two density-based clustering algorithms
DESCRIPTION
Two Density-based Clustering Algorithms. L. Xia (ANL) V. Zutshi (NIU). General Comments. Both are calorimeter first approaches clustering track match fragment…. SiD geometry Si-W ECAL, RPC or Scintillator HCAL. ‘Cheating’ involved in some steps. Clustering: Dist-based. V b. - PowerPoint PPT PresentationTRANSCRIPT
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Two Density-based Clustering Algorithms
L. Xia (ANL)
V. Zutshi (NIU)
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General Comments
• Both are calorimeter first approaches
clustering track match fragment….
• SiD geometry
Si-W ECAL, RPC or Scintillator HCAL
‘Cheating’ involvedin some steps
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I
J Rij
Vf
Vb
V1V2
}{
)||/|(|)||/|(|)||/|(| )(2
332
222
11
ij
VRVVRVVRVi
ijijij eeeD
With V3 = Vf (if (Vf•Rij) > 0) or Vb (if (Vb•Rij) > 0)
• Hit density reflects the closeness from one hit i to a group of hits {j}• {j} = {all calorimeter hits} to decide if hit i should be a cluster seed• {j} = {all hits in a cluster} to decide if hit i should be attached to this cluster
• Consider cell density variation by normalizing distance to local cell separation • Density calculation takes care of the detector geometry• Clustering algorithm then treat all calorimeter hits in the same way
Clustering: Dist-based
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• Find a cluster seed: hit with highest density among remaining hits• Attach nearby hits to a seed to form a small cluster• Attach additional hits based on density calculation
– i = hit been considered, {j} = {existing hits in this cluster}– EM hits, Di > 0.01– HAD hits, Di > 0.001– Grow the cluster until no hits can be attached to it
• Find next cluster seed, until run out of hits
Hit been considered
seed
Hits of a cluster
Clustering: Dist-based
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Define the density neighborhood of a cell i
Neighborhood ± (nly,nz,nphi) windowcentered on the cell
For each cell i calculate the ‘density’ Di over its neighborhood
For each i calculate the ‘gradient’ (Dj – Di)/dij
where j is in the clustering neighborhood
Find max [gradient]ij
The magnitude and sign of max[gradient]i
determines what happens to cell i
Cell i
In this presentationsimply occupancy orno. of cells abovethreshold is used
Clustering: Grad-based
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• if max[gradient]ij < 0 i becomes the ‘root’ and starts a branch of its cluster• if max[gradient]ij > 0 j is the parent of i and attaches i to its branch• if max[gradient]ij == 0 attach i to the nearest j
Clustering: Grad-based
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Cell Density in ECALZH Events
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Cell X vs. Cell Y in ECALZH Event
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Cell Y vs Cell X in ECALOnly cells with Dens.<5
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Cell Y vs Cell X in ECAL5 < cellD < 25
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Cell Y vs Cell X in ECALcellD > 25
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clustering efficiency: single particleParticle ECal hit
efficiencyHCal hit
efficiencyOverall hit efficiency
Overall energy efficiency
Photon (1GeV) 89% 43% 89% 91%
Photon (5GeV) 92% 54% 92% 96%
Photon (10GeV) 92% 61% 92% 97%
Photon (100GeV) 95% 82% 95% >99%
Pion (2 GeV) 78% 59% 75% 71%
Pion (5 GeV) 81% 70% 79% 80%
Pion (10GeV) 84% 80% 83% 85%
Pion (20GeV) 85% 87% 88% 91%•Typical electron cluster energy resolution ~ 21%/sqrt(E)•Typical pion cluster energy resolution ~70%/sqrt(E)•All numbers are for one main cluster (no fragments are included)
Dist-based
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Neutralhadrons
Photons
Chargedhadrons
ECAL
Z-pole Events WW EventsGrad-based
Cluster Efficiency in Z-pole events
0.77
0.96
0.76
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Z-pole Events WW Events
Chargedhadrons
Photons
Neutralhadrons
No. of fragments w/ and w/o cut on fragment size
ECAL
Grad-based
2.70.5 2.7 0.8
2.90.5 2.90.9
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No. of fragments w/ and w/o cut on fragment size
Neutralhadrons
Photons
Chargedhadrons
HCAL
Z-pole Events WW EventsGrad-based
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Neutralhadrons
Photons
Chargedhadrons
ECAL
Z-pole Events WW EventsGrad-based
Fragment size
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Neutralhadrons
Photons
Chargedhadrons
HCAL
Z-pole Events WW EventsGrad-based
Fragment size
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cluster purity : Z pole uds events
• Most of the clusters (89.7%) are pure (only one particle contributes)• For the remaining 10.3% clusters
– 55% are almost pure (more than 90% hits are from one particle)– The rest clusters contain merged showers, part of them are ‘trouble makers’
• On average, 1.2 merged shower clusters/Z pole event
Number of contributingparticles in a cluster
Fraction from largest contributorfor clusters with multi-particles
Dist-based
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Neutralhadrons
Photons
Chargedhadrons
ECAL
Z-pole Events WW EventsGrad-based
0.98 0.95
purity
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Neutralhadrons
Photons
Chargedhadrons
HCAL
Z-pole Events WW EventsGrad-based
0.96 0.91
0.96 0.9
purity
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After track-cluster matchingEnergy of matched clusters
Energy of clusters not matched to any track:neutral candidate
From neutralparticles
From neutralparticles
From chargedparticles
From chargedparticles(fragments)
On average ~3% came from neutral
Energy from charged particlesis more than real neutral-- need to work on it!
Dist-based
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Nhit = 1 1 < Nhit <= 5
10 < Nhit <= 15 15 < Nhit <=20
1 < Nhit <= 10
Nhit > 20
Neutral: any ‘big’ cluster not matched to any trackFragment cluster (histogram) vs. real neutral cluster (dots)
Fragment identification – variable2: distance to any neutrals
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Nhit = 1 1 < Nhit <= 5
5 < Nhit <= 35 Nhit > 35
Fragment identification - variable1: distance to any track
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Fragment identification – variable3: ratio of the two distances
Nhit = 1 1 < Nhit <= 5
10 < Nhit <= 15 15 < Nhit <=20
1 < Nhit <= 10
Nhit > 20
Fragment cluster (histogram) vs. real neutral cluster (dots)
Dist-based
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Fragment identification
Use the three variables to identify fragments:
1. 72% of the energy from fragments is removed2. Only lose 12% of real neutral energy
1 : 1.24 1 : 0.40Eff(neu) ~ 88%
Energy of clusters not matched to any track:neutral candidate
From neutralparticles
From chargedparticles(fragments)
After removingidentified fragments
From chargedparticles(fragments)
From neutralparticles
Dist-based
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Grad-based
Fraction of cells attachedTo main cluster which belong to itAttachment is based on angular distance
Z-pole eventsCharged hadrons
Increasing dist
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Grad-based
Fraction of cells attachedTo main cluster which belong to itAttachment is based on angular distance
Z-pole eventsPhotons
Increasing dist
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Grad-based
Fraction of cells attachedTo main cluster which belong to itAttachment is based on angular distance
Z-pole eventsNeutral hadrons
Increasing dist