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Mining the FIRST Astronomical Survey Imola K. Fodor and Chandrika Kamath Center for Applied Scientific Computing Lawrence Livermore National Laboratory IPAM Workshop January, 2002 Faint Images of the Radio Sky at TwentyCentimeters (FIRST) On-going sky survey, started in 1993 2 When completed, will cover more than 10,000 deg to a flux density limit of 1.0 mJy (milli-Jansky) Current coverage is about 8,000 deg 2 – more than 32,000 two-million pixel images There are about 90 radio sources/deg2 Data available at http://sundog.stsci.edu NRAO Very Large Array (VLA) CASC Sapphire/IKF 2 One goal of FIRST is to identify radio galaxies with a bent-double morphology A bent-double galaxy is … Problem: there is no definition of “bent-double” Rough characteristic: there is a radio emitting “core”, along with a number of (not necessarily two!) sidecomponents that are “bent” around the core Astronomers search manually for bent-doubles Bent-doubles Non bent-doubles CASC Sapphire/IKF 3 Sapphire: use data mining to enhance the visual search for bent-doubles Use galaxies classified by astronomers to model the binary response variable Y Y {bent, non bent} Find features X and model f(X) with desired accuracy ?X & ? f : f ( X ) Yˆ Y Aim: 10% misclassification error, as manual classification is not more accurate FIRST images Pre-processing Denoising Feature extraction Dimension reduction CASC “Good” features Pattern recognition Bent/nonbent coordinates Classification Sapphire/IKF 4 The FIRST catalog is based on fitting 2D elliptical Gaussians to denoised images Image Map 1150 pixels Catalog 720K entries 1550 pixels 32K image maps, 7.1MB each Catalog entry (CE) Radio source (RS) CASC 64 pixels RA DEC Peak Flux Major Axis Minor Axis Position Angle (mJy/bm) (arcsec) (arcsec) (degrees) 00 56 25 -01 15 43 25.38 7.39 2.23 37.9 00 56 26 -01 15 57 5.50 18.30 14.29 94.2 00 56 24 -01 16 31 6.44 19.34 10.19 39.8 Sapphire/IKF 5 A first pre-processing step is to identify potential features to discriminate bents For the FIRST data, we extracted various features based on – radio intensities, angles, distances, … For galaxies with 3 entries – a total of 103 features – three sets of single features, three pairs of double features, and the triple features – possible redundancies Reduce dimension using – domain knowledge – EDA – PCA – GLM step-wise model selection CASC Sapphire/IKF 6 Triple features for three catalog entries P M A N c B b a C CASC Sapphire/IKF 7 Using exploratory data analysis (EDA), we reduced the number of features to 25 Use EDA techniques such as – box-plots – multivariate plots – parallel-coordinate plots – correlation matrix to – explore the data – find unusual observations – eliminate correlations among the features Call these EDA features CASC Sapphire/IKF 8 Example parallel coordinate plot: nine variables split by bentness category x 3/2 sky regions for bent/non-bent x x x x X : unusual large negative correlation CASC Bent Non-bent Sapphire/IKF 9 Principal component analysis (PCA) finds linear combinations of variables Suppose we have p features X ( X , ..., X )' , E[X] 0, E[XX' ] Ψ, and we want a linear combination U with max. variance U a' X, a , a' a 1. By the spectral decomposition theorem, Ψ V Λ V', V ( V , ..., V ), orthogonal, Λ diag ( ,..., ), the first PC, U V X, has maximal variance, and var(U ) var( V1' X ) ... var(U p ) var(Vp' X ) p . The total variance is preserved, 1 p p pxp 1 p 1 p ' 1 1 1 1 var( X ) var(U ). 2 total p i 1 p i i 1 i Dimension reduction: use first k PCs as new “features” CASC Sapphire/IKF 10 We used PCA differently to reduce the number of original features to 20 The first 20 PCs explain 90% of the variance PCs are hard to interpret – instead of using 20 PCs, keep 20 of the original variables Multivariate Analysis (Mardia, Kent, Bibby) – consider the last PC, with the smallest variance p ' U p Vp X i1Vi , p X i – find the largest (in abs value) coefficient V j , p , and discard the corresponding original variable X j – repeat the procedure w/ the second-to-last PC, and iterate until only 20 variables remain Call these PCA features CASC Sapphire/IKF 11 We also used step-wise model selection to reduce the number of variables Binary response: Y = {bent, non-bent} Explanatory variables: X i features Logistic regression, step-wise model selection with the AIC as a measure of goodness (minimize -loglikelihood, with a penalty term for large models) Cannot use all 103 features because of correlations We identified the features selected by EDA or PCA – stepwise model selection => GLM 2 features (25) We identified the features selected by EDA and PCA – stepwise model selection => GLM 3 features (10) – stepwise model selection, including second-order interactions => GLM 4 features (9, +5 interactions) CASC Sapphire/IKF 12 Pattern recognition uses the features from pre-processing to classify the data Training data Extract Features Create Classifier Decision Tree GLM Check for Accuracy Extract Features for Unclassified Data Update Training Data Show Results and Obtain Score Apply Classifier to Unclassified Data An iterative and interactive classification process CASC Sapphire/IKF 13 We use decision trees to classify the radio sources into bents and non-bents Use information gain to split T : set of n examples at a node k : number of classes S {TL , TR }: split T into two Li , Ri : number of class i in TL , TR radius > a? color? color? k Entropy(T ) i1 pi log pi , pi ( Li Ri ) / n | TL | | TR | Gain(T , S ) Entropy(T ) Entropy(TL ) Entropy(TR ) |T | |T | CASC 2 Sapphire/IKF 14 Decision tree created with all the features: Tree 1 Leaf node w/ 11 non-bents Leaf node w/ 4 bents Leaf node w/ 145 items, (145-4) bents, and 4 non-bents Resubstitution error, train/test (90%) set: 2.8% Cross-validation error, train/validate (10%) set: 5.3% CASC Sapphire/IKF 15 Decision tree created with the EDA and PCA features: Tree 2 Resubstitution error: 1.7% Cross-validation error: 5.3% CASC Sapphire/IKF 16 Decision tree created with the GLM 3 features: Tree 3 Resubstitution error: 2.8% Cross-validation error: 0% Using fewer, well-selected variables results in smaller and more accurate trees CASC Sapphire/IKF 17 We also used generalized linear models (GLMs) to classify the galaxies Linear models explain response variables in terms of linear combinations of explanatory variables Y Xβ ε, E (ε ) 0, Cov(ε ) Σ yi 0 1 X i ,1 p1 X i , p1 X iβ, E ( yi ) i , i 1,..., n Least-squares estimate β̂ solves βˆ arg min {( y Xβ)' Σ ( y Xβ)} ˆ Xβˆ No restrictions on the range of fitted values Y GLMs allow such restrictions by modeling g (i ) Xiβ, Var( yi ) V (i ), where g() is a monotone increasing link function 1 CASC Sapphire/IKF 18 Logistic regression is a special GLM suitable for modeling binary responses Y={0,1} Logit link and variance functions i g ( i ) log( ) 1 i V ( i ) i (1 i ) Likelihood non-linear in parameters, no closed-form solution: iteratively reweighted least squares to find β̂ Given β̂ , exp{ X iβˆ } ˆ i , yˆ i I{ˆ p} , ˆ i 1 exp{ X iβ} where I{a} is {0,1} according to {a=False, a=True}, and the fraction p is generally taken to be 0.5 CASC Sapphire/IKF 19 GLM created with the GLM 2 features CASC Sapphire/IKF 20 GLM created with the GLM 3 features CASC Sapphire/IKF 21 GLM created with the GLM 4 features CASC Sapphire/IKF 22 Misclassification errors of best models are below the desired 10% in training set Careful selection of variables reduces error Trees are less sensitive to input features than GLMs GLM 4 has lowest misclassification errors Tree 1 Tree 2 Tree 3 Mean 11.1% 9.5% 8.3% SE 0.4% 0.4% 0.4% GLM 2 GLM 3 GLM 4 Mean 18.74% 7.84% 4.00% SE 4.34% 1.14% 0.91% Misclassification errors based on 10 ten-fold cross-validations in the training set CASC Sapphire/IKF 23 Our methods identified the “interesting” part of the FIRST dataset 15,059 three-entry radio sources in the 2000 catalog 2,577 labeled as bent by all six methods Astronomers can start by exploring the smaller set Tree1 Non-bent 5412 Bent 9647 Tree2 Tree3 GLM2 GLM3 GLM4 All 6 4628 5660 5118 11080 4340 637 10431 9399 9941 3979 10719 2577 Classification results for the entire 2000 catalog Visually explore random samples to assess the percentage of false positives and missed bents CASC Sapphire/IKF 24 Example classifications for previously unlabeled galaxies are encouraging The labels commonly assigned by the six methods are correct in the examples below Bent Non-bent CASC Sapphire/IKF 25 Summary Described how data mining can help identify radio galaxies with bent-double morphology Illustrated specific data mining steps – data pre-processing is very crucial In our experience, data mining is semi-automatic – interaction and feedback required at many stages – domain knowledge is essential Multi-disciplinary collaboration is challenging, but rewarding – astronomy - computer science - statistics There is always room for improvement – alternative techniques – your feedback welcome! CASC Sapphire/IKF 26 The Sapphire team: supporting a multidisciplinary endeavor Chandrika Kamath (Project Lead) Erick Cantú-Paz Imola K. Fodor Nu A. Tang www.llnl.gov/casc/sapphire Thanks to the FIRST scientists: Robert Becker, Michael Gregg, David Helfand, Sally LaurentMuehleisen, and Rick White UCRL-JC-145672. This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract W-7405-Eng-48. CASC Sapphire/IKF 27