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Parallel Computing System for ecient computation of Molecular Similarity based on Negative Electrostatic Potential: First results Raul Torres1 1 Grupo de Química Teórica - Universidad Nacional de Colombia

Research Seminar, 2009

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Parallel Computing System for ecient computation of Mo


TARIS Method

Figure: A. Isopotential Surface Size B. Isopotencial value

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Each node saves:



Data set

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Classication

The similarity matrix obtained with the GPU computing process (CUDA) was analyzed by means of hierarchical clustering using the average linkage method(R Statistical Package).

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General Representation of molecules Every node is represented by [] characters When a node has children, each child is established inside the [] of the parent: [ [][] ] If a weight is associated to a non-leaf node, this value is written after the rst [: [45,889[78,76[][]][987,5[][]] The leaf nodes have no weight associated We propose a canonical representation The sub-trees with more nodes are translated rst Next the sub-trees with more levels are listed rst Next the sub-trees with greater weight are listed rst

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Proposed Kernel Simple kernel:

k (x , y ) = A more complex kernel:

∑ nums (x )nums (y )

s ∈B

∑s ∈B nums (x )nums (y )ws k (x , y ) ws is 1 if wy and wx are 0 (wy and wx are the respective weights of x and y trees) ws = wwyx if wx ≤ wy Otherwise, ws = wwyx k w (x , y ) =

B is the set of balanced sub-string [...] Raul Torres



Proposed Kernel

The weights can be calculated in 9 dierent ways The process is reduced to nd the number of balanced sub-strings founded in both molecules;in other words, a sub-tree. The leaf nodes are not counted as sub-trees The whole string is considered a sub-string

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Proposed Kernel

Tree representation: The red and green circles denote sub-trees that appears in both trees. In this case, the simple kernel is 2 Raul Torres



Proposed Kernel

String representation: The gray area is the same green circle in the previous gure. The red square is related to the red circle too.

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Hardware

CPU: AMD Athlon X2 64 Bits RAM: 2 GB GPU: Geforce 8200 M (CUDA Enabled)

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Parallel programming considerations

The general process is executed over the CPU Host Code: C++

The string comparison process is made in parallel Device Code: CUDA for C

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Experimental congurations Variables (to construct the weight): Isopotential surface size: ISS Isosurface value: IV Factorial design (32 experiments), three states (N)Don't use (A)Accumulated: the summation of all the values of each node gives the weight for the sub-tree (S)Simple: the value of the root node of the sub-tree gives the weight for the sub-tree

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Experimental congurations

W0: There are no weights. Only the structure is important. (N)ISS x (N) IV W1: Accumulated isopotential surface size. (A)ISS x (N) IV W2: Accumulated isopotential surface size times Accumulated isosurface value. (A)ISS x (A) IV W3: Simple isopotential surface size. (S)ISS x (N) IV W4: Accumulated isosurface value. (N)ISS x (A) IV

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Experimental congurations

W5: Simple isosurface value. (N)ISS x (S) IV W6: Accumulated isopotential surface size times Simple isosurface value. (A)ISS x (S) IV W7: Simple isopotential surface size times Simple isosurface value. (S)ISS x (S) IV W8: Simple isopotential surface size times Accumulated isosurface value. (S)ISS x (A) IV

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Experiment W3

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Experiment W8

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Experiment W7

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Experiment W2

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Experiment W0

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Execution time

In general, the execution time is approximately 2 seconds.

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Conclusions We don´t need to accumulate the sizes of the children In general terms, the kernel method used achieves a good classication The pre-assumptions that a string kernel can be applied to tree-like structured data was veried The next eorts of this research will be focused in the application of a kernel that uses the co-rooted tree and a more robust representation of strings named sux tree. The use of CUDA as a programming environment has allow us to perform a several concurrent operations in a fast way than in the serial paradigm Without the need of a cluster of computers, GPU Computing oers a tremendous computational power at low cost. Raul Torres


Appendix

For Further Reading

For Further Reading I

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