utils

GPy/util/misc.py

@@ -0,0 +1,56 @@
+import numpy as np
+
+def linear_grid(D, n = 100, min_max = (-100, 100)):
+    """
+    Creates a D-dimensional grid of n linearly spaced points
+
+    Parameters:
+
+    D:        dimension of the grid
+    n:        number of points
+    min_max:  (min, max) list
+
+
+    """
+
+    g = np.linspace(min_max[0], min_max[1], n)
+    G = np.ones((n, D))
+
+    return G*g[:,None]
+
+def kmm_init(X, m = 10):
+    """
+    This is the same initialization algorithm that is used
+    in Kmeans++. It's quite simple and very useful to initialize
+    the locations of the inducing points in sparse GPs.
+    
+    :param X: data
+    :param m: number of inducing points
+    """
+
+    # compute the distances
+    XXT = np.dot(X, X.T)
+    D = (-2.*XXT + np.diag(XXT)[:,np.newaxis] + np.diag(XXT)[np.newaxis,:])
+
+    # select the first point
+    s = np.random.permutation(X.shape[0])[0]
+    inducing = [s]
+    prob = D[s]/D[s].sum()
+
+    for z in range(m-1):
+        s = np.random.multinomial(1, prob.flatten()).argmax()
+        inducing.append(s)
+        prob = D[s]/D[s].sum()
+
+    inducing = np.array(inducing)
+    return X[inducing]
+
+if __name__ == '__main__':
+    import pylab as plt
+    X = np.linspace(1,10, 100)[:, None]
+    X = X[np.random.permutation(X.shape[0])[:20]]
+    inducing = kmm_init(X, m = 5)
+    plt.figure()
+    plt.plot(X.flatten(), np.ones((X.shape[0],)), 'x')
+    plt.plot(inducing, 0.5* np.ones((len(inducing),)), 'o')
+    plt.ylim((0.0, 10.0))