input patterns that are labeled graphs. Therefore, we implement the kernel function as the graph coverage kernel [22,26]. DS-454 is a subset of DS-1811, and therefore the same classification systems described for DS-1811 apply here.…”

Section: The Considered Pattern Recognition Systemsmentioning

confidence: 99%

Toward a multilevel representation of protein molecules: Comparative approaches to the aggregation/folding propensity problem

Livi

Giuliani

Rizzi

2016

Information Sciences

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This paper builds upon the fundamental work of Niwa et al. [34], which provides the unique possibility to analyze the relative aggregation/folding propensity of the elements of the entire Escherichia coli (E. coli) proteome in a cell-free standardized microenvironment. The hardness of the problem comes from the superposition between the driving forces of intra-and inter-molecule interactions and it is mirrored by the evidences of shift from folding to aggregation phenotypes by single-point mutations [10]. Here we apply several state-of-the-art classification methods coming from the field of structural pattern recognition, with the aim to compare different representations of the same proteins gathered from the Niwa et al. data base; such representations include sequences and labeled (contact) graphs enriched with chemico-physical attributes. By this comparison, we are able to identify also some interesting general properties of proteins. Notably, (i) we suggest a threshold around 250 residues discriminating "easily foldable" from "hardly foldable" molecules consistent with other independent experiments, and (ii) we highlight the relevance of contact graph spectra for folding behavior discrimination and characterization of the E. coli solubility data. The soundness of the experimental results presented in this paper is proved by the statistically relevant relationships discovered among the chemico-physical description of proteins and the developed cost matrix of substitution used in the various discrimination systems.

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“…Last, the work of Livi et al [23] contains an algorithmic motif concerning parallel graph tensor product calculations for inexact graph matching, while their formulation also has a product weight matrix that is computed using a vertex kernel and an edge kernel. However, the product graph is not used to construct a linear system that has to be solved.…”

Section: Related Workmentioning

confidence: 99%

A High-Throughput Solver for Marginalized Graph Kernels on GPU

Tang,

Selvitopi,

Popovici

et al. 2019

Preprint

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We present the design and optimization of a solver for efficient and high-throughput computation of the marginalized graph kernel on General Purpose GPUs. The graph kernel is computed using the conjugate gradient method to solve a generalized Laplacian of the tensor product between a pair of graphs. To cope with the large gap between the instruction throughput and the memory bandwidth of the GPUs, our solver forms the graph tensor product on-the-fly without storing it in memory. This is achieved by using threads in a warp cooperatively to stream the adjacency and edge label matrices of individual graphs by small square matrix blocks called tiles, which are then staged in registers and the shared memory for later reuse. Warps across a thread block can further share tiles via the shared memory to increase data reuse. We exploit the sparsity of the graphs hierarchically by storing only non-empty tiles using a coordinate format and nonzero elements within each tile using bitmaps. We propose a new partition-based reordering algorithm for aggregating nonzero elements of the graphs into fewer but denser tiles to further exploit sparsity.We carry out extensive theoretical analyses on the graph tensor product primitives for tiles of various density and evaluate their performance on synthetic and real-world datasets. Our solver delivers three to four orders of magnitude speedup over existing CPU-based solvers such as GraKeL and GraphKernels. The capability of the solver enables kernel-based learning tasks at unprecedented scales.

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Parallel algorithms for tensor product-based inexact graph matching

Cited by 13 publications

References 24 publications

Using extremal events to characterize noisy time series

Using extremal events to characterize noisy time series

Toward a multilevel representation of protein molecules: Comparative approaches to the aggregation/folding propensity problem

A High-Throughput Solver for Marginalized Graph Kernels on GPU

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