18,845 research outputs found
Rotated Spectral Principal Component Analysis (rsPCA) for Identifying Dynamical Modes of Variability in Climate Systems.
Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatiotemporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable trade-off between frequency resolution and robustness of the PCs leads to high sensitivity to noise and overfitting, which limits the interpretation of the sPCA results. We propose herein a simple nonparametric implementation of sPCA using the continuous analytic Morlet wavelet as a robust estimator of the cross-spectral matrices with good frequency resolution. To improve the interpretability of the results, especially when several modes of similar amplitude exist within the same frequency band, we propose a rotation of the complex-valued eigenvectors to optimize their spatial regularity (smoothness). The developed method, called rotated spectral PCA (rsPCA), is tested on synthetic data simulating propagating waves and shows impressive performance even with high levels of noise in the data. Applied to global historical geopotential height (GPH) and sea surface temperature (SST) daily time series, the method accurately captures patterns of atmospheric Rossby waves at high frequencies (3-60-day periods) in both GPH and SST and El Niño-Southern Oscillation (ENSO) at low frequencies (2-7-yr periodicity) in SST. At high frequencies the rsPCA successfully unmixes the identified waves, revealing spatially coherent patterns with robust propagation dynamics
Foreground component separation with generalised ILC
The 'Internal Linear Combination' (ILC) component separation method has been
extensively used to extract a single component, the CMB, from the WMAP
multifrequency data. We generalise the ILC approach for separating other
millimetre astrophysical emissions. We construct in particular a
multidimensional ILC filter, which can be used, for instance, to estimate the
diffuse emission of a complex component originating from multiple correlated
emissions, such as the total emission of the Galactic interstellar medium. The
performance of such generalised ILC methods, implemented on a needlet frame, is
tested on simulations of Planck mission observations, for which we successfully
reconstruct a low noise estimate of emission from astrophysical foregrounds
with vanishing CMB and SZ contamination.Comment: 11 pages, 6 figures (2 figures added), 1 reference added,
introduction expanded, V2: version accepted by MNRA
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Dynamic Mode Decomposition for Compressive System Identification
Dynamic mode decomposition has emerged as a leading technique to identify
spatiotemporal coherent structures from high-dimensional data, benefiting from
a strong connection to nonlinear dynamical systems via the Koopman operator. In
this work, we integrate and unify two recent innovations that extend DMD to
systems with actuation [Proctor et al., 2016] and systems with heavily
subsampled measurements [Brunton et al., 2015]. When combined, these methods
yield a novel framework for compressive system identification [code is publicly
available at: https://github.com/zhbai/cDMDc]. It is possible to identify a
low-order model from limited input-output data and reconstruct the associated
full-state dynamic modes with compressed sensing, adding interpretability to
the state of the reduced-order model. Moreover, when full-state data is
available, it is possible to dramatically accelerate downstream computations by
first compressing the data. We demonstrate this unified framework on two model
systems, investigating the effects of sensor noise, different types of
measurements (e.g., point sensors, Gaussian random projections, etc.),
compression ratios, and different choices of actuation (e.g., localized,
broadband, etc.). In the first example, we explore this architecture on a test
system with known low-rank dynamics and an artificially inflated state
dimension. The second example consists of a real-world engineering application
given by the fluid flow past a pitching airfoil at low Reynolds number. This
example provides a challenging and realistic test-case for the proposed method,
and results demonstrate that the dominant coherent structures are well
characterized despite actuation and heavily subsampled data
Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
The widespread use of multi-sensor technology and the emergence of big
datasets has highlighted the limitations of standard flat-view matrix models
and the necessity to move towards more versatile data analysis tools. We show
that higher-order tensors (i.e., multiway arrays) enable such a fundamental
paradigm shift towards models that are essentially polynomial and whose
uniqueness, unlike the matrix methods, is guaranteed under verymild and natural
conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical
backbone, data analysis techniques using tensor decompositions are shown to
have great flexibility in the choice of constraints that match data properties,
and to find more general latent components in the data than matrix-based
methods. A comprehensive introduction to tensor decompositions is provided from
a signal processing perspective, starting from the algebraic foundations, via
basic Canonical Polyadic and Tucker models, through to advanced cause-effect
and multi-view data analysis schemes. We show that tensor decompositions enable
natural generalizations of some commonly used signal processing paradigms, such
as canonical correlation and subspace techniques, signal separation, linear
regression, feature extraction and classification. We also cover computational
aspects, and point out how ideas from compressed sensing and scientific
computing may be used for addressing the otherwise unmanageable storage and
manipulation problems associated with big datasets. The concepts are supported
by illustrative real world case studies illuminating the benefits of the tensor
framework, as efficient and promising tools for modern signal processing, data
analysis and machine learning applications; these benefits also extend to
vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker
decomposition, HOSVD, tensor networks, Tensor Train
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