Non Linear Methods for Classification

Parzen-based classifier

class mlpy.Parzen

Parzen based classifier (binary).

Initialization.

alpha()

Return alpha.

b()

Return b.

labels()

Outputs the name of labels.

learn(K, y)

Compute alpha and b.

Parameters:

K: 2d array_like object (N, N)

precomputed kernel matrix

y : 1d array_like object (N)

target values

pred(Kt)

Compute the predicted class.

Parameters :

Kt : 1d or 2d array_like object ([M], N)

test kernel matrix. Precomputed inner products (in feature space) between M testing and N training points.

Returns :

p : integer or 1d numpy array

predicted class

Example:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import mlpy
>>> np.random.seed(0)
>>> mean1, cov1, n1 = [1, 4.5], [[1,1],[1,2]], 20  # 20 samples of class 1
>>> x1 = np.random.multivariate_normal(mean1, cov1, n1)
>>> y1 = np.ones(n1, dtype=np.int)
>>> mean2, cov2, n2 = [2.5, 2.5], [[1,1],[1,2]], 30 # 30 samples of class 2
>>> x2 = np.random.multivariate_normal(mean2, cov2, n2)
>>> y2 = 2 * np.ones(n2, dtype=np.int)
>>> x = np.concatenate((x1, x2), axis=0) # concatenate the samples
>>> y = np.concatenate((y1, y2))
>>> K = mlpy.kernel_gaussian(x, x, sigma=2) # kernel matrix
>>> parzen = mlpy.Parzen()
>>> parzen.learn(K, y)
>>> xmin, xmax = x[:,0].min()-1, x[:,0].max()+1
>>> ymin, ymax = x[:,1].min()-1, x[:,1].max()+1
>>> xx, yy = np.meshgrid(np.arange(xmin, xmax, 0.02), np.arange(ymin, ymax, 0.02))
>>> xt = np.c_[xx.ravel(), yy.ravel()] # test points
>>> Kt = mlpy.kernel_gaussian(xt, x, sigma=2) # test kernel matrix
>>> yt = parzen.pred(Kt).reshape(xx.shape)
>>> fig = plt.figure(1)
>>> cmap = plt.set_cmap(plt.cm.Paired)
>>> plot1 = plt.pcolormesh(xx, yy, yt)
>>> plot2 = plt.scatter(x[:,0], x[:,1], c=y)
>>> plt.show()

Support Vector Classification

See Support Vector Machines (SVMs)

k-Nearest-Neighbor

class mlpy.KNN(k)

k-Nearest Neighbor (euclidean distance)

Parameters :

k : int

number of nearest neighbors

KNN.learn(x, y)

Learn method.

Parameters :

x : 2d array_like object (N x P)

training data

y : 1d array_like integer

class labels (-1 or 1 for binary classification, 1,..., nclasses for multiclass classification)

KNN.pred(t)

Predict KNN model on a test point(s).

Parameters :

t : 1d or 2d array_like object ([M,] P)

test point(s)

Returns :

p : the predicted value(s) on success: -1 or 1 for binary classification, 1, ..., nclasses for multiclass classification, 0 on succes with non unique classification

KNN.nclasses()

Returns the number of classes.

KNN.labels()

Outputs the name of labels.

Example:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import mlpy
>>> np.random.seed(0)
>>> mean1, cov1, n1 = [1, 5], [[1,1],[1,2]], 200  # 200 samples of class 1
>>> x1 = np.random.multivariate_normal(mean1, cov1, n1)
>>> y1 = np.ones(n1, dtype=np.int)
>>> mean2, cov2, n2 = [2.5, 2.5], [[1,0],[0,1]], 300 # 300 samples of class 2
>>> x2 = np.random.multivariate_normal(mean2, cov2, n2)
>>> y2 = 2 * np.ones(n2, dtype=np.int)
>>> mean3, cov3, n3 = [5, 8], [[0.5,0],[0,0.5]], 200 # 200 samples of class 3
>>> x3 = np.random.multivariate_normal(mean3, cov3, n3)
>>> y3 = 3 * np.ones(n3, dtype=np.int)
>>> x = np.concatenate((x1, x2, x3), axis=0) # concatenate the samples
>>> y = np.concatenate((y1, y2, y3))
>>> knn = mlpy.KNN(k=3)
>>> knn.learn(x, y)
>>> xmin, xmax = x[:,0].min()-1, x[:,0].max()+1
>>> ymin, ymax = x[:,1].min()-1, x[:,1].max()+1
>>> xx, yy = np.meshgrid(np.arange(xmin, xmax, 0.1), np.arange(ymin, ymax, 0.1))
>>> xnew = np.c_[xx.ravel(), yy.ravel()]
>>> ynew = knn.pred(xnew).reshape(xx.shape)
>>> ynew[ynew == 0] = 1 # set the samples with no unique classification to 1
>>> fig = plt.figure(1)
>>> cmap = plt.set_cmap(plt.cm.Paired)
>>> plot1 = plt.pcolormesh(xx, yy, ynew)
>>> plot2 = plt.scatter(x[:,0], x[:,1], c=y)
>>> plt.show()