Computational Intelligence - August 2014 - 29

Brightness

but also due to the characteristics of the data
The resolution, coverage, and cadence of the LSST
itself. Astronomical time series are unevenly
sampled due to constraints in the observation
will help us improve our understanding of known
schedules, telescope allocations and other
astrophysical objects and reveal a plethora of
limitations. When observations are taken from
unknown faint and fast-varying phenomena.
Earth the resulting light curves will have
periodic one-day gaps. The sampling is ranintrinsic variable stars can be used as distance markers to study
domized because observations for each object happen at difthe distribution and topology of the Universe. Cepheid and
ferent times every night. The cycles of the moon, bad weather
RR Lyrae stars [15] (Fig. 2a) are considered standard candles
conditions and sky visibility impose additional constraints
because of the relation between their pulsation period and
which translate into data gaps of different lengths. Space
their absolute brightness. It is possible to estimate the distance
observations are also restricted as they are regulated by the satfrom these stars to Earth with the period and the apparent
ellite orbits. Discontinuities in light curves can also be caused
by technical factors: repositioning of the telescopes, calibration
of equipment, electrical, and mechanical failures, etc.
A
B
Astronomical time series are also affected by several noise
sources. These noise sources can be broadly categorized into
two classes. The first class is related to observations, such as the
brightness of closer astronomical objects, and atmospheric
noise due to refraction and extinction phenomena (scattering
of light due to atmospheric dust). On the other hand, there are
Time
noise sources related to the instrumentation, in particular to the
Instant A
Instant B
CCD cameras, such as sensitivity variations of the detector, and
Z
Z
thermal noise. In general, errors in astronomical time series are
non-Gaussian and heterocesdastic, i.e., the variance of the error
is not constant, and changes along the magnitude axis.
Other common problematic situations arising in TDA are
the sample-selection bias and the lack of balance between
classes. Generally the astrophysical phenomena of interest represents a small fraction of the observable sky, hence the vast
X
X
majority of the data belongs to the "background class". This is
(a)
especially noticeable when the objective is to find unknown
phenomena, a task known as novelty detection. Sufficient covA
B
erage and exhaustive labeling are required in order to have a
good representation of the sample, and to assure capturing the
rare objects of interests.
In the following we briefly describe several time-domain
astronomical phenomena emphasizing their scientific interest.
We focus on phenomena that vary in the optical spectrum.
Time
Among the "observable stars" there is a particular group
Instant A
Instant B
called the variable stars [14]-[16]. Variable stars correspond
Z
Z
to stellar objects whose brightness, as observed from Earth,
fluctuates in time above a certain variability threshold defined
by the sensitivity of the instruments. Variable star analysis is a
fundamental pivot in the study of stellar structure and properties, stellar evolution and the distribution and size of our Universe. The major categories of variable stars are briefly
described in the following paragraphs with emphasis on the
X
X
scientific interest behind each of them. For a more in-depth
(b)
definition of the objects and their mechanisms of variability,
Figure 2 (a) Light curve of a pulsating variable star (upper left panel),
the reader can refer to [15]. The relation between different
such as a Cepheid or RR Lyrae. The star pulsates periodically changing in
classes of variable stars is summarized by the tree diagram
size, temperature and brightness which is reflected on its light curve. (b)
Light curve of eclipsing binary star (upper right panel). The lower panels
shown in Fig. 1 [16], [17].
show the geometry of the binary system at the instants where the eclipsThe analysis of intrinsic variable stars is of great importance
es occur. The periodic pattern in the light curve is observed because the
for the study of stellar nuclei and evolution. Some classes of
Earth (X axis) is aligned with the orbital plane of the system (Z axis).

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Table of Contents for the Digital Edition of Computational Intelligence - August 2014