Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
RBF ch1,2,3 Overview of RBF Networks • RBF networks have three layers: input layer , output layer, and hidden layer. • Output is a real value. • One neuron in the input layer corresponds to each predictor variable. • Each neuron in the hidden layer consists of a RBF function(Gaussian,etc) • Each neuron centered on a point with the same dimensions as the predictor variables • The output layer has a weighted sum of outputs from the hidden layers. Overview of RBF Networks Supervised Learning &Unsupervised Learning Supervised Learning: categorized into "regression" and "classification"problems. Unsupervised Learning: We can derive structure from data where we don't necessarily know the effect of the variables. Nonparametric Regression& Parametric Regression Parametric Regression: parameters have meaningful interpretations, such as initial water level or rate of flow Y depends on X Nonparametric Regression: parameters have no particular meaning in relation to the problems to which they are applied. Nonparametric Regression Nonparametric Regression : the primary goal is to estimate the underlying function Y depends on weight and basis function • RBF神經網路在架構上是一種3層前饋網路。 輸入層到輸出層的是非線性的(即:隱藏層 的函數),但是隱藏層到輸出層的映射卻是 線性的(即:輸出層的函數),因此可以加快 網路的學習速度。 • 高維度空間的資料分類問題,比低維度空 間更符合線性分離趨勢。 The idea y Training Data x The idea y Training Data x Basis Functions (Kernels) The idea y Function Learned x Basis Functions (Kernels) The idea y Nontraining Sample Function Learned x Basis Functions (Kernels) Linear model m Formula: f (x) wii (x) i 1 Example Linear Models • Polynomial f ( x) wi x i i ( x) x , i 0,1, 2, i i • Fourier Series f ( x) wk exp j 2k0 x k k ( x) exp j 2k0 x , k 0,1, 2, Single-Layer Perceptrons as Universal Aproximators y w2 w1 Hidden Units 1 x= wm 2 x1 x2 m xn m f (x) aswii (x) Radial Basis Function Networks i 1 Universal Aproximators y w2 w1 Hidden Units 1 x= wm 2 x1 x2 m xn With sufficient number of radial-basis-function units, it can also be a universal approximator. Linear model