Multivariate Discriminant Analysis applied to classification of ne CC events in MINOS Update

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Multivariate Discriminant Analysisapplied to
classification of ne CC events in MINOS-Update-

• Alex Sousa
• Tufts University
• MINOS Collaboration Meeting _at_ Fermilab
• 09/18/2004

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Changes since Ely

• Using new MDC sample fully reprocessed with R1.9.
• Consolidation of analysis framework
• Developed in C/ROOT, independent of Minossoft
  downstream of ntuple generation.
• Unsynced Reco and Truth trees Handling -
  corrected some bugs and increased algorithm speed
  and robustness.
• Easy reading of analysis variables with cuts and
  easy creation of oscillated samples - sample
  generation problem with handling nt fixed
• New Event Display
• CVS repository of the code available on the Tufts
  MINOS server.

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Analysis Overview
MDC ntuples
Variables ntuple
Variable generation
Sample selection
Cuts
Computation of results
Event Display
MDA output
SAS Input format
Variable selection
MDA classification
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Samples

• Sample contents
• Constructed from 20 nm, 9 ne, and 39 nt MDC
  ntuples processed with release R1.9 in the batch
  farm and in the Tufts server.
• Visible energy and track length cuts optimized
  through use of decision trees (see Maylis talk)
• Mild containment cut eliminates background from
  nm truncated at the end of the detector
• Training Sample

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Samples

• Test Sample

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Variable Selection

• Variable selection is performed using SAS
  Stepwise discriminant procedure
• Original 77 variables sorted by discriminant
  power
• 45 variables selected for running on the training
  sample
• Best results for 18 variables
• uv_rms
• plane_n
• ph_pe
• nstrip
• uv_kurt
• trk_plane_ntrklike
• e_hit_total
• ntrack
• s_hit_trans_ratio
• shw_nstrip_ratio

• trk_pe_ratio shw_ph_nstrip max_pe_plane chisq_ndf
• uv_asym_peak e_hit_long e_hit_trans
  trk_chi2_ndof

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Some Selected Variables
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MDA output (Probability Distributions)
Training Sample
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Threshold Determination

• Calculate the training sample Figure Of Merit for
  several possible thresholds. Apply threshold
  corresponding to highest FOM to test sample
  classification.

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Results (Energy Distributions )
Test Sample (no threshold)
NC
ne
Signal
BG
BG
nm
nt
BG
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Results (Energy Distributions )
Test Sample (T0.88)
NC
ne
nm
nt
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Results (Energy Distributions )
Test Sample (T0.92)
ne
NC
nm
nt
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Results (Efficiencies )
Test Sample ( no osc, no threshold)
NC
ne
nt
nm
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Results (Efficiencies )
Test Sample (osc, no threshold)
NC
ne
nm
nt
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Results (Efficiencies )
Test Sample (T0.88)
NC
ne
nt
nm
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Results (Efficiencies )
Test Sample (T0.92)
NC
ne
nt
nm
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Results (ne appearance signal)
Test Sample (T0.88)
Test Sample (T0.92)
SignalBG
SignalBG
BG
BG
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Results (comparison table)
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Some events
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Some events
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Some events
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Current and Future Work

• Investigate discriminating power of cosq vs f
  distributions.
• Look at other less trivial threshold cuts in the
  probability space. Evaluate method stability in
  multiple randomly generated test samples.
• Fit signal and background histograms to the test
  sample instead of fixing a threshold.
• Apply method to the Near Detector MDC files.

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Fitting (very preliminary)

• Instead of defining probability thresholds, fit
  the complete MDA probability histograms defined
  on the training sample to the ones obtained from
  classification on the test sample.

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Fitting (very preliminary)
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Fitting (very preliminary)
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MDA Procedure

• Define a set of variables that
  appropriately describes the data sample.
• Calculate the covariance matrix for each class
  
• Determine the Mahalanobis distance to each class
  for each event
• Compute the probabilities for an event to belong
  to each class (scores).

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Energy Distributions
Training Sample (no threshold)
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Energy Distributions
Training Sample (T0.88)
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Energy Distributions
Training Sample (T0.92)