19,010 research outputs found
Nonparametric Feature Extraction from Dendrograms
We propose feature extraction from dendrograms in a nonparametric way. The
Minimax distance measures correspond to building a dendrogram with single
linkage criterion, with defining specific forms of a level function and a
distance function over that. Therefore, we extend this method to arbitrary
dendrograms. We develop a generalized framework wherein different distance
measures can be inferred from different types of dendrograms, level functions
and distance functions. Via an appropriate embedding, we compute a vector-based
representation of the inferred distances, in order to enable many numerical
machine learning algorithms to employ such distances. Then, to address the
model selection problem, we study the aggregation of different dendrogram-based
distances respectively in solution space and in representation space in the
spirit of deep representations. In the first approach, for example for the
clustering problem, we build a graph with positive and negative edge weights
according to the consistency of the clustering labels of different objects
among different solutions, in the context of ensemble methods. Then, we use an
efficient variant of correlation clustering to produce the final clusters. In
the second approach, we investigate the sequential combination of different
distances and features sequentially in the spirit of multi-layered
architectures to obtain the final features. Finally, we demonstrate the
effectiveness of our approach via several numerical studies
Multivariate Approaches to Classification in Extragalactic Astronomy
Clustering objects into synthetic groups is a natural activity of any
science. Astrophysics is not an exception and is now facing a deluge of data.
For galaxies, the one-century old Hubble classification and the Hubble tuning
fork are still largely in use, together with numerous mono-or bivariate
classifications most often made by eye. However, a classification must be
driven by the data, and sophisticated multivariate statistical tools are used
more and more often. In this paper we review these different approaches in
order to situate them in the general context of unsupervised and supervised
learning. We insist on the astrophysical outcomes of these studies to show that
multivariate analyses provide an obvious path toward a renewal of our
classification of galaxies and are invaluable tools to investigate the physics
and evolution of galaxies.Comment: Open Access paper.
http://www.frontiersin.org/milky\_way\_and\_galaxies/10.3389/fspas.2015.00003/abstract\>.
\<10.3389/fspas.2015.00003 \&g
Data clustering using a model granular magnet
We present a new approach to clustering, based on the physical properties of
an inhomogeneous ferromagnet. No assumption is made regarding the underlying
distribution of the data. We assign a Potts spin to each data point and
introduce an interaction between neighboring points, whose strength is a
decreasing function of the distance between the neighbors. This magnetic system
exhibits three phases. At very low temperatures it is completely ordered; all
spins are aligned. At very high temperatures the system does not exhibit any
ordering and in an intermediate regime clusters of relatively strongly coupled
spins become ordered, whereas different clusters remain uncorrelated. This
intermediate phase is identified by a jump in the order parameters. The
spin-spin correlation function is used to partition the spins and the
corresponding data points into clusters. We demonstrate on three synthetic and
three real data sets how the method works. Detailed comparison to the
performance of other techniques clearly indicates the relative success of our
method.Comment: 46 pages, postscript, 15 ps figures include
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