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A segmented principal component analysis applied to calorimetry information at ATLAS

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Title: A segmented principal component analysis applied to calorimetry information at ATLAS


1
A segmented principal component analysisapplied
to calorimetry information at ATLAS
Federal University of Rio de Janeiro -
UFRJ Brazilian Center for Physics Research - CBPF
H. P. Lima Jr, J. M. de Seixas
  • ACAT 2005 - May 22-27, Zeuthen, Germany

2
Outline
  • Scenario
  • Signal processing
  • Data assembling
  • Data compaction (segmented principal component
    analysis)
  • Particle discrimination (neural network)
  • Conclusions

3
Scenario
  • The ATLAS trigger system comprises three
    distinct levels of event selection LVL1, LVL2
    and Event Filter.
  • From an initial bunch crossing rate of 40 MHz,
    the trigger system will select events up to 100
    Hz for permanent storage.
  • LVL1 operates at 40 MHz with reduced granularity
    information in order to take a fast decision. It
    also defines Regions of Interest (RoI) that will
    guide the LVL2 selection process.
  • At LVL2 complex algorithms operate over full
    granularity information, with a maximum latency
    of 10 ms.
  • The three levels of selection use information
    provided by the calorimeter system due to its
    fast response and the detailed energy deposition
    profiles it provides.

The ATLAS trigger system.
4
Calorimeter system
  • The ALTAS calorimeter is very segmented and
    presents high granularity.
  • The proposed system should address 11
    subdetectors layers of the electromagnetic and
    hadronic calorimeters
  • Pre-sampler, barrel
  • EM Calo, barrel, front layer
  • EM Calo, barrel, middle layer
  • EM Calo, barrel, back layer
  • Pre-sampler, endcap
  • EM Calo, endcap, front layer
  • EM Calo, endcap, middle layer
  • EM Calo, endcap, back layer
  • Hadronic Calo, barrel, layer 0
  • Hadronic Calo, barrel, layer 1
  • Hadronic Calo, barrel, layer 3

Cross section of the EM Calorimeter.
5
Signal processing
  • The proposed signal processing approach will
    operate at Level 2, on calorimeter data, in order
    to
  • Reduce the high computational load due to the
    high granularity of the information
  • Speed up the selection process
  • Achieve higher particle identification
    efficiency (main focus on electrons/jets
    channel).
  • Proposed techniques
  • Segmented principal component analysis ? in
    order to explore the highly segmented calorimeter
    system, data representation is made at the layer
    level instead of global random process
    representation.
  • Neural networks for particle identification ?
    projected data will be concatenated and fed into
    a feedforward neural network for electron/jet
    discrimination.

6
Data assembling
  • Simulated LVL2 data produced in the Athena
    environment were used. They correspond to jets
    and two signatures of the Higgs boson in the
    following decays H?2e-2µ and H?4e-.
  • Two types of data assembling were tested direct
    and ring.
  • Direct assembling ? each data vector is
    organized group cells in the way they appear in
    the RoI layer.
  • Ring assembling ? for each calorimeter layer,
    the cell with the highest deposited energy is
    identified, and the data vector is formed by
    sequentially grouping rings of cells around this
    marked cell.
  • This type of assembling puts in evidence the
    energy deposition pattern of the incident
    particle, which is an important feature that
    makes further classification easier to achieve.

1
25
2
2
Principal component extraction
1
24
25
5 x 5 RoI
data vector
(cell 1 has the highest deposited energy)
7
Data compaction
  • Due to the high complexity of the calorimeter
    system, raw random vectors have up to 3115
    components (calorimeter cells).
  • The following table illustrates the level of
    compaction achieved for each subdetector layer,
    for different levels of random process energy
    preservation.

Subdetector Layer Original Dimension Fraction of energy Fraction of energy Fraction of energy Fraction of energy Fraction of energy Fraction of energy Fraction of energy Fraction of energy Fraction of energy Fraction of energy
Subdetector Layer Original Dimension 82 82 85 85 90 90 95 95 98 98
Subdetector Layer Original Dimension ring direct ring direct ring direct ring direct ring direct
Pre-sampler - barrel 105 1 18 2 20 3 24 5 31 16 42
EM Calo barrel front layer 800 5 166 6 187 11 233 35 309 109 390
EM Calo barrel middle layer 400 3 64 3 74 4 95 7 131 29 173
EM Calo barrel back layer 200 1 32 2 38 3 52 6 77 27 108
Pre-sampler - endcap 60 1 13 1 14 3 19 5 27 12 36
EM Calo endcap front layer 720 3 175 4 194 6 232 15 290 45 350
EM Calo endcap middle layer 400 2 36 3 42 4 53 6 75 16 106
EM Calo endcap back layer 200 2 15 3 18 5 26 11 42 37 70
Hadronic Calo barrel layer 0 100 8 35 12 40 23 50 41 63 60 76
Hadronic Calo barrel layer 1 90 15 37 21 41 32 48 45 59 66 72
Hadronic Calo barrel layer 2 40 15 19 16 21 19 25 25 30 31 36
TOTAL 3115 56 610 73 689 113 857 201 1134 448 1459
8
Data compaction
  • The following figures illustrate how much we
    gain with ring data assembling.

It is point out ring data assembling allows
higher levels of compaction, as expected, since
data vectors are organized according to the
energy deposition pattern. For ring data
assembling 11 components preserve 90 of the
energy.
9
Particle identification
  • Particle identification is performed by a simple
    three layer feedforward neural network. All
    neurons have hyperbolic tangent as activation
    function.
  • The input layer receives the calorimeter data
    projections, concatenated as a single input
    vector.

10
Particle identification
  • Network training was realized with the Resilient
    Backpropagation (RPROP) algorithm.
  • This training algorithm eliminates the harmful
    effects of the magnitudes of the partial
    derivatives. Only the sign of the derivative is
    used to determine the direction of the weight
    update.
  • First runs of training were realized by
    splitting randomly the complete data set
    available (24068 electrons and 2066 jets) into
    two data sets with the same size training and
    testing.
  • A training step comprised a random selection of
    a electron/jet pair in order to avoid
    overtraining on electrons due to the different
    statistics.
  • Preliminary results 90 efficiency.

11
Conclusions
  • The segmented PCA is a very attractive signal
    processing approach to the calorimeter
    information at ATLAS. The reasons are the high
    segmentation of the subdetectors and their high
    granularity.
  • Ring data assembling, following the energy
    deposition pattern, achieved considerably higher
    levels of compaction than the simple organized
    group cells of each RoI. Results demonstrate that
    a compaction level of more than 96 is achieved
    if 90 of the energy is preserved.
  • Another possible approach under study is the use
    of ring sums for data assembling, also making the
    energy deposition pattern clear.
  • The relevance of the principal components will
    be also investigated in order to verify the
    importance of each component to the neural
    classifier.
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