Computational Intelligence - August 2014 - 30

18.5

19
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19
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20

20
0

-1 -0.5 0 0.5
Phase

1000 2000 3000
HJ D [days]

1

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Magnitude

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0

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HJ D [days]

(a)

17
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0

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(c)

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0 0.5
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(b)

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15.8

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0

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17.2

1000 2000 3000
HJ D [days]

-1 -0.5 0 0.5
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1

(d)

Figure 3 Light curve and phase diagram of an RR Lyrae (a), Cepheid (b), Mira (c) and eclipsing binary star (d), respectively. The phase diagram
is obtained using the underlying period of the light curves and the epoch folding transformation [15]. If the folding period is correct a clear profile of the periodicity will appear in the phase diagram.

brightness measured from the telescope [18]. Type 1A Supernovae [15] are also standard candles, although they can be used
to trace much longer distances than Cepheids and RR Lyrae
[19]. The period of eclipsing binary stars [15] (Fig. 2b) is a key
parameter in astrophysics studies as it can be used to calculate
the radii and masses of the components [20]. Light curves and
phase diagrams of periodic variable stars are shown in Fig. 3.
III. Review of Computational Intelligence
Applications in TDA

Time-domain astronomers are faced with a wide array of scientific questions that are related to the detection, identification
and modeling of variable phenomena such as those presented
in the previous Section. We may classify these problems broadly
as follows:
1) Extract information from the observed time series in
order to understand the underlying processes of its source.
2) Use previous knowledge of the time-varying universe to
classify new variable sources automatically. How do we
characterize what we know?
3) Find structure in the data. Find what is odd and different
from everything known. How do we compare astronomical objects? What similarity measure do we use?
The computational intelligence and machine learning fields
provide methods and techniques to deal with these problems in
a robust and automated way. Problem 1) is a problem of modeling, parametrization and regression (kernel density estimation). Problem 2) corresponds to supervised classification (artificial neural networks, random forests, support vector
machines). Problem 3) deals with unsupervised learning, feature
space distances and clustering (k nearest neighbors, self-organizing maps). The correct utilization of these methods is key to

30

IEEE ComputatIonal IntEllIgEnCE magazInE | august 2014

dealing with the deluge of available astronomical data. In the
following section we review particular cases of computational
intelligence based applications for TDA.
A. Periodic Variable Star Discrimination

We begin this review with a case of parameter estimation from
light curves using information theoretic criteria. Precise
period estimations are fundamental in the analysis of periodic
variable stars and other periodic phenomena such as transiting
exoplanets. In [21] the correntropy kernelized periodogram
(CKP), a metric for period discrimination for unevenly sampled time series, was presented. This periodogram is based on
the correntropy function [22], an information theoretic functional that measures similarity over time using statistical information contained in the probability density function (pdf) of
the samples. In [21] the CKP was tested on a set of 5,000 light
curves from the MACHO survey [1] previously classified by
experts. The CKP achieved a true positive rate of 97% having
no false positives and outperformed conventional methods
used in astronomy such as the Lomb-Scargle periodogram
[23], ANOVA and string length.
In [24] the CKP was used as the core of a periodicity discrimination pipeline for light curves from the EROS-2 survey [2]. The method was calibrated using a set of 100,000
synthetic light curves generated from multivariate models
constructed following the EROS-2 data. Periodicity thresholds and rules to adapt the kernel parameters of the CKP
were obtained in the calibration phase. Approximately 32 million light curves from the Large and Small Magellanic clouds
were tested for periodicity. The pipeline was implemented for
GPGPU architectures taking 18 hours to process the whole
EROS-2 set on a cluster with 72 GPUs. A catalog of 120



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