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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

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## Potpourri

Vishnu V. Zutshi

for the

Cluster Separability

AHCal Meeting,DESY,Oct03

### 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 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

AHCal Meeting,DESY,Oct03

### ‘Separability’ vs. Distance

AHCal Meeting,DESY,Oct03

### 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. Distance

AHCal Meeting,DESY,Oct03

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

AHCal Meeting,DESY,Oct03

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

3x3/1x1

5x5/3x3

AHCal Meeting,DESY,Oct03

### ‘Resolution’

3x3

1x1

5x5

AHCal Meeting,DESY,Oct03

### Test-beam Geometry

HCal

Implemented in G4

Tail-catcher

ECal

AHCal Meeting,DESY,Oct03

### 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

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

AHCal Meeting,DESY,Oct03

### Charged Pion Event

AHCal Meeting,DESY,Oct03

### Tail-catcher

AHCal Meeting,DESY,Oct03

### Extruder Line

AHCal Meeting,DESY,Oct03

### Extruded Strip w/ 10 holes

AHCal Meeting,DESY,Oct03

### 10-hole Die

AHCal Meeting,DESY,Oct03

### 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