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  • 1. 66//1010//20132013 Training in Neural Network • Learn values of weights from I/O pairs • Start with random weights • Load training example’s input • Observe computed input • Modify weights to reduce difference • Iterate over all training examples • Terminate when weights stop changing OR when error is very small Single Layer Perceptrons • A network with all the inputs connected directly to the output (figure 1) • In simple cases, feature space is divided by drawing a hyperplane across it, which is Known as a decision boundary • Problems which can be thus classified are linearly separable (figure 2) ++ ++ ++ ++ -- -- -- -- xx11 xx22 FigureFigure 11 FigureFigure 22
  • 2. 66//1010//20132013 Single Layer Perceptrons • Classical Measure of Error – Squared error – Where Err is the difference between the target value and the output by the network • Weight Modifying – Use gradient descent to reduce the squared error by calculating the partial derivative of E with respect to each weight j jj xinfErr Err Err E *** )('−= ∂ ∂ = ∂ ∂ ww : Learning Rate: Learning Rate Error Back-Propagation The gradient descent • The gradient of the error E gives the direction where the error function at the current setting of the w will increase. In order to decrease E, we take a small step in the opposite direction, -G
  • 3. 66//1010//20132013 Error Back-Propagation The gradient descentThe gradient descent InIn 22D (one weight)D (one weight) By repeating this over and over, we moveBy repeating this over and over, we move "downhill" in"downhill" in EE until we reach a minimumuntil we reach a minimum Error Back-Propagation The gradient descentThe gradient descent
  • 4. 66//1010//20132013 Single Layer Perceptrons – a basic application • Suppose we have data about the height and the age of a population of 100 people. • So we can plot a 2D sketch (x is the age, y the height) • How can we predict the height of a 101th person, given his age? UsingUsing aa modelmodel of the data. The simplestof the data. The simplest model can be :model can be : y = wy = w11 x + wx + w00 This may exactly be the equation of theThis may exactly be the equation of the output of a neuron networkoutput of a neuron network Different Non-Linearly Separable Problems StructureStructure ExclusiveExclusive--OROR ProblemProblem Classes withClasses with Meshed regionsMeshed regions Most GeneralMost General Region ShapesRegion Shapes SingleSingle--LayerLayer TwoTwo--LayerLayer ThreeThree--LayerLayer AA AABB BB AA AABB BB AA AABB BB BB AA BB AA BB AA
  • 5. 66//1010//20132013 Multilayer Perceptrons(MLP) HiddenHidden LayerLayer Output LayerOutput Layer AdjustableAdjustable wweightseights IntputIntput LayerLayer AdjustableAdjustable wweightseights InputInputUnitUnits(ExternalStimuli)s(ExternalStimuli) OutputValuesOutputValues Types of Layers • Input layer (units) – Introduces input values into the network – No activation function or other processing • Hidden layer(s) – Perform classification of features – Two hidden layers are sufficient to solve any problem – Features imply more layers may be better • Output layer – Functionally just like the hidden layers – Outputs are passed on to the world outside the neural network
  • 6. 66//1010//20132013 MLP Characteristics • Input propagates in a forward direction, layer-by-layer basis – also called Multilayer Feedforward Network, MLP • Non-linear activation function – differentiable – nonlinearity prevent reduction to single-layer perceptron • One or more layers of hidden neurons – progressively extracting more meaningful features from input patterns • High degree of connectivity Problems of MLP • Nonlinearity and high degree of connectivity makes theoretical analysis difficult • Output vector rather than a single output value • Error at output layer is clear, but error at the hidden layers seems mysterious • Learning process is hard to visualize • So, Error Back-Propagation Algorithm (BPA) is a computationally efficient training for MLP