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SOFT COMPUTING & COMPUTATIONAL INTELLIGENCE • • • • • • • Biologically inspired computing models Compatible with human expertise/reasoning Intensive numerical computations Data and goal driven Model-free learning Fault tolerant Real world/novel applications RENSSELAER SOFT COMPUTING & COMPUTATIONAL INTELLIGENCE • • • • • • Artificial Neural Networks (ANN) Fuzzy Logic Genetic Algorithms (GAs) Fractals/Chaos Artificial life Wavelets ANNs • Data mining FL GAs RENSSELAER Biological neuron hair cell dendrites (sensory transducer) signal flow synapse axon hillock cell body axon synapse RENSSELAER Artificial neuron i1 w1 inputs i2 w2 i3 o w3 weighted sum of the inputs output 1 nonlinear transfer function w1 i1+w2 i2 +w3 i3 o sigmoid 0 w1 i1+w2 i2 +w3 i3 RENSSELAER Neural net yields weights to map inputs to outputs Molecular weight w11 Neural Network h w11 H-bonding Hydrofobicity Electrostatic interactions w34 Molecular Descriptor Boiling Point Biological response h w23 Observable Projection There are many algorithms that can determine the weights for ANNs RENSSELAER Neural networks in a nutshell • A problem can be formulated and represented as a mapping problem from m n • Such a map can be realized by an ANN, which is a framework of basic building blocks of McCulloch-Pitts neurons • The neural net can be trained to conform with the map based on samples of the map and will reasonably generalize to new cases it has not encountered before RENSSELAER Neural network as a map m n 0000000 0000001 0000010 0000011 ... 1111111 map from R7to R1 1 0 R7 R1 64 Figure 1.1 The seven-bit parity problem posed as a mapping problem. R1 Map from R4096 to R1 64 R1 R2 R2 Figure 1.2 Determining the radius of a 64x64 B&W image of a circle, posed as a formal mapping problem. RENSSELAER McCulloch-Pitts Neuron x1 sum w1 w2 f() w3 x3 wN xN w x i 1 N y i i y f sum 1 f sum 1 e sum RENSSELAER Neural network as collection of M-P neurons x1 x2 w 111 w 112 w 113 1 f() w 211 f() f() 11 f() w 22 w 123 Output w 3 neuron f() w 321 f() w 232 First hidden layer Second hidden layer E y o 2 noutputs j 1 j tj wjin 1 wjin w ji dE w ji dw ji RENSSELAER Kohonen SOM for text retrieval on WWW newsgroups WEBSOM node u21 Click arrows to move to neighboring nodes on the map. Instructions Re: Fuzzy Neural Net References Needed Derek Long , 27 Oct 1995, Lines: 24. Distributed Neural Processing Jon Mark Twomey, 28 Oct 1995, Lines: 12. Distributed Neural Processing Jon Mark Twomey, 28 Oct 1995, Lines: 12. Re: neural-fuzzy TiedNBound, 11 Dec 1995, Lines: 10. New neural net C library available Simon Levy, 2 Feb 1996, Lines: 15. Re: New neural net C library available Michael Glover, Sun, 04 Feb 1996, Lines: 25. From Guido De Boeck SOM’s for Data Mining To be published (Springer Verlag)