08.09.09 G.Ososkov NEC-2009 1

Pattern recognition methods for data Pattern recognition methods for data handling of the CBM experimenthandling of the CBM experiment

Gennady OsoskovLIT JINR, Dubna, Russia

Andrey and Semeon Lebedevs GSI, Darmstadt, Germany and LIT JINR, Dubna, Russia

email: ososkov@jinr.ru

Talk on the NEC-2009, Varna 07-14 September, 2009

08.09.09 G.Ososkov NEC-2009 2

CBM at FAIRCBM at FAIR

Facility for Antiproton and Ion Research• accelerator complex serving several experiments at a time (up to 5) from a broad community• SIS100 and SIS300 synchrotrons• highest beam intensities!(e.g. 2x1013/s 90 GeV protons and 109 Au ions/s at 45 AGeV beam energy)• rare isotope beams• first experiments ~2012, fully operational ~2016

Condenced BarionMatter

GSI, Darmstadt, Germany

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The CBM setupThe CBM setupfor electron identification for muon identification

STS (Silicon Tracking System): track, vertex and momentum reconstructionMVD (MultiVetex Detector): determination of secondary verticesRICH (Ring Imaging CHerenkov): electron identification (two designs)MuCH : (Muon CHambers): muon identificationTRD (Transition Radiation Detector) : global tracking and identification of electronsTOF: (Time Of Flight) : time of flight measurement for hadron identificationECAL (Electromagnetic CALorimeter): measurement of photons and neutral particles

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MuCH and TRDMuCH and TRD challengeschallengescommon for both types of detectors – massive absorbers

Aternating detector-absorber layout for continuos tracking of the muons through the iron absorber

Two MuCH designs to measure: 1. Low mass vector mesons

5 Fe absorbers (125 cm), p> 1.5 GeV/c

2. Charmonium

6 Fe absorbers (225 cm) p> 2.8 GeV/c 2(3) detector stations between the absorbers high hit density (up to 1 hit per cm2 per event), high

event rates (107 events/s), position resolution < 300 μm

TRD

Tracking and electron identification via energy losses 12 identical layers grouped in 3 stations Layer=absorber-radiator and MWPC readout Stations: 5m, 7m, 9m Pad size: 0.03cm-0.05cm across and 0.27cm-3.3cm along the pad

MuCH

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CBM RICH detectorCBM RICH detectorRICH in CBM will serve for electron identification for momenta up to 10 GeV/c –in order to study vector mesons and J/Ψ

Sketch of the STS and the RICH detector, Sketch of the STS and the RICH detector, track extrapolation and track projection track extrapolation and track projection onto the photodetector planeonto the photodetector plane

Two different options of RICH are under discussions: Two different options of RICH are under discussions: LargeLarge length 2.5 m, mirror size 22 m2, 200k channels CompactCompact length 1.5 m, mirror 11.8 m2, 55k channels

mirrorsphotodetectors

Main problems of ring recognition •high ring density (~200 rings per event, many secondary electrons);• many overlapping rings;• distortions and elliptic shapeelliptic shape of the rings;•measurement errors (the dimensions of sensitive pad are 0.6x0.6 cm and mean ring radius is ~6 cm).•ring-track matching (high density of projected tracks)

A fragment of photodetector plane

In average there are 2-3 K-pointsper event forming 200-300 rings

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CBM data peculiaritiesCBM data peculiaritiesThe particular features of the data from the CBM detector data arrives at an extremely high rate: about 800 particles per central event at

reaction rates up to 10 MHz. signal particles are very rare (<J/psi> ~ 10-6, ratio of low-mass vector mesons ~ 10-5) recognized patterns are discrete and have a quite complex structure, due to very

sophisticated designs of used detectors (strip- and straw tube chambers etc) noise counts are numerous and correlated;

Requirements to process such data- the maximum speed of data analysis – no triggers, only on-line!- the satisfactory accuracy and efficiency of methods of estimating

physical parameters interesting for experimentalists

- all software must be coordinated into the CBM framework available for each of collaboration members

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Global tracking algorithmGlobal tracking algorithmcombines local track-following with the next global track joining in eventcombines local track-following with the next global track joining in event

Initial seeds are tracks reconstructed in STS (L1 tracking by a fast cellular automaton)

Tracking is based on Track following Kalman Filter (KF) Validation gate Different hit-to-track association techniques

Two main steps: Tracking Global track selection

STS

MUCHTRD TOF

L1 STS tracking

Global LIT tracking

Hit-to-track merging

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Track following and Kalman FilterTrack following and Kalman Filter

1km km

1km 1kx

km

kxkx

kx

kx

kx

kx

1kkx

1kkx

1kx

0x

Track propagationTrack propagation through absorber

material

We regard a track in space as a dynamic system with the state vector

Its dynamic is with transport matrix . Measurements relate to xk

via projection matrix . Here ek, wk are corresponding errors, independent random values with zero mean

1 1 1k k k kx F x w

1kF k k k km H x e

kH

, , , ,T

x yx x y t t q p

PredictionResiduals 1 1k k

k k k kr m H x

Residuals covar. matrix1 1k k T

k k k k kR V H C H

Filtrationafter adding next hit, Kalman gain matrix Kk, new xk , Rk and Ck are calculated. Total track χ2 is increased by

2 1Tk k kr R r

Validation gate at station k-1:1 T

k k kv r R r d

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Track propagationTrack propagation• Extrapolation. Two models:

– Straight line in case of absence of magnetic field.– Solution of the equation of motion in a magnetic field with the 4th order Runge-Kutta

method, with a parallel integration of the derivatives.

• Material Effects.– Energy loss (ionization: Bethe-Bloch,

bremsstrahlung: Bethe-Heitler, pair production)

– Multiple scattering (Gaussian approximation)

• Navigation.– Based on the ROOT TGeoManager.

The Algorithm:Trajectory is divided into steps. For each step:

Straight line approximation for finding intersections with different materials (geometry navigator)Geometrical extrapolation of the trajectory

Material effects are added at each intersection point

Track propagation components

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KF details:KF details: 1. Different hit-to-track assignments• BranchingBranching

– Branch is created for each hit in the validation gate.

Track recognition efficiency 0.949

• Nearest NeighborNearest Neighbor– The closest by a Euclidean statistical

distance hit from a validation gate is assigned to track.

Track recognition efficiency 0.927

• WeightingWeighting– No track splitting, it collects all the

hits in the validation gate.Track recognition efficiency 0.941

2. Track selection Aim: remove clone and ghost tracksTracks are sorted by their quality, obtained by chi-square and track length

to check for shared hits we loop over sorted tracks by their quality to collect used hits,then if in each new track the number of shared hits is too high, - it is rejected

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Data processing for CBM RICHData processing for CBM RICH

RICH hits (blue), found rings (red), track projections (green).

Data processing stages: Ring recognition and their parameters evaluation Compensating the optical distortions lead to elliptic shapeselliptic shapes of rings

Large RICH Compact RICH

Results of radius restoration for momentum < 25 GeV/c

Matching the rings found to tracks of particles which are of interest for physicists EliminatingEliminating fake ringsfake rings which could lead to wrong physical conclusions Accomplishing the particle identificationparticle identification with the fixed level of the ring recognition efficiency

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Ring recognition algorithmRing recognition algorithm

Global search. Filter: algorithm compares all ring-candidates and chooses only good rings, rejecting clone and fake rings.

Standalone ring finder.

Local search of ring-candidates, based on local selection of hits and Hough Transform.

Two steps:

99%

1%

Time consumption

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Ring recognition algorithm, local search

Preliminary selection of hitsPreliminary selection of hits Histogram of ring centersHistogram of ring centers

Fast HoughFast HoughTransformTransform

Ellipse fitterEllipse fitter

Ring quality Ring quality calculation calculation

Remove hits Remove hits of found ringof found ring (only best (only best matched hits)matched hits)

Ring arrayRing array

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Rejection of fake ring candidates, ring quality calculation

ANN output value for correctly found (solid line) ANN output value for correctly found (solid line) and fake (dashed line) rings and fake (dashed line) rings

Nine ring parameters selected for ring quality calculation:• number of hits in ring; • chi-squared• biggest angle between neighboring hits;• number of hits in a small corridor around the ring; • position of ring on photodetector plane; • major and minor half axes of ellipse; • rotation angle of the ellipse vs. azimuthal angle.

• ANNANN derivesderives ring quality ring quality from from thesethese parameters. parameters. • TThe ANN output he ANN output provides aprovides a ring ring quality quality parameterparameter or probability, or probability, whether ring-candidate was found whether ring-candidate was found correctly or not.correctly or not.

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Ring recognition algorithm, global search

Reject candidate with worse quality if it Reject candidate with worse quality if it

shares more than Nshares more than Nmaxmax hits with a better hits with a better

quality ring candidate.quality ring candidate.

NNmaxmax is set to 30% of the total number is set to 30% of the total number

of hits in ringof hits in ring

RICH ring fitting methodsCircle fittingCircle fitting Ellipse fittingEllipse fitting

• NewtonNewton method for nonlinear method for nonlinear equations with one variable equations with one variable is usedis used• 3-4 iterations3-4 iterations• aalgorithmlgorithm is very robust to the initial is very robust to the initial parametersparameters

• pprogram realizationrogram realization of the of the COPCOP (Chernov-Ososkov-Pratt)(Chernov-Ososkov-Pratt), based on , based on the minimization of the functionalthe minimization of the functional 2 2XP Ax Bxy Cy Dx Ey F

• general, as conic section

• Rings in the photodetector plane have a slight elliptic shape

• usage in ring finding algorithm

• Taubin method is usedTaubin method is used• Minimize P(x) by A,B,C,D,E,F, but Minimize P(x) by A,B,C,D,E,F, but measuring deviations measuring deviations along normals to along normals to the curvethe curve. . • non-linearity is avoided by Tailor non-linearity is avoided by Tailor expansionexpansion• non-iterative very fast direct algorithm• no need of starting parameter values

Mean B/A for Mean B/A for CBM RICH ringsCBM RICH rings = 0.9= 0.9Ref: N. Chernov J Math Im Vi, 27 (2007), 231-239.

Thanks to A.Ayriyan (JINR, Dubna) and N. Chernov (USA)Ref: Comp Ph Com Volume 33, Issue 4, 1984, 329-333

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Ring parameter correctionRing parameter correction

Why?How?

B distribution BEFORE BEFORE correction B distribution AFTERAFTER correction

B correction mapB distribution onto photodetector plane

Example for minor half axis of ellipse (B)

Resolution 3.3%

Resolution 1.7%

cm cm

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Ring finding efficiencyRing finding efficiencyTypical reaction for CBM -> central Au+Au collisions at 25 AGeV beam energy (UrQMD)

Compact RICHCompact RICHLarge RICHLarge RICH

Accepted rings = rings with >= 5 hits

Large Compact

radiator gas and length N2 length 2.5 m CO2 length 1.5 mphotodetector size (No. of channels) 9 m2 (200k) 2.4 m2 (55k)

Efficiency for e+ and e- embedded in central Au+Au collisions at 25 AGeV beam energy

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Why do we need waveletsWhy do we need waveletsfor handling invariant mass spectra?for handling invariant mass spectra?

-we need them when S/B ratio is << 1

1. Smoothing after background subtractionwithout losing any essential information

2. resonance indicating even in presence of background

3. evaluating peak parameters

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Math background

Wavelet transfom is a convolution of invariant mass spectrum f(x) and

a special biparametric wavelet function . Most famous example of wavelet

noisy signal transformed into a surfaceposition

is “Mexican hat”

where ψ(x)= is in fact, the 2d derivative

n=2 of a gaussian

with σ=1, x0=0, A=1

Wavelet-analysis is used, in common, as a mean for smoothing signals and filtering them from noise

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Specifics to keep in mind

1. remarcable robustness to noise and1. remarcable robustness to noise and

corresponding wavelets

2. Gibbs effect on edges2. Gibbs effect on edges

variiation of granulation bin missingvariiation of granulation bin missing

3. Continuos wavelets are 3. Continuos wavelets are non-orthogonalnon-orthogonaland therefore are quite rare used.and therefore are quite rare used.4. Wavelet G4. Wavelet G22 transforms a gaussian transforms a gaussian

g(x;A,xg(x;A,xoo,,σσ) into wavelet ) into wavelet of the sameof the sameorderorder, but with parameters of that gaussian:, but with parameters of that gaussian:

It is true for any order n and leads to the idea and leads to the idea

of looking for the peak parameters directly in Gof looking for the peak parameters directly in G22 domain without its inverting domain without its inverting

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How to estimate peak parameters How to estimate peak parameters in Gin G22 wavelet domain wavelet domain

Let us have a noisy inv. mass spectrumLet us have a noisy inv. mass spectrum

1. transform it by G1. transform it by G2 2 into wavelet domain 2. into wavelet domain 2.

look for the wavelet look for the wavelet surface surface maximum maximum

2

322

2

5 )ˆˆ(

ˆˆ

maxˆ

a

a

WA

bmax ,amax . From the formula for WG2(a,b;x0,σ)g one can derive analyticalexpressions for its maximum x0 and . which should correspond to the found bmax ,amax . Thus we can use coordinates of the maximum as estimations of wanted peak parametersax ˆ,ˆ0From them we can obtain halfwidth ,

amplitude

and even the integral 2AI

peak has bell-shape form

5

ˆˆ

a

5max a

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Real problemsReal problems 1. CBM spectra 1. CBM spectra Low-mass dileptons (muon channel) ω. Gauss fit

of reco signalM=0.7785σ =0.0125A=1.8166Ig=0.0569

ω. WaveletsM=0.7700σ =0.0143A=1.8430Iw=0.0598

- ω– wavelet spectrum

ω.

ω-meson

φ-meson

Even φ- and mesons have been visiblein the wavelet space, so we could extract their parameters.

Thanks to Anna Kiseleva

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2. Wavelet application for resonance structure study

Invariant mass distributions of γγ pairs without (upper panel) and with (bottom panel) the background subtraction.

d

c

thanks to V.Toneevthanks to V.Toneev

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2. Wavelet application for resonance structure study - II

The invariant mass distribution of The invariant mass distribution of γγγγ pairs pairs GGaussian waveletsaussian wavelets of the 8-th order of the 8-th orderfor for dC dC interactionsinteractions. A srip of abscissa . A srip of abscissa

shown in logarithmic scaleshown in logarithmic scale

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Back to CBM tracking and RICH ring Back to CBM tracking and RICH ring recognitionrecognition

Speeding up is the main problem nowSpeeding up is the main problem nowStatus of speeding upStatus of speeding up on the CBM tracking exampleTwo stages:1. Optimizing all tracking algorithms to make them as fast as possible2. Invent parallelization

Optimizing step 1:Optimizing step 1: number of branchesMotivation: The main problem with branching algorithm is that its computational and memory requirements can grow with time and saturate computing system.Solution: Only a limited number of the nearest hits in the validation gate can start a new branch.

Maximum number of hits in the

validation gate30 20 15 10 7 5 4 3 2 1

Tracking efficiency,% 93.1 93.1 93.1 93.1 93.1 93.1 93.1 92.9 92.9 91.8

Time, s/event 1.91 1.63 1.37 1.05 0.8 0.62 0.52 0.44 0.34 0.20

4 times faster!

MUCH tracking, UrQMD 25 AGeV Au-Au + 10 muons CPU: Intel C2D P8400

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Optimizing step 2: Optimizing step 2: fast search of hitsfast search of hits

Motivation

-Hits are sorted by x position-Binary search is used to find Min and Max index

2 2cov posdX k

pos Maximum measurement error on the station

Fast search of hits

Loop over MIN and MAX

indices

Loop over MIN and MAX

indices

2 times increase in speed!

1.05 s/event -> 0.52 s/event(MUCH tracking, UrQMD+10mu)

CPU: Intel C2D P8400

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Optimizing step 3: Optimizing step 3: simple geometrysimple geometry

• Monte Carlo geometry– Very detailed (800k nodes)– Navigation is based on the ROOT TGeo

• Simplified geometry– There is no need for detailed geometry for tracking purposes– Stations and passive materials are approximated as planes perpendicular to beam

pipe• Reduction of number of nodes from 800k to 100

– Navigation in such geometry is much more simple

CPU: Intel C2D P8400

Efficiency [%] / time [sec/event]

ROOT TGeo Simplified Speed up factor

Branching 94.9 / 0.88 94.0 / 0.20 4.4

NN 92.6 / 0.20 92.2 / 0.06 3.3

Weighting 94.0 / 0.31 92.6 / 0.11 2.8

The total optimization The total optimization speed up factor is speed up factor is on the level of 8-10on the level of 8-10

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Parallelism on the level of duo cores CPUParallelism on the level of duo cores CPU

Serial ParallelThe easiest solution by applying the Intel library

Intel Threading Building Blocks

CPU: Intel C2D P8400 with 2 coresserial and parallel nearest neighbor method:

Speed up factor: 1.59

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Summary and outlookSummary and outlook Track and ring recognition methods for the CBM experiment were

discussed, vital need of speeding up all recognition algorithms was stressed

The variation of reconstruction time depends on selected parameters in the track and ring finders trading efficiency vs. speed.

Corresponding algorithms were significantly optimized in terms of calculation speed without loosing any efficiency (gain is ~ 10 times!)

All developed algorithms were tested on large statistics of simulated events, included then into the CBM framework and are intensively used now by CBM collaboration members

Possibilities to elaborate parallel versions of these algorithms look promising, but need a more advanced computing systems

Particle identification methods and wavelet approaches for handling invariant mass spectrum were also implemented in corresponding software, tested and applied for simulated and real data handling

New approaches like Boosted decision Tree and Fuzzy inferences are studied to improve the efficiency of recognition

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Thanks for your attention!Thanks for your attention!

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Back-up slidesBack-up slides

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OutlineOutline

1. Artificial Intelligence (AI) and pattern recognition (PR)

2. The CBM experiment

3. CBM data peculiarities and corresponding PR problems

4. Global tracking for MuCH and TRD

5. RICH ring recognition

6. Particle identification

7. Invariant mass spectrum handling by wavelets

8. Speeding up approaches

9. Summary and outlook

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What is Artificial Intelligence (AI)What is Artificial Intelligence (AI)

Turing's “polite” definition: If a machine acts as intelligently as a human being, then it is as intelligent as a human being.

AIAI is a hierarchical system for information processing and coordinating physical actions according to a prescribed goal.

AI system can input data automatically and has such features of the human intellect as

Information perception and processing for feature extraction and decision making;

Ability for learning and self-learning, for generalizing the learned knowledge and methods of already solved problems;

Ability to present results in a form suitable for human understanding

This AI feature is usually interpreted as This AI feature is usually interpreted as Pattern Pattern RecognitionRecognition

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Pattern RecognitionPattern RecognitionPattern recognition (PR) takes in raw data (patterns)

and classify them on the basis either a priori knowledge or statistical information extracted from the patterns. The patterns to be classified are usually groups of measurements or observations, defining points in an appropriate multidimensional space.

The most known PR methods applied in HEP are: Hought transform Kalman filter Cellular automata Artificial Neural Networks Boosted Decision Trees Fuzzy (soft) approaches Wavelet analysis

tracking, ring recognition

Partical identification

Image enhancement, data compression

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Recognition methods in HEPRecognition methods in HEP• Local track-following is a typical example:

– algorithms starts from selecting of a few initial points, – then predicts the next point position using some of already

found points for extrapolating with a known track model– found points are added to the current track candidate– the candidate is rejected after a certain number of bad attempts

• Global The method is called global when all points enter into an event

recognition algorithm in a similar manner. Such an algorithm may be considered a general handling of the

total set of measured coordinates of an event. The examples of global approach for track chambers are

- template selection - Hough transform (variable slope histogramming) - neural networks

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Solution of the initial value problem: Radon-Hough transform (RHT) from measurement space to parameter space

The Method of Variable Slope HistogramsVariable Slope Histograms is a particular case of the Hough transform for straight lines recognition, which implementation is much faster than the classic RHT. Similar algorithm was developed as well for the circle recognition, but it operates in 3-D space.However, RHT is too time-consuming and needs cardinal speeding up to be used for CBM

Point-to-line correspondence

x=x0+tx zx0=x-tx z

Radon-Hough transformRadon-Hough transform