Implementation of the Supervised Growing Cell Structure on the CNAPS Neurocomputer

Execution time of the SGCS for one training step on the CNAPS neurocom-puter. The non-linear rise of the graph is due to the folding of the cells in the current implementation of the algorithm: If more than 256 Cells are required, two ore more cells are associated with one PN, which leads to a larger computational effort. Our SGCS implementation runs on a CNAPS neurocomputer with at least 16 up to 256 processing nodes. The following results have been achieved on a machine with 256 PNs at 25 MHz clock cycle. For 64 input nodes, k cells and 8 output nodes the execution time for a training step is approximately (200 + k*0.4) µs (Fig. 5); with 2 input nodes and 2 output nodes this number reduces to (150 + k*0.1) µs. A complete training cycle with 2048 cells and insertion of a new cell each 100 learning steps takes less than 5 minutes. The output vector calculation during the recall phase takes about one third of the training time, which in fact makes SGCS a superior choice for real-time classification tasks. We compared the SGCS implementation on the CNAPS to a C++ implementation running on a PC (80486/33MHz). Our finding was that for a network size of up to 256 cells the CNAPS implementation executes more than 300 times faster. 6 References [1] Fritzke B, "Growing Cell Structures-a self organizing network for unsupervised and supervised learning " , Each cell (PN) gets a 1 Byte cell-ID which comprises the associated PN number. A specific cell is selected by sending the cell-ID in quest to all nodes which make a comparison with their own ID and set their x-flag correspondingly. The neighborhood information is represented in a two-dimensional 1 bit connection matrix. Each cell occupies a row in the matrix, an element C ij indicating the connection of cell i with cell j; C ij =0: not connected , C ij =1: connected. It makes sense to connect each cell with itself in addition: C ii =1. The winner cell selects all its neighbors (4.1.7) by sending its winner-ID to all other PNs. Any receiving cell uses that ID as an index into its own connection matrix row. The selected matrix element C i,Winner-ID is copied to the cell´s x-flag, keeping thus all neighbors active. Each PN holds a variable χ which is set to winner learning factor ε w …