Concept

Nonlinear dimensionality reduction

Related publications (497)

Efficient Reduction Techniques for the Simulation and Optimization of Parametrized Systems

This thesis is concerned with the development, analysis and implementation of efficient reduced order models (ROMs) for the simulation and optimization of parametrized partial differential equations (PDEs). Indeed, since the high-fidelity approximation of ...

EPFL2015

Estimation in Functional Lagged Regression

Lukasz Kidzinski

The paper introduces a functional time series (lagged) regression model. The impulse-response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L-2 in applications. A spectral approach to the estima ...

Wiley-Blackwell2015

MATHICSE Technical Report : A reduced basis finite element heterogeneous multiscale method for Stokes flow in porous media

Assyr Abdulle, Ondrej Budác

A reduced basis Darcy-Stokes finite element heterogeneous multiscale method (RB-DS-FE-HMM) is proposed for the Stokes problem in porous media. The multiscale method is based on the Darcy-Stokes finite element heterogeneous multiscale method (DS-FE-HMM) int ...

MATHICSE2015

Signal structure: from manifolds to molecules and structured sparsity

Sofia Karygianni

Effective representation methods and proper signal priors are crucial in most signal processing applications. In this thesis we focus on different structured models and we design appropriate schemes that allow the discovery of low dimensional latent struct ...

EPFL2015

Robust Principal Component Analysis on Graphs

Pierre Vandergheynst, Michael Bronstein, Xavier Bresson, Nauman Shahid, Vasilis Kalofolias

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first iss ...

2015

Structure Modeling of High Dimensional Data

Mahdad Hosseini Kamal

The digitization of our most common appliances has led to a literal data deluge, some- times referred to as Big Data. The ever increasing volume of data we generate, coupled with our desire to exploit it ever faster, forces us to come up with innovative da ...

EPFL2015

Probing the Unfolded Configurations of a β-Hairpin Using Sketch-Map

Michele Ceriotti, Gareth Aneurin Tribello, Michele Parrinello

This work examines the conformational ensemble involved in beta-hairpin folding by means of advanced molecular dynamics simulations and dimensionality reduction. A fully atomistic description of the protein and the surrounding solvent molecules is used, an ...

Amer Chemical Soc2015

Verification of Component-based Systems via Predicate Abstraction and Simultaneous Set Reduction

Simon Bliudze, Qiang Wang

This paper presents a novel safety property verification approach for component-based systems modelled in BIP (Behaviour, Interaction and Priority), encompassing multiparty synchronisation with data transfer and priority. Our contributions consist of: (1 ...

Springer2015

Rehabilitation of Count-based Models for Word Vector Representations

Rémi Philippe Lebret, Ronan Collobert

Recent works on word representations mostly rely on predictive models. Distributed word representations (aka word embeddings) are trained to optimally predict the contexts in which the corresponding words tend to appear. Such models have succeeded in captu ...

Springer International Publishing2015

A reduced basis localized orthogonal decomposition

Assyr Abdulle, Patrick Henning

In this work we combine the framework of the Reduced Basis method (RB) with the framework of the Localized Orthogonal Decomposition (LOD) in order to solve parametrized elliptic multiscale problems. The idea of the LOD is to split a high dimensional Finite ...

2015

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