* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download PowerPoint-presentatie
Survey
Document related concepts
Donald O. Hebb wikipedia , lookup
Neurocomputational speech processing wikipedia , lookup
Synaptic gating wikipedia , lookup
Eyeblink conditioning wikipedia , lookup
Neural modeling fields wikipedia , lookup
Feature detection (nervous system) wikipedia , lookup
Perceptual learning wikipedia , lookup
Learning theory (education) wikipedia , lookup
Convolutional neural network wikipedia , lookup
Concept learning wikipedia , lookup
Machine learning wikipedia , lookup
Recurrent neural network wikipedia , lookup
Transcript
Neural Networks Chapter 9 Universiteit Leiden Unsupervised Competitive Learning • • • • • Competitive learning Winner-take-all units Cluster/Categorize input data Compression through vector quantization. Feature mapping Unsupervised Competitive Learning 1 2 1 2 3 3 4 5 Unsupervised Competitive Learning winner output input (n-dimensional) Simple Competitive Learning • Winner: hi wij j wi j wi* wi i • In biological network: Lateral inhibition • In ANN: search for maximum. Simple Competitive Learning • Equivalent if w’s and ’s are normalized to unit length: winner is the unit closest to : | wi* | | wi | i Simple Competitive Learning • Update weights for winning neuron only wi* j ( j wi* j ) • (Standard competitive learning rule.) • Moves w towards . Simple Competitive Learning • Update rule for all neurons: wij Oi ( j wi* j ) Oi* 1 Oi 0 if ii * Simple Competitive Learning [insert Figure 9.2.] NB: if weights and inputs normalized, then everything on unit sphere. Simple Competitive Learning • Dead Unit Problem Solutions – Initialize weights tot samples from the input – Leaky learning: also update the weights of the losers (but with a smaller ) – Arrange neurons in a geometrical way: update also neighbors – Turn on input patterns gradually – Conscience mechanism: make it easier for frequent losers to win. – Add noise to input patterns Graph Bipartioning • Patterns: edges = dipole stimuli • Edges sharing a node will be close together, hence tend to end up in same cluster. • Two output units. Vector Quantization • Classes are represented by prototype vectors • For storage and transmission of speech and image data. • Voronoi tessellation Vector Quantization Learning Vector Quantization • Labelled sample data • Multiple prototypes per class • Update rule depends on current classification: If winner class is incorrect, then move prototype away from input vector! ( j wi* j ) wi* j ( wi* j ) j if class is correct if class is incorrect Learning Vector Quantization Feature Mapping • Geometrical arrangement of output units • Nearby outputs correspond to nearby input patterns • Feature Map • Topology preserving map Self Organizing Map • Determine the winner (the neuron of which the weight vector has the smallest distance to the input vector) • Move the weight vector w of the winning neuron towards the input i i i w w Before learning After learning Self Organizing Map • Impose a topological order onto the competitive neurons (e.g., rectangular map) • Let neighbors of the winner share the “prize” (The “postcode lottery” principle) • After learning, neurons with similar weights tend to cluster on the map Self Organizing Map Example for twodimensioal input. Self Organizing Map Update neighboring weights. Self Organizing Map • Input: uniformly randomly distributed points • Output: Map of 202 neurons • Training – Starting with a large learning rate and neighborhood size, both are gradually decreased to facilitate convergence Self Organizing Map Self Organizing Map Nonlinear mappings are possible! Self Organizing Map A very nonlinear nonlinear mapping… Self Organizing Map Self Organizing Map Feature Mapping • Retinotopic Map: spatial organization of the neuronal responses to visual stimuli. • Somatosensory Map: (The somatosensory system is a diverse sensory system comprising the receptors and processing centres to produce the sensory modalities such as touch, temperature, proprioception (body position), and nociception (pain).) • Tonotopic Map: (Tonotopy (from Greek tono- and topos = place) refers to the spatial arrangement of where sounds of different frequency are processed in the brain. Tones close to each other in terms of frequency are represented in topologically neighbouring regions in the brain.) Feature Mapping Feature Mapping Feature Mapping Feature Mapping Kohonen’s Algorithm wij (i, i )( j wij ) * (i, i ) exp( | ri ri* | / 2 ) * 2 2 Travelling Salesman Problem wi ( (i )( wi ) ( wi1 2wi wi1 )) 2 (i ) exp( wi / 2 ) exp( j 2 2 w j / 2 ) 2 Hybrid Learning Schemes supervised unsupervised Counterpropagation • First layer uses standard competitive learning • Second (output) layer is trained using delta rule wij ( i Oi )V j wij ( i wij )V j Radial Basis Functions • First layer with normalized Gaussian activation functions 2 g j ( ) exp( j / 2 ) exp( k 2 j 2 k / 2 ) 2 k