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Classification PSF Analysis • A New Analysis Tool: Insightful Miner • Classification Trees • From Cuts Classification Trees: Recasting of the GLAST PSF Analysis • Energy Dependencies • Present status of GLAST PSFs Bill Atwood, Nov. 2002 1 GLAST A Data Mining Tool An Miner Analysis Program! Bill Atwood, Nov. 2002 2 GLAST Miner Details What is a Data Miner? A Traditional “CUT” o A graphical user programming environment o An ensemble of Data Manipulation Tools o A Set of Data Modelling Tools INPUT OUTPUT A Properties Browser to set parameters o A “widget” scripting language o An interface to data bases Why use a Data Miner? o Fast and Easy prototyping of Analysis o Encourages “exploration” o Allows a more “Global” View of Analysis Bill Atwood, Nov. 2002 3 GLAST Classification Trees Branch 1 Root Given a “catagorical varible” split the data into two pieces using “best” independent continuous varible Example: VTX.Type = Use “Entropy” to deside which Independent varible to use: k if “vertex” direction is best 2 if “best-track” direction is best Continue process – treating each branch as a new “root.” Terminate according to statistics in last node and/or change in Entropy Branch 2 Entropy = 1 Example: Classification Tree from Miner pik log( pik ) Where k is over catagories and i is the ith Node (There are other criteria) Bill Atwood, Nov. 2002 4 GLAST Classification Trees Why use Classification Trees? 1. Simplicity of method – recursive application of a decision making rule 2. Easily captures non-linear behavior in predictors as well As interactions amoung them 3. Not limited to just 2 catagories There are numerous text on this subject…… In the following analysis Classification Trees will be used to: Bill Atwood, Nov. 2002 Separate out the good “vertex” events Predict how “good” and event really is 5 GLAST GLAST PSF Analysis This portion of the code Reads in the data Culls out bad data Adds new columns for analysis Makes Global Cuts Splits the data into 2 pieces Thin Radiators Thick Radiators ( ACD.DOCA > 350 & Energy > .5*MC.Energy) (TKR.1.z0 > 250) Bill Atwood, Nov. 2002 6 GLAST The VTX Classification Tree Relative amounts of Catagories Relative amount of Data Bill Atwood, Nov. 2002 7 GLAST CPA: To Vertex or not to Vertex? Probability is not continuous – its essentially binned by the finite number of leaves (ending nodes) There is a “gap” at .5 - Use that to determine which solution to use Bill Atwood, Nov. 2002 8 GLAST Do the Vertex Split! Predictor created by Classification Tree Use 2-Track Solution From “Thin” Split Use 1-Track Solution Rename probability column The data are now divided into 2 subsets according to the Probability that the 2-Track (“vertex”) solution is best. No data have been eliminated – Failed Vertexed solutions Are tried again as 1-Track events Bill Atwood, Nov. 2002 9 GLAST Bin the PSF Continuous Variable Catagroical Variable Target Class: Class #1 – MS PSF Limited Bin Bill Atwood, Nov. 2002 10 GLAST 2 Track Classification Tree Bill Atwood, Nov. 2002 11 GLAST 1 Track Classification Tree Bill Atwood, Nov. 2002 12 GLAST Combining Bill Atwood, Nov. 2002 13 Results GLAST Example PSF’s At FoM Max 100 MeV PSF-68 =2.7o 95/68 = 2.65 1000 MeV: PSF-68 = .35o 95/68 = 2.3 10000 MeV : PSF-68 = .1o 95/68 = 2.9 Bill Atwood, Nov. 2002 14 GLAST Before and After Trees Using Classification Trees PSF: 2.1o 95%/68% :2.34 Aeff: 1387 cm2 Bill Atwood, Nov. 2002 15 GLAST Before and After Trees Best results obtained using the “cuts” to achieve a good PSF 3 . 5 5 . 4 0 0 5 2 0 . 4 3 . 0 Aeff 2 . 5 0 0 0 2 5 . 3 0 0 5 1 0 . 3 Aef 2 . 0 PSF68 PSF68 2 . 5 PSF95/68 0 0 0 1 95/68 Ratio 2 . 0 5 . 2 1 . 5 0 0 5 0 . 2 1 . 5 1 . 0 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 5 . 1 0 . 0 0 . 6 1 . 0 2 . 0 4 . 0 3 . 0 e l g n A . x t V 5 . 0 6 . 0 V T X A n g l e Bill Atwood, Nov. 2002 16 GLAST After Trees Using Classification Trees PSF: 2.1o 95%/68% :2.34 Aeff: 1387 cm2 Bill Atwood, Nov. 2002 17 GLAST