def lle_noise():
''' LLE under noise for assignment 7'''
datafile = np.load('flatroll_data.npz');
data = datafile['Xflat'];
noisyData1 = data + np.random.randn(data.shape[0],data.shape[1])*np.sqrt(0.2);
noisyData2 = data + np.random.randn(data.shape[0],data.shape[1])*np.sqrt(1.8);
Y1 = imp.lle(noisyData1, 1, 'knn', 14, 1e0);
Y2 = imp.lle(noisyData1, 1, 'knn',50,1e-2);
Y3 = imp.lle(noisyData2, 1, 'knn',7,1e-1);
Y4 = imp.lle(noisyData2, 1, 'knn', 50, 1e-2);
pl.figure();
pl.subplot(2,2,1);
pl.scatter(noisyData1[0,:],noisyData1[1,:],c=Y1);
pl.title('Low noise, k=14');
pl.subplot(2,2,2);
pl.scatter(noisyData1[0,:],noisyData1[1,:],c=Y2);
pl.title('Low noise, k=50');
pl.subplot(2,2,3);
pl.scatter(noisyData2[0,:],noisyData2[1,:],c=Y3);
pl.title('High noise, k=7');
pl.subplot(2,2,4);
pl.scatter(noisyData2[0,:],noisyData2[1,:],c=Y4);
pl.title('High noise, k=50');
pl.show();
def test_lle(self):
n = 500
Xt = 10. * np.random.rand(n, 2)
X = np.append(Xt, 0.5 * np.random.randn(n, 8), 1)
# Rotate data randomly.
X = np.dot(X,
self.randrot(10).T)
with self.subTest(n_rule='knn', k=30):
Xp = imp.lle(X, 2, n_rule='knn', k=30, tol=1e-3)
#self.plot(Xt, Xp, 'knn')
with self.subTest(n_rule='eps-ball', epsilon=5.):
Xp = imp.lle(X, 2, n_rule='eps-ball', epsilon=5., tol=1e-3)
#self.plot(Xt, Xp, 'eps-ball')
with self.subTest(n_rule='eps-ball', epsilon=0.5):
with self.assertRaises(
ValueError,
msg='Graph should not be connected and raise ValueError.'):
imp.lle(X, 2, n_rule='eps-ball', epsilon=0.5, tol=1e-3)
def lle_test():
n = 500
print n
Xt = 10 * np.random.rand(2, n)
X = np.append(Xt, 0.5 * np.random.randn(8, n), 0)
# Rotate data randomly.
X = np.dot(randrot(10), X)
for (n_rule, param) in [['knn', 30], ['eps-ball', 5], ['eps-ball', 0.5]]:
try:
Xp = imp.lle(X, 2, n_rule, param)
except Exception as inst:
print 'lle crashed for n_rule = ' + n_rule + ' = ' + str(
param) + ':'
print inst.args
continue
pl.figure(figsize=(14, 8))
pl.subplot(1, 3, 1)
pl.scatter(Xt[0, :], Xt[1, :], 30)
pl.title('True 2D manifold')
pl.ylabel('x_2')
pl.xlabel('x_1')
pl.xticks([], [])
pl.yticks([], [])
pl.subplot(1, 3, 2)
pl.scatter(Xp[0, :], Xp[1, :], 30, Xt[0, :])
pl.title(n_rule + ': embedding colored via x_1')
pl.xlabel('x_1')
pl.ylabel('x_2')
pl.xticks([], [])
pl.yticks([], [])
pl.subplot(1, 3, 3)
pl.scatter(Xp[0, :], Xp[1, :], 30, Xt[1, :])
pl.title(n_rule + ': embedding colored via x_2')
pl.xlabel('x_1')
pl.ylabel('x_2')
pl.xticks([], [])
pl.yticks([], [])
pl.show()
print 'Tests for LLE passed? Check the figures!'
def lle_test():
n = 500
print n
Xt = 10*np.random.rand(2,n);
X = np.append( Xt, 0.5*np.random.randn(8,n), 0 );
# Rotate data randomly.
X = np.dot(randrot(10),X);
for (n_rule, param) in [ ['knn',30],['eps-ball',5],['eps-ball',0.5] ]:
#for (n_rule, param) in [ ['knn',30]]:
try:
Xp = imp.lle(X, 2, n_rule, param);
except Exception as inst:
print 'lle crashed for n_rule = ' + n_rule + ' = ' + str(param) + ':'
print inst.args
pl.figure(figsize=(14,8))
pl.subplot(1,3,1)
pl.scatter(Xt[0,:], Xt[1,:],30)
pl.title('True 2D manifold')
pl.ylabel('x_2')
pl.xticks([],[]); pl.yticks([],[])
pl.subplot(1,3,2);
pl.scatter(Xp[0,:], Xp[1,:], 30, Xt[0,:]);
pl.title(n_rule +': embedding colored via x_1');
pl.xlabel('x_1')
pl.xticks([],[]); pl.yticks([],[])
pl.subplot(1,3,3);
pl.scatter(Xp[0,:], Xp[1,:], 30, Xt[1,:]);
pl.title(n_rule +': embedding colored via x_2');
pl.xticks([],[]); pl.yticks([],[])
print 'Tests for LLE passed? Check the figures!'
print '\n(time the test takes on my notebook: approx. 2.5 seconds)'
def my_lle_test():
X = np.array([[0, 1, 0, 1], [0, 0, 1, 1]])
imp.lle(X, 2, 'knn', 2)
def lle_visualize(dataset='flatroll'):
''' visualization of LLE for assignment 6'''
if dataset == 'flatroll':
datafile = np.load('flatroll_data.npz');
data = datafile['Xflat'];
trueEmbedding = datafile['true_embedding'];
#15, 1e-1
Y = imp.lle(data, 1, 'knn', 9, 18e-3);
pl.figure();
pl.subplot(1,2,1);
pl.scatter(data[0,:],data[1,:],c=trueEmbedding);
pl.title('True embedding');
pl.colorbar();
pl.subplot(1,2,2);
pl.scatter(data[0,:],data[1,:],c=Y);
pl.title('LLE embedding');
pl.colorbar();
pl.show();
if dataset == 'swissroll':
datafile = np.load('swissroll_data.npz');
data = datafile['x_noisefree'];
trueEmbedding = datafile['z'];
#6,1e-4
Y = imp.lle(data,2,'knn',6,1e-4);
fig = pl.figure();
ax = fig.add_subplot(221, projection='3d');
ax.scatter(data[0,:],data[1,:],data[2,:],c=trueEmbedding[0,:]);
pl.title('True embedding');
ax = fig.add_subplot(222, projection='3d');
ax.scatter(data[0,:],data[1,:],data[2,:],c=Y[0,:]);
pl.title('LLE embedding');
pl.subplot(2,2,3);
pl.scatter(trueEmbedding[0,:],trueEmbedding[1,:],c=trueEmbedding[0,:]);
pl.title('True embedding');
pl.subplot(2,2,4);
pl.scatter(Y[0,:],Y[1,:],c=Y[0,:]);
pl.title('LLE embedding');
pl.show();
if dataset == 'fishbowl':
datafile = np.load('fishbowl_data.npz');
data = datafile['x_noisefree'];
trueEmbedding = datafile['z'];
Y = imp.lle(data,2,'knn',7,1e-10);
fig = pl.figure();
ax = fig.add_subplot(221, projection='3d');
ax.scatter(data[0,:],data[1,:],data[2,:],c=trueEmbedding[0,:]);
pl.title('True embedding');
ax = fig.add_subplot(222, projection='3d');
ax.scatter(data[0,:],data[1,:],data[2,:],c=Y[0,:]);
pl.title('LLE embedding');
pl.subplot(2,2,3);
pl.scatter(trueEmbedding[0,:],trueEmbedding[1,:],c=trueEmbedding[0,:]);
pl.title('True embedding');
pl.subplot(2,2,4);
pl.scatter(Y[0,:],Y[1,:],c=Y[0,:]);
pl.title('LLE embedding');
pl.show();