50,418 research outputs found
Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis
In this paper, we study a natural extension of Multi-Layer Perceptrons (MLP)
to functional inputs. We show that fundamental results for classical MLP can be
extended to functional MLP. We obtain universal approximation results that show
the expressive power of functional MLP is comparable to that of numerical MLP.
We obtain consistency results which imply that the estimation of optimal
parameters for functional MLP is statistically well defined. We finally show on
simulated and real world data that the proposed model performs in a very
satisfactory way.Comment: http://www.sciencedirect.com/science/journal/0893608
Representation of Functional Data in Neural Networks
Functional Data Analysis (FDA) is an extension of traditional data analysis
to functional data, for example spectra, temporal series, spatio-temporal
images, gesture recognition data, etc. Functional data are rarely known in
practice; usually a regular or irregular sampling is known. For this reason,
some processing is needed in order to benefit from the smooth character of
functional data in the analysis methods. This paper shows how to extend the
Radial-Basis Function Networks (RBFN) and Multi-Layer Perceptron (MLP) models
to functional data inputs, in particular when the latter are known through
lists of input-output pairs. Various possibilities for functional processing
are discussed, including the projection on smooth bases, Functional Principal
Component Analysis, functional centering and reduction, and the use of
differential operators. It is shown how to incorporate these functional
processing into the RBFN and MLP models. The functional approach is illustrated
on a benchmark of spectrometric data analysis.Comment: Also available online from:
http://www.sciencedirect.com/science/journal/0925231
Continuous-variable quantum neural networks
We introduce a general method for building neural networks on quantum
computers. The quantum neural network is a variational quantum circuit built in
the continuous-variable (CV) architecture, which encodes quantum information in
continuous degrees of freedom such as the amplitudes of the electromagnetic
field. This circuit contains a layered structure of continuously parameterized
gates which is universal for CV quantum computation. Affine transformations and
nonlinear activation functions, two key elements in neural networks, are
enacted in the quantum network using Gaussian and non-Gaussian gates,
respectively. The non-Gaussian gates provide both the nonlinearity and the
universality of the model. Due to the structure of the CV model, the CV quantum
neural network can encode highly nonlinear transformations while remaining
completely unitary. We show how a classical network can be embedded into the
quantum formalism and propose quantum versions of various specialized model
such as convolutional, recurrent, and residual networks. Finally, we present
numerous modeling experiments built with the Strawberry Fields software
library. These experiments, including a classifier for fraud detection, a
network which generates Tetris images, and a hybrid classical-quantum
autoencoder, demonstrate the capability and adaptability of CV quantum neural
networks
Theoretical Interpretations and Applications of Radial Basis Function Networks
Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains
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Estimation of physical variables from multichannel remotely sensed imagery using a neural network: Application to rainfall estimation
Satellite-based remotely sensed data have the potential to provide hydrologically relevant information about spatially and temporally varying physical variables. A methodology for estimating such variables from multichannel remotely sensed data is presented; the approach is based on a modified counterpropagation neural network (MCPN) and is both effective and efficient at building complex nonlinear input-output function mappings from large amounts of data. An application to high-resolution estimation of the spatial and temporal variation of surface rainfall using geostationary satellite infrared and visible imagery is presented. Test results also indicate that spatially and temporally sparse ground-based observations can be assimilated via an adaptive implementation of the MCPN method, thereby allowing on-line improvement of the estimates
Bicriteria data compression
The advent of massive datasets (and the consequent design of high-performing
distributed storage systems) have reignited the interest of the scientific and
engineering community towards the design of lossless data compressors which
achieve effective compression ratio and very efficient decompression speed.
Lempel-Ziv's LZ77 algorithm is the de facto choice in this scenario because of
its decompression speed and its flexibility in trading decompression speed
versus compressed-space efficiency. Each of the existing implementations offers
a trade-off between space occupancy and decompression speed, so software
engineers have to content themselves by picking the one which comes closer to
the requirements of the application in their hands. Starting from these
premises, and for the first time in the literature, we address in this paper
the problem of trading optimally, and in a principled way, the consumption of
these two resources by introducing the Bicriteria LZ77-Parsing problem, which
formalizes in a principled way what data-compressors have traditionally
approached by means of heuristics. The goal is to determine an LZ77 parsing
which minimizes the space occupancy in bits of the compressed file, provided
that the decompression time is bounded by a fixed amount (or vice-versa). This
way, the software engineer can set its space (or time) requirements and then
derive the LZ77 parsing which optimizes the decompression speed (or the space
occupancy, respectively). We solve this problem efficiently in O(n log^2 n)
time and optimal linear space within a small, additive approximation, by
proving and deploying some specific structural properties of the weighted graph
derived from the possible LZ77-parsings of the input file. The preliminary set
of experiments shows that our novel proposal dominates all the highly
engineered competitors, hence offering a win-win situation in theory&practice
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