6,920 research outputs found
Deep Learning Reveals Underlying Physics of Light-matter Interactions in Nanophotonic Devices
In this paper, we present a deep learning-based (DL-based) algorithm, as a
purely mathematical platform, for providing intuitive understanding of the
properties of electromagnetic (EM) wave-matter interaction in nanostructures.
This approach is based on using the dimensionality reduction (DR) technique to
significantly reduce the dimensionality of a generic EM wave-matter interaction
problem without imposing significant error. Such an approach implicitly
provides useful information about the role of different features (or design
parameters such as geometry) of the nanostructure in its response
functionality. To demonstrate the practical capabilities of this DL-based
technique, we apply it to a reconfigurable optical metadevice enabling
dual-band and triple-band optical absorption in the telecommunication window.
Combination of the proposed approach with existing commercialized full-wave
simulation tools offers a powerful toolkit to extract basic mechanisms of
wave-matter interaction in complex EM devices and facilitate the design and
optimization of nanostructures for a large range of applications including
imaging, spectroscopy, and signal processing. It is worth to mention that the
demonstrated approach is general and can be used in a large range of problems
as long as enough training data can be provided
Detecting spatial patterns with the cumulant function. Part I: The theory
In climate studies, detecting spatial patterns that largely deviate from the
sample mean still remains a statistical challenge. Although a Principal
Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions
(EOF) decomposition, is often applied on this purpose, it can only provide
meaningful results if the underlying multivariate distribution is Gaussian.
Indeed, PCA is based on optimizing second order moments quantities and the
covariance matrix can only capture the full dependence structure for
multivariate Gaussian vectors. Whenever the application at hand can not satisfy
this normality hypothesis (e.g. precipitation data), alternatives and/or
improvements to PCA have to be developed and studied. To go beyond this second
order statistics constraint that limits the applicability of the PCA, we take
advantage of the cumulant function that can produce higher order moments
information. This cumulant function, well-known in the statistical literature,
allows us to propose a new, simple and fast procedure to identify spatial
patterns for non-Gaussian data. Our algorithm consists in maximizing the
cumulant function. To illustrate our approach, its implementation for which
explicit computations are obtained is performed on three family of of
multivariate random vectors. In addition, we show that our algorithm
corresponds to selecting the directions along which projected data display the
largest spread over the marginal probability density tails.Comment: 9 pages, 3 figure
Stacking-Based Deep Neural Network: Deep Analytic Network for Pattern Classification
Stacking-based deep neural network (S-DNN) is aggregated with pluralities of
basic learning modules, one after another, to synthesize a deep neural network
(DNN) alternative for pattern classification. Contrary to the DNNs trained end
to end by backpropagation (BP), each S-DNN layer, i.e., a self-learnable
module, is to be trained decisively and independently without BP intervention.
In this paper, a ridge regression-based S-DNN, dubbed deep analytic network
(DAN), along with its kernelization (K-DAN), are devised for multilayer feature
re-learning from the pre-extracted baseline features and the structured
features. Our theoretical formulation demonstrates that DAN/K-DAN re-learn by
perturbing the intra/inter-class variations, apart from diminishing the
prediction errors. We scrutinize the DAN/K-DAN performance for pattern
classification on datasets of varying domains - faces, handwritten digits,
generic objects, to name a few. Unlike the typical BP-optimized DNNs to be
trained from gigantic datasets by GPU, we disclose that DAN/K-DAN are trainable
using only CPU even for small-scale training sets. Our experimental results
disclose that DAN/K-DAN outperform the present S-DNNs and also the BP-trained
DNNs, including multiplayer perceptron, deep belief network, etc., without data
augmentation applied.Comment: 14 pages, 7 figures, 11 table
Representing complex data using localized principal components with application to astronomical data
Often the relation between the variables constituting a multivariate data
space might be characterized by one or more of the terms: ``nonlinear'',
``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or,
more general, ``complex''. In these cases, simple principal component analysis
(PCA) as a tool for dimension reduction can fail badly. Of the many alternative
approaches proposed so far, local approximations of PCA are among the most
promising. This paper will give a short review of localized versions of PCA,
focusing on local principal curves and local partitioning algorithms.
Furthermore we discuss projections other than the local principal components.
When performing local dimension reduction for regression or classification
problems it is important to focus not only on the manifold structure of the
covariates, but also on the response variable(s). Local principal components
only achieve the former, whereas localized regression approaches concentrate on
the latter. Local projection directions derived from the partial least squares
(PLS) algorithm offer an interesting trade-off between these two objectives. We
apply these methods to several real data sets. In particular, we consider
simulated astrophysical data from the future Galactic survey mission Gaia.Comment: 25 pages. In "Principal Manifolds for Data Visualization and
Dimension Reduction", A. Gorban, B. Kegl, D. Wunsch, and A. Zinovyev (eds),
Lecture Notes in Computational Science and Engineering, Springer, 2007, pp.
180--204,
http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-173750210-
An Adaptive Neuro-Fuzzy Inference System Based Approach to Real Estate Property Assessment
This paper describes a first effort to design and implement an adaptive neuro-fuzzy inference system based approach to estimate prices for residential properties. The data set consists of historic sales of homes in a market in Midwest USA and it contains parameters describing typical residential property features and the actual sale price. The study explores the use of fuzzy inference systems to assess real estate property values and the use of neural networks in creating and fine tuning the fuzzy rules used in the fuzzy inference system. The results are compared with those obtained using a traditional multiple regression model. The paper also describes possible future research in this area.
Protosymbols that integrate recognition and response
We explore two controversial hypotheses through robotic implementation: (1) Processes involved in recognition and response are tightly coupled both in their operation and epigenesis; and (2) processes involved in symbol emergence should respect the integrity of recognition and response while exploiting the periodicity of biological motion. To that end, this paper proposes a method of recognizing and generating motion patterns based on nonlinear principal component neural networks that are constrained to model both periodic and transitional movements. The method is evaluated by an examination of its ability to segment and generalize different kinds of soccer playing activity during a RoboCup match
Neural network setups for a precise detection of the many-body localization transition: finite-size scaling and limitations
Determining phase diagrams and phase transitions semi-automatically using
machine learning has received a lot of attention recently, with results in good
agreement with more conventional approaches in most cases. When it comes to
more quantitative predictions, such as the identification of universality class
or precise determination of critical points, the task is more challenging. As
an exacting test-bed, we study the Heisenberg spin-1/2 chain in a random
external field that is known to display a transition from a many-body localized
to a thermalizing regime, which nature is not entirely characterized. We
introduce different neural network structures and dataset setups to achieve a
finite-size scaling analysis with the least possible physical bias (no assumed
knowledge on the phase transition and directly inputing wave-function
coefficients), using state-of-the-art input data simulating chains of sizes up
to L=24. In particular, we use domain adversarial techniques to ensure that the
network learns scale-invariant features. We find a variability of the output
results with respect to network and training parameters, resulting in
relatively large uncertainties on final estimates of critical point and
correlation length exponent which tend to be larger than the values obtained
from conventional approaches. We put the emphasis on interpretability
throughout the paper and discuss what the network appears to learn for the
various used architectures. Our findings show that a it quantitative analysis
of phase transitions of unknown nature remains a difficult task with neural
networks when using the minimally engineered physical input.Comment: v2: published versio
How to Solve Classification and Regression Problems on High-Dimensional Data with a Supervised Extension of Slow Feature Analysis
Supervised learning from high-dimensional data, e.g., multimedia data, is a challenging task. We propose an extension of slow feature analysis (SFA) for supervised dimensionality reduction called graph-based SFA (GSFA). The algorithm extracts a label-predictive low-dimensional set of features that can be post-processed by typical supervised algorithms to generate the final label or class estimation. GSFA is trained with a so-called training graph, in which the vertices are the samples and the edges represent similarities of the corresponding labels. A new weighted SFA optimization problem is introduced, generalizing the notion of slowness from sequences of samples to such training graphs. We show that GSFA computes an optimal solution to this problem in the considered function space, and propose several types of training graphs. For classification, the most straightforward graph yields features equivalent to those of (nonlinear) Fisher discriminant analysis. Emphasis is on regression, where four different graphs were evaluated experimentally with a subproblem of face detection on photographs. The method proposed is promising particularly when linear models are insufficient, as well as when feature selection is difficult
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