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 Data gathering 1 Abbe value 2 Distribution of Abbe values in sample SAX 3 Transformation Measuring distances HV space 4 Histograms and variograms HV coordinates Optimal parameters Borderline Results 5 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 Distribution of Abbe values in sample HV space Results End 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 � n − 1 i =1 ( x i +1 − x i ) 2 n A ( x ) = � n 2( n − 1) i =1 ( x i − ¯ x ) 2 Bc. Martin Vo Searching in Light Curves

Data gathering Abbe value SAX Distribution of Abbe values in sample HV space Results End Bc. Martin Vo Searching in Light Curves

Data gathering Abbe value SAX Distribution of Abbe values in sample HV space Results End 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 Distribution of Abbe values in sample HV space Results End Bc. Martin Vo Searching in Light Curves

Data gathering Abbe value SAX Transformation HV space Measuring distances Results End Symbolic Aggregate approXimation Curve (i.e. time series) → word Bc. Martin Vo Searching in Light Curves

Data gathering Abbe value SAX Transformation HV space Measuring distances Results End 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 Transformation HV space Measuring distances Results End Transformation Piecewise Aggregate Approximation of time series Transformation from n dimensions to w dimensions n w j c i = w � ¯ c j n j = n w ( i − 1)+1 Bc. Martin Vo Searching in Light Curves

Data gathering Abbe value SAX Transformation HV space Measuring distances Results End Transformation Piecewise Aggregate Approximation of time series Transformation from n dimensions to w dimensions n w j c i = w � ¯ c j n j = n w ( i − 1)+1 Transformation into the symbolic representation Bc. Martin Vo Searching in Light Curves

Data gathering Abbe value SAX Transformation HV space Measuring distances Results End Measuring distances Bc. Martin Vo Searching in Light Curves

Data gathering Abbe value SAX Transformation HV space Measuring distances Results End Distances of the letters � n � w � D sax ( ˆ Q , ˆ � c i )) 2 � C ) ≡ w · ( dist (ˆ q i , ˆ � i =1 Distance function as lookup table Bc. Martin Vo Searching in Light Curves

Data gathering Abbe value Histograms and variograms SAX HV coordinates HV space Optimal parameters Results Borderline End Histograms and variograms Bc. Martin Vo Searching in Light Curves

Data gathering Abbe value Histograms and variograms SAX HV coordinates HV space Optimal parameters Results Borderline End 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 Histograms and variograms SAX HV coordinates HV space Optimal parameters Results Borderline End Optimal parameters Which size of the alphabet would be the most optimal? Bc. Martin Vo Searching in Light Curves

Data gathering Abbe value Histograms and variograms SAX HV coordinates HV space Optimal parameters Results Borderline End 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 Histograms and variograms SAX HV coordinates HV space Optimal parameters Results Borderline End 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 Histograms and variograms SAX HV coordinates HV space Optimal parameters Results Borderline End 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 Histograms and variograms SAX HV coordinates HV space Optimal parameters Results Borderline End Borderline in HV space Bc. Martin Vo Searching in Light Curves

Data gathering Abbe value Histograms and variograms SAX HV coordinates HV space Optimal parameters Results Borderline End Bc. Martin Vo Searching in Light Curves

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