added Chapter08

Chapter08/Chapter08_mcode/data_example.m

+% Generation of example data
+
+example_nr = 3; % Three examples
+n = 1000; % Number of points
+noise = 1; % Noise level
+
+% Make and show the data
+[X,T,x,dim] = make_data(example_nr, n, noise);
+
+cmap = interp1([-1; -0.5; 0; 0.5; 1],[0,0,0.5; 0,0.5,1; 1,1,1; 1,0,0; 0.5,0,0],linspace(-1,1,256));
+X_colors = cmap([1+63,end-63],:); 
+
+figure
+scatter(X(:,2),X(:,1),20,X_colors(T(:,1)+1,:),'filled','MarkerEdgeColor',[0 0 0])
+box on, axis ij image, axis([0.5,dim(2)+0.5,0.5,dim(1)+0.5])
+title('training')
+
+%% Before training, you should make data have zero mean
+
+c = mean(X,1);
+xc = x-c;
+Xc = X-c;
+
+figure
+scatter(Xc(:,2),Xc(:,1),20,X_colors(T(:,1)+1,:),'filled','MarkerEdgeColor',[0 0 0])
+axis equal
+box on, axis ij image, axis([0.5-c(2),dim(2)+0.5-c(2),0.5-c(1),dim(1)+0.5-c(1)])
+title('Zero mean training')
+
+
+
+
+
+
+
+
+
+
+
+

Chapter08/Chapter08_mcode/make_data.m

+function [X,T,x,dim] = make_data(example_nr, n, noise)
+% Generate data for training a simple neural network.
+% 
+% function [X,T,x,dim] = make_data(example_nr, n, noise)
+% 
+% Input:
+%   example_nr - a number 1 - 3 for each example
+%   n - number of points in each data set
+%   noise - a number to increase or decrease the noise level (if changed, 
+%       choose between 0.5 and 2)
+% Output:
+%   X - 2n x 2 array of points (there are n points in each class)
+%   T - 2n x 2 target values
+%   x - regular sampled points on the area covered by the points that will
+%       be used for testing the neural network
+%   dim - dimensionality of the area covered by the points
+% 
+% Authors: Vedrana Andersen Dahl and Anders Bjorholm Dahl - 25/3-2020
+%   vand@dtu.dk, abda@dtu.dk
+% 
+
+if (nargin < 3)
+    noise = 1;
+end
+if (nargin < 2)
+    n = 200;
+end
+
+if ( mod(n,2) == 1 )
+    n = n+1;
+end
+
+dim = [100,100];
+[QX,QY] = ndgrid(1:dim(1),1:dim(2));
+x = [QX(:),QY(:)];
+K = [n,n];
+T = [ones(K(1),1)*[1 0];ones(K(2),1)*[0 1]];
+
+switch example_nr
+    case 1
+        X = [noise*10*randn(K(1),2)+[30,30];noise*10*randn(K(2),2)+[70,70]];
+    case 2
+        rand_ang = rand(K(1),1)*2*pi;
+        X = [noise*5*randn(K(1),2) + 30*[cos(rand_ang), sin(rand_ang)];
+            noise*5*randn(K(2),2)] + (dim+1)/2;
+    case 3
+        X = [noise*10*randn(K(1)/2,2)+[30,30];noise*10*randn(K(1)/2,2)+[70,70];
+            10*randn(K(2)/2,2)+[30,70];10*randn(K(2)/2,2)+[70,30]];
+    otherwise
+        disp('Example number should be 1, 2, or 3.')
+end
+
+
+
+

Chapter08/make_data.py

+#%%
+
+import numpy as np
+
+
+def make_data(example_nr, n = 200, noise = 1):
+    '''
+    Generate data for training a simple neural network.
+    
+        Arguments:
+            example_nr: a number 1 to 3 for each example.
+            n: number of points in each class set.
+            noise: noise level, best between 0.5 and 2.
+        Returns:
+            X: 2 x 2n array of points (there are n points in each class).
+            T: 2 x 2n target values.
+            x: grid points for testing the neural network.
+            dim: size of the area covered by the grid points.
+
+        Authors: Vedrana Andersen Dahl and Anders Bjorholm Dahl - 25/3-2020
+        vand@dtu.dk, abda@dtu.dk
+    '''
+
+    rg = np.random.default_rng()
+    
+    dim = (100, 100)
+    
+    QX, QY = np.meshgrid(range(0, dim[0]), range(0, dim[1]))
+    x_grid = np.c_[np.ravel(QX), np.ravel(QY)]
+    
+    #  Targets: first half class 0, second half class 1
+    T = np.vstack((np.tile([True, False], (n, 1)), 
+                   np.tile([False, True], (n, 1))))
+    
+    if example_nr == 1 :  # two separated clusters
+
+        X = np.vstack((np.tile([30., 30.], (n, 1)), 
+                       np.tile([70., 70.], (n, 1))))
+        X += rg.normal(size=X.shape, scale=10*noise)  # add noise
+
+    elif example_nr == 2 :  # concentric clusters
+
+        rand_ang = 2 * np.pi * rg.uniform(size=n)
+        X = np.vstack((30 * np.array([np.cos(rand_ang), np.sin(rand_ang)]).T, 
+                       np.tile([0., 0.], (n, 1))))
+        X += [50, 50]  # center
+        X += rg.normal(size=X.shape, scale=5*noise)# add noise
+    
+    elif example_nr == 3 :  # 2x2 checkerboard 
+        n1 = n//2
+        n2 = n//2 + n%2  # if n is odd n2 will have 1 element more
+
+        X = np.vstack((np.tile([30., 30.], (n1, 1)), 
+                       np.tile([70., 70.], (n2, 1)),
+                       np.tile([30. ,70.], (n1, 1)),
+                       np.tile([70., 30.], (n2, 1))))
+        X += rg.normal(size=X.shape, scale=10*noise)  # add noise
+
+    else:
+        print('No data returned - example_nr must be 1, 2, or 3')
+    
+    o = rg.permutation(range(2*n))
+    
+    return X[o].T, T[o].T, x_grid.T, dim
+
+
+#%% Test of the data generation
+if __name__ == "__main__":
+    #%%
+
+    import matplotlib.pyplot as plt
+    
+    n = 1000
+    noise = 1
+    
+    fig, ax = plt.subplots(1, 3)
+    for i, a in enumerate(ax):
+        example_nr = i + 1
+        X, T, x_grid, dim = make_data(example_nr, n, noise)
+        a.scatter(X[0][T[0]], X[1][T[0]], c='r', alpha=0.3, s=15)
+        a.scatter(X[0][T[1]], X[1][T[1]], c='g', alpha=0.3, s=15)
+        a.set_aspect('equal', 'box')
+        a.set_title(f'Example {i} data')
+    
+    plt.show()
+    
+    
+    #%% Before training, you should make data zero mean
+    
+    c = np.mean(X, axis=1, keepdims=True)
+    X_c = X - c
+    
+    fig, ax = plt.subplots(1,1)
+    ax.scatter(X_c[0][T[0]], X_c[1][T[0]], c='r', alpha=0.3, s=15)
+    ax.scatter(X_c[0][T[1]], X_c[1][T[1]], c='g', alpha=0.3, s=15)
+    ax.set_aspect('equal', 'box')
+    plt.title('Zero-mean data')
+    plt.show()
+
+
+
+
+
+
+
+
+# %%