The Self-Organizing Map (SOM) algorithm has attracted an ever increasing amount of interest among researches and practitioners in a wide variety of elds The SOM and a variant of it, the LVQ, have been analyzed extensively, a number of variants of them have been developed and, perhaps most notably, they have been applied extensively within elds ranging from engineering sciences to medicine, biology, and economics We have collected a comprehensive list of 3343 scienti c papers that use the algorithms, have bene ted from them, or contain analyses of them The list is intended to serve as a source for literature surveys We have provided both a thematic and a keyword index to help nding articles of interest

Bibliography of Self-Organizing Map (SOM) Papers: 1981-1997

We present a modification of Kohonens SOFMin order to simulate cortical plasticity induced by coactivation patterns. This is accomplished by introducing a probabilistic mode of stimulus presentation and by substituting the winner-takes- all mechanism by selecting the winner from a set of best matching neurons.

Modification of Kohonen's SOFM to Simulate Cortical Plasticity Induced by Coactivation Input Patterns

A system that optically performs complex transforms, such as Fourier transforms. The system includes a pixel addressable spatial modulator that, in parallel, adjusts the phase of the light of each pixel. The modulator can be a reflective or transmissive type device. A transform lens, such as a Fourier lens, performs a two dimensional transform of the pixels outputs. This operation is repeated for the characteristic function (real and imaginary) of the function. The transformed outputs of the characteristic functions are sampled by a light detector and processed by a computer using simple fast operations, such as addition, into the final transform.

Two dimensional transform generator

We designed and built a high-capacity neural network based on volume holographic interconnections in a photorefractive crystal. We used this system to implement a Kohonen topological map. We describe and justify our optical setup and present some experimental results of self-organization in the learning database.

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High-capacity photorefractive neural network implementing a kohonen topological map.

We have constructed an optical neural-network system with learning
capability by using a Pockels readout optical modulator. The system
has a two-dimensional structure that permits easy optical alignment and
can handle images without scanning. Learning signals are calculated
optically with two liquid-crystal devices by a matrix–matrix
outer-product method. The calculated learning signals are added
directly to the weights memorized on the Pockels readout optical
modulator. A two-layer network is implemented, and the learning and
recognition of four alphabetical characters are realized according to
the delta rule.

Optical learning neural network with a Pockels readout optical modulator

Optically addressed ferroelectric liquid-crystal devices present certain characteristics that make them attractive for all-optical implementations of neural architectures. This is particularly true for the implementation of analog self-organizing systems such as Kohonen's self-organizing map. The optical architecture proposed here is based on the principle of a resonator memory. The main novelty lies in the two-dimensional, continuous, binary information encoding and organization. Basic operations such as neural decision, weight updating, and information spatial ordering are investigated. The principle of a learning procedure close to the Hebbian rule is discussed.

All-optical implementation of a self-organizing map: a preliminary approach.

We present an optical implementation of an improved version of the Kohonen map neural network applied to the recognition of handwritten digits taken from a postal code database. Improvements result from the introduction of supervision during the learning stage, a technique that also simplifies the map layer labeling. The experimental implementation is based on a frequency-multiplexed raster computer-generated hologram used to realize the required N(4) interconnection. The setup is shown to be equivalent to a 64-channel correlator. Computer simulations are used to study various detection and classification procedures. The results of the optical experiments, obtained with binary phase computer-generated holograms, are presented and shown to be in excellent agreement with the simulations.

64-channel correlator implementing a Kohonen-like neural network for handwritten-digit recognition

We present some experimental results obtained with an all-optical implementation of a self-organizing map. The system is based on two ferroelectric liquid-crystal, bistable optically addressed spatial light modulators (BOASLM's) used as parallel read/write optical memories and as thresholding devices. Modifications made to adapt the basic algorithm to the BOASLM's are studied in computer simulations that predict training-class loss due to the simplified decision stage as the principal drawback. Experimental results show good system behavior in recognition mode, demonstrating generalization properties and confirming the choice of a BOASLM memory. All-optical learning is shown in simple cases, and the elementary BOASLM decision function is confirmed as the major limiting factor. The ultimate possible system performance is discussed, and ways of overcoming present limits are suggested.

All-optical implementation of a self-organizing map: Learning and taxonomy capability assessment.

Two methods of reducing the dynamic range of the transmittance of computer-generated interconnection holograms are presented and compared. The holograms are used in an optical implementation of an associative memory to connect the input and the output planes but are representative of more generalN(4) interconnection holograms. Because the holograms play a double correlation-reconstruction role, the standard spectrum-smoothing techniques (e.g., random phase) cannot be applied. We show, in computer simulations and optical experiments, that by using deterministic phase functions that can be realized in the optical system (defocusing the hologram or controlling the phases of the diffraction spots of a Dammann grating used in the system input) the hologram dynamic range can be lowered, reducing the errors during the hologram binarization and increasing the hologram's diffraction efficiency.

K. Heggarty

Papers

All-optical implementation of a self-organizing map: a preliminary approach.

64-channel correlator implementing a Kohonen-like neural network for handwritten-digit recognition

All-optical implementation of a self-organizing map: Learning and taxonomy capability assessment.

Two methods of reducing the dynamic range of a holographic filter.