11,361 research outputs found
Dimensionality Reduction Mappings
A wealth of powerful dimensionality reduction methods has been established which can be used for data visualization and preprocessing. These are accompanied by formal evaluation schemes, which allow a quantitative evaluation along general principles and which even lead to further visualization schemes based on these objectives. Most methods, however, provide a mapping of a priorly given finite set of points only, requiring additional steps for out-of-sample extensions. We propose a general view on dimensionality reduction based on the concept of cost functions, and, based on this general principle, extend dimensionality reduction to explicit mappings of the data manifold. This offers simple out-of-sample extensions. Further, it opens a way towards a theory of data visualization taking the perspective of its generalization ability to new data points. We demonstrate the approach based on a simple global linear mapping as well as prototype-based local linear mappings.
Wide Field Imaging. I. Applications of Neural Networks to object detection and star/galaxy classification
[Abriged] Astronomical Wide Field Imaging performed with new large format CCD
detectors poses data reduction problems of unprecedented scale which are
difficult to deal with traditional interactive tools. We present here NExt
(Neural Extractor): a new Neural Network (NN) based package capable to detect
objects and to perform both deblending and star/galaxy classification in an
automatic way. Traditionally, in astronomical images, objects are first
discriminated from the noisy background by searching for sets of connected
pixels having brightnesses above a given threshold and then they are classified
as stars or as galaxies through diagnostic diagrams having variables choosen
accordingly to the astronomer's taste and experience. In the extraction step,
assuming that images are well sampled, NExt requires only the simplest a priori
definition of "what an object is" (id est, it keeps all structures composed by
more than one pixels) and performs the detection via an unsupervised NN
approaching detection as a clustering problem which has been thoroughly studied
in the artificial intelligence literature. In order to obtain an objective and
reliable classification, instead of using an arbitrarily defined set of
features, we use a NN to select the most significant features among the large
number of measured ones, and then we use their selected features to perform the
classification task. In order to optimise the performances of the system we
implemented and tested several different models of NN. The comparison of the
NExt performances with those of the best detection and classification package
known to the authors (SExtractor) shows that NExt is at least as effective as
the best traditional packages.Comment: MNRAS, in press. Paper with higher resolution images is available at
http://www.na.astro.it/~andreon/listapub.htm
Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians
In this paper we propose a new Koopman operator approach to the decomposition
of nonlinear dynamical systems using Koopman Gramians. We introduce the notion
of an input-Koopman operator, and show how input-Koopman operators can be used
to cast a nonlinear system into the classical state-space form, and identify
conditions under which input and state observable functions are well separated.
We then extend an existing method of dynamic mode decomposition for learning
Koopman operators from data known as deep dynamic mode decomposition to systems
with controls or disturbances. We illustrate the accuracy of the method in
learning an input-state separable Koopman operator for an example system, even
when the underlying system exhibits mixed state-input terms. We next introduce
a nonlinear decomposition algorithm, based on Koopman Gramians, that maximizes
internal subsystem observability and disturbance rejection from unwanted noise
from other subsystems. We derive a relaxation based on Koopman Gramians and
multi-way partitioning for the resulting NP-hard decomposition problem. We
lastly illustrate the proposed algorithm with the swing dynamics for an IEEE
39-bus system.Comment: 8 pages, submitted to IEEE 2018 AC
A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps
The Self-OrganizingMap (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topologypreservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topologypreservation, particularly using Kohonen's model. In this work, two methods for measuring the topologypreservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving ma
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