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Potpourri. Vishnu V. Zutshi for the NICADD/NIU group. Cluster Separability. Separability. For any two classes or clusters the classification rule can basically be stated as: P(c1|x) > P(c2|x)

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Potpourri

Potpourri

Vishnu V. Zutshi

for the

NICADD/NIU group


Cluster Separability

AHCal Meeting,DESY,Oct03


Separability
Separability

  • For any two classes or clusters the classification rule can basically be stated as:

    P(c1|x) > P(c2|x)

  • The separability of two clusters or classification error probability depends on the difference between P(c1|x) and P(c2|x)

  • Many measures can be constructed to quantify this

AHCal Meeting,DESY,Oct03


For example
For Example…..

For best separability clusters should have small within class

variance and large between class distance.

J = trace{Sw-1 Sm} where Sw = S PiSi

Si is the covariance matrix for cluster ci

Sm is the covariance matrix w.r.t. the global mean

AHCal Meeting,DESY,Oct03


Track parameters
Track Parameters

AHCal Meeting,DESY,Oct03


Separability vs distance
‘Separability’ vs. Distance

AHCal Meeting,DESY,Oct03


Another measure
Another Measure….

  • B = a*(mi-mk)T *({Si+Sk}/2)-1 *(mi-mk) +

    b*ln{(|(Si+Sk)/2|)/sqrt(| Si || Sk |)}

    m = mean and S = covariance

    the first term gives the separation due to mean difference

    the second term due to covariance difference

AHCal Meeting,DESY,Oct03


Separability vs distance1
‘Separability’ vs. Distance

AHCal Meeting,DESY,Oct03


Ratio of measures m x m n x n
Ratio of measures (m x m/n x n)

AHCal Meeting,DESY,Oct03


Ratio of measures m x m n x n1
Ratio of measures (m x m/n x n)

3x3/1x1

5x5/3x3

AHCal Meeting,DESY,Oct03


Resolution
‘Resolution’

3x3

1x1

5x5

AHCal Meeting,DESY,Oct03


Test beam geometry
Test-beam Geometry

HCal

Implemented in G4

Tail-catcher

ECal

AHCal Meeting,DESY,Oct03


G4 setup
G4 Setup

  • GEANT 4.5.2.p01

  • Mokka physics lists

  • For convenience General Particle Source linked in

  • Aggregate hits by cell with track contributions

  • ASCII output format (others can be put in)

AHCal Meeting,DESY,Oct03


Data format
Data Format

EVENT evt_no

ECAL no_hits

layer_no … x y z cell_edep abs_edep ntrak

track_no track_edep

HCAL …

TAILCATCHER

AHCal Meeting,DESY,Oct03


Hcal face side view
HCal Face & Side View

AHCal Meeting,DESY,Oct03


Charged pion event
Charged Pion Event

AHCal Meeting,DESY,Oct03


Tail catcher
Tail-catcher

AHCal Meeting,DESY,Oct03


Extruder line
Extruder Line

AHCal Meeting,DESY,Oct03


Extruded strip w 10 holes
Extruded Strip w/ 10 holes

AHCal Meeting,DESY,Oct03


10 hole die
10-hole Die

AHCal Meeting,DESY,Oct03


Tail catcher next steps
Tail-catcher Next Steps

  • Steel from Fermilab ?

  • Need to have a stable design to go hunting

  • With the simulation now ready this should happen soon

AHCal Meeting,DESY,Oct03


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