Searching in Light Curves Bc. Martin Vo Masaryk University - - PowerPoint PPT Presentation

Data gathering Abbe value SAX HV space Results End

Searching in Light Curves

• Bc. Martin Vo

Masaryk University Department of Theoretical Physics and Astrophysics Czech Republic Supported by grant LD-15113 of Czech Ministry of Education, Youth and Sports

COST BIG SKY EARTH WG meeting Bucharest, 3 July

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End

Table of contents

1

Data gathering

2

Abbe value Distribution of Abbe values in sample

3

SAX Transformation Measuring distances

4

HV space Histograms and variograms HV coordinates Optimal parameters Borderline

5

Results Method precision Searching in OGLE II

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End

Data gathering

Sample for training and testing methods Quasars Non-variable stars Be stars RR Lyrae Cepheids Long periodic variable stars Stars with double period Source OGLE II OGLE III MACHO db

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Distribution of Abbe values in sample

Abbe value

Abbe value tells whether a trend is present Variable curves have Abbe value near to 0 and non-variable near to 1 A = square difference of two succesive measurements variance A(x) = n 2(n − 1) n−1

i=1 (xi+1 − xi)2

n

i=1(xi − ¯

x)2

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Distribution of Abbe values in sample

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Distribution of Abbe values in sample

For prefiltering curves without trend was set Abbe value treshold as 0.5

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Distribution of Abbe values in sample

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Transformation Measuring distances

Symbolic Aggregate approXimation

Curve (i.e. time series) → word

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Transformation Measuring distances

Transformation

Piecewise Aggregate Approximation of time series Transformation from n dimensions to w dimensions

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Transformation Measuring distances

Transformation

Piecewise Aggregate Approximation of time series Transformation from n dimensions to w dimensions ¯ ci = w n

n w j

• j= n

w (i−1)+1

cj

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Transformation Measuring distances

Transformation

Piecewise Aggregate Approximation of time series Transformation from n dimensions to w dimensions ¯ ci = w n

n w j

• j= n

w (i−1)+1

cj Transformation into the symbolic representation

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Transformation Measuring distances

Measuring distances

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Transformation Measuring distances

Distances of the letters

Dsax( ˆ Q, ˆ C) ≡ n w ·

• w
• i=1

(dist (ˆ qi, ˆ ci))2 Distance function as lookup table

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Histograms and variograms HV coordinates Optimal parameters Borderline

Histograms and variograms

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Histograms and variograms HV coordinates Optimal parameters Borderline

Coordinates in HV space

Finding coordinates in HV space of the inspected object

1 Create template sample of searched objects 2 Transform light curves into histogram and variogram words 3 Compare inspected light curve with the template 4 Find shortest distances in histogram and variogram axis 5 Designate these distances as the coordinates in our space

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Histograms and variograms HV coordinates Optimal parameters Borderline

Optimal parameters

Which size of the alphabet would be the most optimal?

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Histograms and variograms HV coordinates Optimal parameters Borderline

Optimal parameters

Which size of the alphabet would be the most optimal? Which length (or letter/day ratio) of the word would be the best?

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Histograms and variograms HV coordinates Optimal parameters Borderline

Optimal parameters

Which size of the alphabet would be the most optimal? Which length (or letter/day ratio) of the word would be the best? Would these values be the same for histogram word and variogram word?

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Histograms and variograms HV coordinates Optimal parameters Borderline

Optimal parameters

GridSearch Searching thru all possible combinations of parameters length of alphabet number of days per letter histogram 7 97.5 variogram 17 9

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Histograms and variograms HV coordinates Optimal parameters Borderline

Borderline in HV space

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Histograms and variograms HV coordinates Optimal parameters Borderline

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Method precision Searching in OGLE II

Method precision

Confusion matrix Predicted [%] QSO Another QSO 77 23 Another 10 90 F1 score is 0.75

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End Method precision Searching in OGLE II

Searching in OGLE II

Border probability level was increased (TP = 0.37 and TN = 0.98) Almost 4 million objects (in LMC, SMC and BUL) were inspected There are almost 8 thousand qso candidates

• Bc. Martin Vo

Searching in Light Curves

Data gathering Abbe value SAX HV space Results End

Thank you for your attention

• Bc. Martin Vo

Searching in Light Curves