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FeaturesDocumentation.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title>FeaturesDocumentation</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>
<script src="toc.js"></script>
<script type="text/javascript">
$(function() {
table_of_contents();
});
</script>
<style type="text/css">
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<h1 id="Feature-Analysis-for-Time-Series">Feature Analysis for Time Series<a class="anchor-link" href="#Feature-Analysis-for-Time-Series">¶</a></h1>
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<p><center><strong>Authors:</strong> Isadora Nun <a href="mailto:isadoranun@seas.harvard.edu">isadoranun@seas.harvard.edu</a> , Pavlos Protopapas <a href="mailto:pavlos@seas.harvard.edu">pavlos@seas.harvard.edu</a></p>
<p><strong>Contributors:</strong> Karim Pichara, Rahul Dave, Daniel Acuña, Nicolás Castro, Cristobal Mackenzie, Andrés Riveros, Brandon Sim and Ming Zhu<center></p>
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<h2 id="Introduction-">Introduction <a name="Introduction" /><a class="anchor-link" href="#Introduction-">¶</a></h2>
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<p>A time series is a sequence of observations (data points) that are arranged based on the time of their ocurrence. The hourly measurement of wind speeds in meteorology, the minute by minute recording of electrical activity along the scalp in electroencephalography, the weekly changes of stock prices in finances, are just some examples among many others.</p>
<p>Some of the main properties one would expect to find in a time series are [1]:</p>
<ul>
<li>the data is not generated independently</li>
<li>their dispersion varies in time</li>
<li>they are often governed by a trend and they have cyclic components</li>
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<p>The study and analysis of time series can have multiple ends: get a better understanding of the mechanism generating the data, predict future outcomes and behaviours, classification and characterization of events, etc.</p>
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<p>In time-domain astronomy, data gathered from the telescopes is usually represented in the form of light-curves. These are time series that show the brightness variation of an object through a period of time (for a visual representation see video below). Based on the variability characteristics of the light-curves, celestial objects can be classified into different groups (quasars, long period variables, eclipsing binaries, etc.) and consequently be studied in depth independently.</p>
<p>In order to characterize this variability, some of the existing methods use machine learning algorithms that build their decision on the light-curves features. Features, the topic of the following work, are numerical descriptors that aim to characterize and distinguish the different variability classes. They can go from basic statistical measures such as the mean or the standard deviation, to complex time-series characteristics such as the autocorrelation function.</p>
<p>In this document we present a library with a compilation of some of the existing light-curve features. The main goal is to create a collaborative and open tool where every user can characterize or analyze an astronomical photometric database while also contributing to the library by adding new features. However, it is important to highlight that this library is not restricted to the astronomical field and could also be applied to any kind of time series.</p>
<p>Our vision is to be capable of analyzing and comparing light-curves from all the available astronomical catalogs in a standard and universal way. This would facilitate and make more efficient tasks as modeling, classification, data cleaning, outlier detection and data analysis in general. Consequently, when studying light-curves, astronomers and data analysts would be on the same wavelength and would not have the necessity to find a way of comparing or matching different features.
In order to achieve this goal, the library should be run in every existent survey (MACHO, EROS, OGLE, Catalina, Pan-STARRS, etc) and future surveys (LSST) and the results should be ideally shared in the same open way as this library.</p>
<p>The way a user can contribute to the library as well as every feature that we have developed so far are explained throughout this document. A Readme file is also available in case of needing extra information.</p>
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<h6 id="Video-1:-Light-Curve-of-Triple-Star">Video 1: Light-Curve of Triple Star<a class="anchor-link" href="#Video-1:-Light-Curve-of-Triple-Star">¶</a></h6>
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<p>The video below shows how data from the brightness intensity of a star through time results on a light-curve. In this particular case we are observing a complex triple system in which three stars have mutual eclipses as each of the stars gets behind or in front of the others.</p>
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<p>The following figure [5] presents example light-curves of each class in the MACHO survey. The x-axis is the modified Julian Date (MJD), and the y-axis is the MACHO B-magnitude.</p>
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<h6 id="Figure-1:-Some-variability-classes">Figure 1: Some variability classes<a class="anchor-link" href="#Figure-1:-Some-variability-classes">¶</a></h6>
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<h2 id="The-library">The library<a class="anchor-link" href="#The-library">¶</a></h2>
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<h3 id="How-to-cite-FATS">How to cite FATS<a class="anchor-link" href="#How-to-cite-FATS">¶</a></h3>
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<p>The user can cite this library by:</p>
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<li>making reference to the arXiv article available in <a href="http://arxiv.org/abs/1506.00010">http://arxiv.org/abs/1506.00010</a> </li>
<li>directly using the Bibtex entry in <a href="http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2015arXiv150600010N&data_type=BIBTEX&db_key=PRE&nocookieset=1">http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2015arXiv150600010N&data_type=BIBTEX&db_key=PRE&nocookieset=1</a>. </li>
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<p><a id='Vectors'></a></p>
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<h3 id="Library-structure">Library structure<a class="anchor-link" href="#Library-structure">¶</a></h3>
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<p>The library is coded in python and can be downloaded for free from the github website <a href="https://github.com/isadoranun/tsfeat">https://github.com/isadoranun/tsfeat</a>. The main idea is that any user can run it in its own database but can also add new features through the github system. For a quick guide on how to use github visit <a href="https://guides.github.com/activities/hello-world/">https://guides.github.com/activities/hello-world/</a>.</p>
<p>It is also possible to obtain the library by downloading the python package from <a href="https://pypi.python.org/pypi/FATS">https://pypi.python.org/pypi/FATS</a> or by directly installing it from the terminal as follows:</p>
<p><em>$ pip install FATS</em></p>
<p>The library receives as input the time series data and returns as output a vector with the calculated features. In order to calculate all the available features, the data should be an array containing the following vectors and in the following order:</p>
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<li><strong>magnitude</strong></li>
<li>time</li>
<li>error</li>
<li>magnitude2 </li>
<li>aligned magnitude</li>
<li>aligned magnitude2</li>
<li>aligned time</li>
<li>aligned error</li>
<li>aligned error2</li>
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<p>Nevertheless, the magnitude vector is the only input strictly required by the library given that it is necessary for the calculation of all the features. The remaining vectors are optional since they are needed just by some features. In other words, if the user does not have this addtional data, it is still possible to calculate the features that do not need them. For a description of each vector see <a href="#ImportLC">below</a>.</p>
<p>This is an example of how the input could look like if you have only magnitude and time as input vectors:</p>
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<p>The library structure is divided into two main parts. Part one: <em>Feature.py</em>, is a wrapper class that allows the user to select the features to be calculated based on the available time series vectors or to specify a list of features. Part two: <em>FeatureFunciontLib.py</em>, contains the actual code for calculating the features. Each feature has its own class with at least two functions:</p>
<p><strong>init:</strong> receives the necessary parameters (when needed) for the feature calculation. It also defines the required vectors for the computation (e.g. magnitude and time).</p>
<p><strong>fit:</strong> returns the calculated feature. The output can only take one value; features like the autocorrelation function must consequently be summarized in one single scalar.</p>
<p>The following code is an example of a class in <em>FeatureFunciontLib.py</em> that calculates the slope of a linear fit to the light-curve:</p>
<p>class LinearTrend(Base):</p>
<pre><code>def __init__(self):
self.Data=['magnitude','time']
def fit(self,data):
magnitude = data[0]
time = data[1]
regression_slope = stats.linregress(time, magnitude)[0]
return regression_slope
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<p>If the user wants to contribute with feature(s) to the library, it (they) must be added to <em>FeatureFunctionLib.py</em> following the explained format. There is no need to modify <em>Feature.py</em>. The user should also add a validity test to the unit test file (see explanation <a href="#UnitTest">further down</a>).</p>
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<h3 id="Choosing-the-features">Choosing the features<a class="anchor-link" href="#Choosing-the-features">¶</a></h3>
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<p>The library allows the user to either choose the specific features of interest to be calculated or to calculate them all simultaneously. Nevertheless, as already mentioned, the features are divided depending on the input data needed for their computation (magnitude, time, error, second data, etc.), this will be used as an automatic selection parameter. For example, if the user wants to calculate all the available features but he/she only has the vectors <em>magnitude</em> and <em>time</em>, solely the features that need <em>magnitude</em>, <em>time</em> or <em>magnitude</em> and <em>time</em> as an input will be computed.</p>
<p><strong>Note:</strong> some features depend on other features and consequently must be computed together. For instance, <em>Period_fit</em> returns the false alarm probability of the estimated period. It is necessary then to calculate also the period <em>PeriodLS</em>.</p>
<p>The list of all the possible features with their corresponding input data, additional parameters and literature source is presented in the following table:</p>
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<p>Some examples of how to choose the features from the library to be calculated are presented next:</p>
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<h4 id="--List-of-features-as-an-input:">- List of features as an input:<a class="anchor-link" href="#--List-of-features-as-an-input:">¶</a></h4>
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<p>The user should add <em>featureList = </em> and next provide the features to be calculated as a list (between square brackets). In the following case we aim to calculate the Standard deviation and Stetson L of the data:</p>
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<h4 id="--Available-data-as-an-input:">- Available data as an input:<a class="anchor-link" href="#--Available-data-as-an-input:">¶</a></h4>
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<p>In case the user does not have the seven input vectors mentioned <a href="#Vectors">above</a>, it is necessary to specify the available data by adding <em>Data =</em> followed by the list of vectors between brackets. In the example below we calculate all the features that can be computed with the <em>magnitude</em> and <em>time</em> as an input.</p>
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<pre>Warning: the feature Beyond1Std could not be calculated because ['magnitude', 'error'] are needed.
Warning: the feature CAR_mean could not be calculated because ['magnitude', 'time', 'error'] are needed.
Warning: the feature CAR_sigma could not be calculated because ['magnitude', 'time', 'error'] are needed.
Warning: the feature CAR_tau could not be calculated because ['magnitude', 'time', 'error'] are needed.
Warning: the feature Color could not be calculated because ['magnitude', 'time', 'magnitude2'] are needed.
Warning: the feature Eta_color could not be calculated because ['magnitude', 'time', 'magnitude2'] are needed.
Warning: the feature Q31_color could not be calculated because ['magnitude', 'time', 'magnitude2'] are needed.
Warning: the feature StetsonJ could not be calculated because ['magnitude', 'time', 'error', 'magnitude2', 'error2'] are needed.
Warning: the feature StetsonK could not be calculated because ['magnitude', 'error'] are needed.
Warning: the feature StetsonK_AC could not be calculated because ['magnitude', 'time', 'error'] are needed.
Warning: the feature StetsonL could not be calculated because ['magnitude', 'time', 'error', 'magnitude2', 'error2'] are needed.
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<h4 id="--List-of-features-and-available-data-as-an-input:">- List of features and available data as an input:<a class="anchor-link" href="#--List-of-features-and-available-data-as-an-input:">¶</a></h4>
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<p>It is also an option to provide the available time series input vectors and calculate with this data all the possible features from a feature list:</p>
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<pre>Warning: the feature CAR_sigma could not be calculated because ['magnitude', 'time', 'error'] are needed.
Warning: the feature Color could not be calculated because ['magnitude', 'time', 'magnitude2'] are needed.
Warning: the feature SlottedA_length could not be calculated because ['magnitude', 'time'] are needed.
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<h4 id="--Excluding-list-as-an-input">- Excluding list as an input<a class="anchor-link" href="#--Excluding-list-as-an-input">¶</a></h4>
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<p>The user can also create a list of features to be excluded from the calculation. To do so, <em>excludeList=</em> must be added followed by the list between brackets. This would imply that every possible feature will be calculated except those in the excluding list.</p>
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<pre>Warning: the feature Beyond1Std could not be calculated because ['magnitude', 'error'] are needed.
Warning: the feature CAR_mean could not be calculated because ['magnitude', 'time', 'error'] are needed.
Warning: the feature CAR_sigma could not be calculated because ['magnitude', 'time', 'error'] are needed.
Warning: the feature CAR_tau could not be calculated because ['magnitude', 'time', 'error'] are needed.
Warning: the feature Color could not be calculated because ['magnitude', 'time', 'magnitude2'] are needed.
Warning: the feature Eta_color could not be calculated because ['magnitude', 'time', 'magnitude2'] are needed.
Warning: the feature Q31_color could not be calculated because ['magnitude', 'time', 'magnitude2'] are needed.
Warning: the feature StetsonJ could not be calculated because ['magnitude', 'time', 'error', 'magnitude2', 'error2'] are needed.
Warning: the feature StetsonK could not be calculated because ['magnitude', 'error'] are needed.
Warning: the feature StetsonL could not be calculated because ['magnitude', 'time', 'error', 'magnitude2', 'error2'] are needed.
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<h4 id="--All-the-features:">- All the features:<a class="anchor-link" href="#--All-the-features:">¶</a></h4>
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<p>To calculate all the existent features in the library, the user should add <em>Data='all'</em> followed by <em>featureList = None</em> as shown in the next example. Obviously, in order to do this, the user must have provided all the needed time series input vectors.</p>
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<h3 id="Library-output">Library output<a class="anchor-link" href="#Library-output">¶</a></h3>
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<p>When calculating the features of a light-curve, the output can be returned in three different formats:</p>
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<li>"dict": returns a vector with the name of each feature followed by its value.</li>
<li>"array": returns a vector with only the features values.</li>
<li>"features" : returns a vector with the list of the calculated features.</li>
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<p>The following example shows how to implement the first option:</p>
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