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UW-Madison ECE 539 - Lecture 9 MLP (I) - Feed-forward Model

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Lecture 9 MLP (I): Feed-forward ModelOutlineMulti-Layer Perceptron StructureTwo Layer Perceptron XOR GateDecision Boundaries of XORMLP Nonlinear MappingMLP Feed-forward model NotationMLP Feed-forward modelApplications to ClassificationApplications to ApproximationIntro. ANN & Fuzzy SystemsLecture 9 MLP (I): Feed-forward Model(C) 2001 by Yu Hen Hu2Intro. ANN & Fuzzy SystemsOutline•Multi-Layer Perceptron Structure•Feed Forward Model•XOR Example•MLP Applications(C) 2001 by Yu Hen Hu3Intro. ANN & Fuzzy SystemsMulti-Layer Perceptron Structure A Three Layer Feed-forward Multi-Layer Perceptronwwwwww111M122M1NMNOutput LayerHidden Layer #2Input LayerHidden Layer #1(C) 2001 by Yu Hen Hu4Intro. ANN & Fuzzy SystemsTwo Layer Perceptron XOR Gate Let x1, x2  {0, 1}, theny1 = sgn(x1 – x2 – 0.5) = x1 AND y2 = sgn(x2 – x1 – 0.5) = x2 AND z = sgn(y1 + y2 – 0.5) = y1 OR y2+++zx xyy11221-1-11-0.5 -0.511-0.52x1x(C) 2001 by Yu Hen Hu5Intro. ANN & Fuzzy SystemsDecision Boundaries of XOR•Linear Hyper-planes as decision boundaries x1 – x2 – 0.5 = 0; and x2 – x1 – 0.5 = 0 -0.500.511.5-0.500.511.5zx1x2(C) 2001 by Yu Hen Hu6Intro. ANN & Fuzzy SystemsMLP Nonlinear Mapping 12.5z1xy134525515111(C) 2001 by Yu Hen Hu7Intro. ANN & Fuzzy SystemsMLP Feed-forward model Notation •(k) – Index of individual feature vectors, 1  k  K. •() -- Layer index, superscript, 0    L.  = 0  input layer,  = L  output layer •i, j – ith and jth neuron in each layer, subscript Example: •zi()(k): the output of ith neuron in the  th layer corresponding to the kth feature vector. •wij(): the value of the synaptic weight that connect the output of the jth neuron at  1th layer to the jth neuron at the  th layer. The value of the weight is updated once every epoch.(C) 2001 by Yu Hen Hu8Intro. ANN & Fuzzy SystemsMLP Feed-forward model •Note that , and •The input layer usually consists of linear elements. Thus, a 2-layer MLP will have two layers of non-linear neurons: the hidden layer, and the output layer. 1)()1(0kz )1()(0iiwNjjijiNjjijiiiikzwkawkukukufkz0)1()()1(1)1()()()()()()()()()])(exp[1/(1))(()((C) 2001 by Yu Hen Hu9Intro. ANN & Fuzzy SystemsApplications to Classification •Classification: Match output class to target class. MLP assigns each input feature vector to a membership of a particular class i. Multi-LayerPerceptron0 1 0 0 00 0 1 0 0TargetclassOutputclassInput feature vector(C) 2001 by Yu Hen Hu10Intro. ANN & Fuzzy SystemsApplications to Approximation •Approximation (regression, modeling) : Targets are real numbers instead of binary class membership. Multi-LayerPerceptron.1 .1 .1 .2 .3.3 .4 .1 .9 .99TargetOutputInput


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UW-Madison ECE 539 - Lecture 9 MLP (I) - Feed-forward Model

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