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

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

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. Electromagnetic Calorimeter Hadronic Calorimeter Data assembling Principal component extraction high dimension Neural classifier low dimension electron / jet decision

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. 5 x 5 RoI 1 2 25 1 2 24 25 data vector Principal component extraction (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 82 %85 %90 %95 %98 % ring di rect ring di rect ring di rect ring di rect ring di rect Pre-sampler - barrel1051182203245311642 EM Calo – barrel – front layer800516661871123335309109390 EM Calo – barrel – middle layer400364374495713129173 EM Calo – barrel – back layer20013223835267727108 Pre-sampler - endcap601131143195271236 EM Calo – endcap – front layer7203175419462321529045350 EM Calo – endcap – middle layer40023634245367516106 EM Calo – endcap – back layer20021531852611423770 Hadronic Calo – barrel – layer 01008351240235041636076 Hadronic Calo – barrel – layer 19015372141324845596672 Hadronic Calo – barrel – layer 240151916211925 303136 TOTAL3115566107368911385720111344481459

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. ring assembling Principal Component Variance (%) EM Calo – barrel – front layer ring assembling original dimension = 800 direct assembling original dimension = 800 Principal Component Variance (%) EM Calo – barrel – front layer

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. Pre-sampler, barrel EM Calo, barrel, front layer Hadronic Calo, barrel, layer 2 Segmented PCA extraction Data projection Information concatenation electron / jet decision

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.