A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks

Iwen, Mark A.; Ong, Benjamin W.

doi:10.1137/16m1058467

Cited by 41 publications

(44 citation statements)

References 31 publications

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“…However, no bounds on the number of obtained (local and final) POD are given. [89] investigates distributed SVD computation on tree structures and features an error bound but for a given target reduced rank. In comparison, the HAPOD prescribes a (mean projection) error bound by which the rank of the decomposition is determined.…”

Section: Related Workmentioning

confidence: 99%

First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: Model derivation and realizability theory

Schneider

Leibner

2020

Journal of Computational Physics

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Moment models are a class of specialized approximate models for kinetic transport equations. These models transform the kinetic equation to a system of equations for weighted velocity averages of the solution, called moments, thereby removing the velocity dependency. The properties of the resulting models depend on the chosen weight functions for the moments and on the approach used to close the equations. Closing the system by specifying a linear ansatz function results in linear models that are comparatively easy to solve but may show non-physical behaviour. Minimum-entropy moment closures, on the other hand, conserve many of the fundamental physical properties but require the solution of a non-linear optimization problem for every cell in the space-time grid. In addition, these models are only well-defined if the moments can be kept within a particular subset of the real coordinate space, the so-called realizable set, which is particularly challenging for higher-order numerical solvers.Schließlich beschäftigen wir uns mit der Möglichkeit einer zusätzlichen Modellreduktion für parameterabhängige Momentenmodelle. Hierzu nutzen wir die Reduzierte-Basis-Methode und berechnen mit der Hauptkomponentenanalyse ("Proper Orthogonal Decomposition", POD) ein reduziertes Modell. Wir stellen die hierarchische approximative POD (HAPOD) vor, ein universelles und einfach zu implementierendes Verfahren um eine approximative POD zu berechnen. Die HAPOD nutzt eine fast beliebig an die verfügbaren Ressourcen anpassbare Baumstruktur, so dass jeder Rechenknoten nur die POD einer relativ kleinen Teilmenge der Eingangsvektoren berechnen muss. Wir führen eine ausführliche theoretische Analyse der HAPOD durch und zeigen die Anwendbarkeit auf lineare Momentenmodelle sowie eine gegenüber der POD deutlich verbesserte Effizienz.

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Section: Related Workmentioning

confidence: 99%

First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: Model derivation and realizability theory

Schneider

Leibner

2020

Journal of Computational Physics

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“…Third, it could be rewarding to also consider versions of OMS for additional empirical GMRA variants including, e.g., those which rely on adaptive constructions [37], GMRA constructions in which subspaces that minimize different criteria are used to approximate the data in each partition element (see, e.g., [27]), and distributed GMRA constructions which are built up across networks using distributed clustering [4] and SVD [30] algorithms. Such variants could prove valuable with respect to reducing the overall computational storage and/or runtime requirements of OMS in different practical situations.…”

Section: Discussionmentioning

confidence: 99%

On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds

Iwen

Krahmer

Krause-Solberg

et al. 2021

Discrete Comput Geom

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This paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension. We provide a convex recovery method based on the Geometric Multi-Resolution Analysis and prove recovery guarantees with a near-optimal scaling in the intrinsic manifold dimension. Our method is the first tractable algorithm with such guarantees for this setting. The results are complemented by numerical experiments confirming the validity of our approach.

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“…Therefore, the SVD cannot be computed without compromising the privacy of the data as it is required to have all data stored in a single location. Nonetheless, the distributed calculation of the SVD can be performed if we make use of some results presented by Iwen et al 60 They propose the partition of the original matrix

boldX

, on which we want to apply the decomposition, into

k

block matrices, that is.

boldX = [X_{1} ∣ X_{2} ∣ ⋯ ∣ X_{k}]

, to, subsequently, compute in parallel the SVD decomposition of each of these blocks.…”

Section: Privacy‐preserving Training Algorithm For Autoencodersmentioning

confidence: 99%

DSVD‐autoencoder: A scalable distributed privacy‐preserving method for one‐class classification

2020

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One-class classification has gained interest as a solution to certain kinds of problems typical in a wide variety of real environments like anomaly or novelty detection. Autoencoder is the type of neural network that has been widely applied in these one-class problems. In the Big Data era, new challenges have arisen, mainly related with the data volume. Another main concern derives from Privacy issues when data is distributed and cannot be shared among locations. These two conditions make many of the classic and brilliant methods not applicable. In this paper, we present distributed singular value decomposition (DSVDautoencoder), a method for autoencoders that allows learning in distributed scenarios without sharing raw data. Additionally, to guarantee privacy, it is noniterative and hyperparameter-free, two interesting characteristics when dealing with Big Data. In comparison with the state of the art, results demonstrate that DSVD-autoencoder provides a highly competitive solution to deal with very large data sets by reducing training from several hours to seconds while maintaining good accuracy.

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A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks

Cited by 41 publications

References 31 publications

First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: Model derivation and realizability theory

First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: Model derivation and realizability theory

On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds

DSVD‐autoencoder: A scalable distributed privacy‐preserving method for one‐class classification

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