def test_nmf(self):
test_cases = [np.mat([[1,2,3],[2,4,6],[4,17,13]], dtype = np.double),
np.mat([[1,0,0]], dtype = np.double)]
for in_mat in test_cases:
red = Nmf(2)
d_mat = DenseMatrix(in_mat)
#wd_init, hd_init = red.random_init(d_mat)
wd_init, hd_init = red.v_col_init(d_mat)
s_mat = SparseMatrix(in_mat)
ws_init = SparseMatrix(wd_init)
hs_init = SparseMatrix(hd_init)
wd_mat, hd_mat = Linalg.nmf(d_mat, wd_init, hd_init)
ws_mat, hs_mat = Linalg.nmf(s_mat, ws_init, hs_init)
#TESTED IT AGAINST MATLAB IMPLEMENTATION - ALL GOOD
#print wd_mat.mat
#print hd_mat.mat
#print ws_mat.mat.todense()
#print hs_mat.mat.todense()
print "V:", in_mat
print "WH:", (ws_mat*hs_mat).mat.todense()
np.testing.assert_array_almost_equal(wd_mat.mat,
ws_mat.mat.todense(), 2)
np.testing.assert_array_almost_equal(hd_mat.mat,
hs_mat.mat.todense(), 2)
def train(self, matrix_a, matrix_b):
"""
If cross validation is set to True, it performs generalized
cross validation. (Hastie, Tibshirani and Friedman, Second edition,
page 244).
"""
if not self._crossvalidation:
return Linalg.ridge_regression(matrix_a, matrix_b, self._param,
self._intercept)[0]
else:
min_err_param = 0
min_err = np.Inf
gcv_err = np.Inf
N = matrix_a.shape[0]
for param in self._param_range:
mat_x, S_trace, err1 = Linalg.ridge_regression(matrix_a, matrix_b, param,
self._intercept)
nom = pow(1 - S_trace / N, 2) * N
if nom != 0:
gcv_err = (err1 * err1) / nom
if gcv_err < min_err:
min_err = gcv_err
min_err_param = param
#print "lambda:", min_err_param
return Linalg.ridge_regression(matrix_a, matrix_b, min_err_param,
self._intercept)[0]
def test_nmf(self):
test_cases = [np.mat([[1,2,3],[2,4,6],[4,17,13]], dtype = np.double),
np.mat([[1,0,0]], dtype = np.double)]
for in_mat in test_cases:
red = Nmf(2)
d_mat = DenseMatrix(in_mat)
#wd_init, hd_init = red.random_init(d_mat)
wd_init, hd_init = red.v_col_init(d_mat)
s_mat = SparseMatrix(in_mat)
ws_init = SparseMatrix(wd_init)
hs_init = SparseMatrix(hd_init)
wd_mat, hd_mat = Linalg.nmf(d_mat, wd_init, hd_init)
ws_mat, hs_mat = Linalg.nmf(s_mat, ws_init, hs_init)
#TESTED IT AGAINST MATLAB IMPLEMENTATION - ALL GOOD
#print wd_mat.mat
#print hd_mat.mat
#print ws_mat.mat.todense()
#print hs_mat.mat.todense()
print "V:", in_mat
print "WH:", (ws_mat*hs_mat).mat.todense()
np.testing.assert_array_almost_equal(wd_mat.mat,
ws_mat.mat.todense(), 2)
np.testing.assert_array_almost_equal(hd_mat.mat,
hs_mat.mat.todense(), 2)
def train(self, matrix_a, matrix_b):
"""
If cross validation is set to True, it performs generalized
cross validation. (Hastie, Tibshirani and Friedman, Second edition,
page 244).
"""
if not self._crossvalidation:
return Linalg.ridge_regression(matrix_a, matrix_b, self._param,
self._intercept)[0]
else:
min_err_param = 0
min_err = np.Inf
gcv_err = np.Inf
N = matrix_a.shape[0]
for param in self._param_range:
mat_x, S_trace, err1 = Linalg.ridge_regression(matrix_a, matrix_b, param,
self._intercept)
nom = pow(1 - S_trace / N, 2) * N
if nom != 0:
gcv_err = (err1 * err1) / nom
if gcv_err < min_err:
min_err = gcv_err
min_err_param = param
#print "lambda:", min_err_param
return Linalg.ridge_regression(matrix_a, matrix_b, min_err_param,
self._intercept)[0]
def apply(self, matrix_):
matrix_.assert_positive()
#w_init, h_init = self.nndsvd_init(matrix_)
w_init, h_init = self.v_col_init(matrix_)
#w_init, h_init = self.random_init(matrix_)
w, h = Linalg.nmf(matrix_, w_init, h_init)
return w, Linalg.pinv(h)
def apply(self, matrix_):
matrix_.assert_positive()
#w_init, h_init = self.nndsvd_init(matrix_)
w_init, h_init = self.v_col_init(matrix_)
#w_init, h_init = self.random_init(matrix_)
w, h = Linalg.nmf(matrix_, w_init, h_init)
return w, Linalg.pinv(h)
def test_pinv(self):
test_cases = self.pinv_test_cases
for in_mat, expected_out in test_cases:
out_mat = Linalg.pinv(DenseMatrix(in_mat))
np.testing.assert_array_almost_equal(out_mat.mat, expected_out, 7)
out_mat = Linalg.pinv(SparseMatrix(in_mat))
np.testing.assert_array_almost_equal(out_mat.mat.todense(),
expected_out, 7)
def test_pinv(self):
test_cases = self.pinv_test_cases
for in_mat, expected_out in test_cases:
out_mat = Linalg.pinv(DenseMatrix(in_mat))
np.testing.assert_array_almost_equal(out_mat.mat, expected_out, 7)
out_mat = Linalg.pinv(SparseMatrix(in_mat))
np.testing.assert_array_almost_equal(out_mat.mat.todense(),
expected_out, 7)
def test_sparse_svd(self):
test_cases = self.svd_test_cases
for x, u_expected, s_expected, v_expected in test_cases:
for dim in [2,3,6]:
u, s, v = Linalg.svd(SparseMatrix(x),dim)
np.testing.assert_array_almost_equal(np.abs(u.mat.todense()), np.abs(u_expected), 2)
np.testing.assert_array_almost_equal(np.abs(s), np.abs(s_expected), 2)
np.testing.assert_array_almost_equal(np.abs(v.mat.todense()), np.abs(v_expected), 2)
u, s, v = Linalg.svd(SparseMatrix(x),1)
np.testing.assert_array_almost_equal(np.abs(u.mat.todense()), np.abs(u_expected[:,0:1]), 2)
np.testing.assert_array_almost_equal(np.abs(s), np.abs(s_expected[0:1]), 2)
np.testing.assert_array_almost_equal(np.abs(v.mat.todense()), np.abs(v_expected[:,0:1]), 2)
def test_dense_svd(self):
test_cases = self.svd_test_cases
for x, u_expected, s_expected, v_expected in test_cases:
for dim in [2,3,6]:
u, s, v = Linalg.svd(DenseMatrix(x),dim)
np.testing.assert_array_almost_equal(u.mat, u_expected, 2)
np.testing.assert_array_almost_equal(s, s_expected, 2)
np.testing.assert_array_almost_equal(v.mat, v_expected, 2)
u, s, v = Linalg.svd(DenseMatrix(x),1)
np.testing.assert_array_almost_equal(u.mat, u_expected[:,0:1], 2)
np.testing.assert_array_almost_equal(s, s_expected[0:1], 2)
np.testing.assert_array_almost_equal(v.mat, v_expected[:, 0:1], 2)
def test_intercept_lstsq_regression(self):
a = DenseMatrix(np.matrix([[1, 1],[2, 3],[4, 6]]))
b = DenseMatrix(np.matrix([[12, 15, 18],[21, 27, 33],[35, 46, 57]]))
res = DenseMatrix(np.matrix([[1, 2, 3],[4, 5, 6],[7, 8, 9]]))
res1 = Linalg.lstsq_regression(a, b)
res2 = Linalg.lstsq_regression(a, b, intercept=True)
np.testing.assert_array_almost_equal(res2.mat[:-1,:], res[0:2,:].mat, 6)
np.testing.assert_array_almost_equal(res2.mat[-1,:], res[2:3,:].mat, 6)
new_a = a.hstack(DenseMatrix(np.ones((a.shape[0], 1))))
self.assertGreater(((a * res1) - b).norm(), ((new_a * res2) - b).norm())
def test_dense_svd(self):
test_cases = self.svd_test_cases
for x, u_expected, s_expected, v_expected in test_cases:
for dim in [2, 3, 6]:
u, s, v = Linalg.svd(DenseMatrix(x), dim)
np.testing.assert_array_almost_equal(u.mat, u_expected, 2)
np.testing.assert_array_almost_equal(s, s_expected, 2)
np.testing.assert_array_almost_equal(v.mat, v_expected, 2)
u, s, v = Linalg.svd(DenseMatrix(x), 1)
np.testing.assert_array_almost_equal(u.mat, u_expected[:, 0:1], 2)
np.testing.assert_array_almost_equal(s, s_expected[0:1], 2)
np.testing.assert_array_almost_equal(v.mat, v_expected[:, 0:1], 2)
def test_sparse_lstsq_regression(self):
test_cases = self.pinv_test_cases
for m, m_inv in test_cases:
m1 = SparseMatrix(m)
id_ = SparseMatrix.identity(m1.shape[0])
res = Linalg.lstsq_regression(m1, id_)
np.testing.assert_array_almost_equal(res.mat.todense(), m_inv, 7)
approx1 = (m1 * res).mat.todense()
res2 = Linalg.lstsq_regression(m1, id_, intercept=True)
new_a = m1.hstack(SparseMatrix(np.ones((m1.shape[0], 1))))
approx2 = (new_a * res2).mat.todense()
def test_sparse_lstsq_regression(self):
test_cases = self.pinv_test_cases
for m, m_inv in test_cases:
m1 = SparseMatrix(m)
id_ = SparseMatrix.identity(m1.shape[0])
res = Linalg.lstsq_regression(m1, id_)
np.testing.assert_array_almost_equal(res.mat.todense(), m_inv, 7)
approx1 = (m1 * res).mat.todense()
res2 = Linalg.lstsq_regression(m1, id_, intercept=True)
new_a = m1.hstack(SparseMatrix(np.ones((m1.shape[0], 1))))
approx2 = (new_a * res2).mat.todense()
def nndsvd_init(self, matrix_):
def matrix_abs(mat_):
mat_p = mat_.get_non_negative()
mat_n_abs = mat_p - mat_
return mat_p + mat_n_abs
def padd_zeros(matrix_, axis, thickness):
matrix_type = type(matrix_)
if axis == 0:
append_mat = matrix_type(
np.zeros((thickness, matrix_.shape[1])))
return matrix_.vstack(append_mat)
elif axis == 1:
append_mat = matrix_type(
np.zeros((matrix_.shape[0], thickness)))
return matrix_.hstack(append_mat)
u, s, v = Linalg.svd(matrix_, self._reduced_dimension)
rank = u.shape[1]
w = [[]] * rank
h = [[]] * rank
vt = v.transpose()
w[0] = sqrt(s[0]) * matrix_abs(u[:, 0])
h[0] = sqrt(s[0]) * matrix_abs(vt[0, :])
for i in range(1, rank):
uu = u[:, i]
vv = vt[i, :]
uup = uu.get_non_negative()
uun = uup - uu
vvp = vv.get_non_negative()
vvn = vvp - vv
n_uup = uup.norm()
n_uun = uun.norm()
n_vvp = vvp.norm()
n_vvn = vvn.norm()
termp = n_uup * n_vvp
termn = n_uun * n_vvn
if (termp >= termn):
w[i] = sqrt(s[i] * termp) * uup / n_uup
h[i] = sqrt(s[i] * termp) * vvp / n_vvp
else:
w[i] = sqrt(s[i] * termn) * uun / n_uun
h[i] = sqrt(s[i] * termn) * vvn / n_vvn
w = matrix_.nary_hstack(w)
h = matrix_.nary_vstack(h)
w.remove_small_values(0.0000000001)
h.remove_small_values(0.0000000001)
if (rank < self._reduced_dimension):
w = padd_zeros(w, 1, self._reduced_dimension - rank)
h = padd_zeros(h, 0, self._reduced_dimension - rank)
return w, h
def train(self, matrix_a, matrix_b=None):
"""
If cross validation is set to True, it performs generalized
cross validation. (Hastie, Tibshirani and Friedman, Second edition,
page 244).
TODO: not yet!
"""
pid = str(getpid())
logdir = 'convergence/'+pid
call(['mkdir', '-p', logdir])
# mkdir -p convergence/pid
self._trainId += 1 # For logging purposes
if not self._crossvalidation:
if self._projector:
matrix_b = matrix_a
W, costs = Linalg.tracenorm_regression(matrix_a, matrix_b, self._param, self._iterations, self._intercept)
print_tuple_list(costs, logdir+'/'+str(self._trainId)+'-lmbd-'+str(self._param))
return W
elif matrix_b == None:
raise ValueError("Unable to perform cross-validation without a phrase space")
else:
min_err_param = 0
min_err = np.Inf
gcv_err = np.Inf
N = matrix_a.shape[0]
for param in self._param_range:
mat_x, S_trace, err1 = Linalg.ridge_regression(matrix_a, matrix_b, param,
self._intercept)
nom = pow(1 - S_trace / N, 2) * N
if nom != 0:
gcv_err = (err1 * err1) / nom
if gcv_err < min_err:
min_err = gcv_err
min_err_param = param
#print "lambda:", min_err_param
return Linalg.ridge_regression(matrix_a, matrix_b, min_err_param,
self._intercept)[0]
def test_intercept_lstsq_regression(self):
a = DenseMatrix(np.matrix([[1, 1], [2, 3], [4, 6]]))
b = DenseMatrix(np.matrix([[12, 15, 18], [21, 27, 33], [35, 46, 57]]))
res = DenseMatrix(np.matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]))
res1 = Linalg.lstsq_regression(a, b)
res2 = Linalg.lstsq_regression(a, b, intercept=True)
np.testing.assert_array_almost_equal(res2.mat[:-1, :], res[0:2, :].mat,
6)
np.testing.assert_array_almost_equal(res2.mat[-1, :], res[2:3, :].mat,
6)
new_a = a.hstack(DenseMatrix(np.ones((a.shape[0], 1))))
self.assertGreater(((a * res1) - b).norm(),
((new_a * res2) - b).norm())
def test_dense_lstsq_regression(self):
test_cases = self.pinv_test_cases
for m, m_inv in test_cases:
m1 = DenseMatrix(m)
id_ = DenseMatrix.identity(m1.shape[0])
res = Linalg.lstsq_regression(m1, id_)
np.testing.assert_array_almost_equal(res.mat, m_inv, 7)
def nndsvd_init(self,matrix_):
def matrix_abs(mat_):
mat_p = mat_.get_non_negative()
mat_n_abs = mat_p - mat_
return mat_p + mat_n_abs
def padd_zeros(matrix_, axis, thickness):
matrix_type = type(matrix_)
if axis == 0:
append_mat = matrix_type(np.zeros((thickness, matrix_.shape[1])))
return matrix_.vstack(append_mat)
elif axis == 1:
append_mat = matrix_type(np.zeros((matrix_.shape[0], thickness)))
return matrix_.hstack(append_mat)
u, s, v = Linalg.svd(matrix_, self._reduced_dimension);
rank = u.shape[1]
w = [[]]*rank
h = [[]]*rank
vt = v.transpose()
w[0] = sqrt(s[0]) * matrix_abs(u[:,0])
h[0] = sqrt(s[0]) * matrix_abs(vt[0,:])
for i in range(1,rank):
uu = u[:,i]
vv = vt[i,:]
uup = uu.get_non_negative()
uun = uup - uu
vvp = vv.get_non_negative()
vvn = vvp - vv
n_uup = uup.norm()
n_uun = uun.norm()
n_vvp = vvp.norm()
n_vvn = vvn.norm()
termp = n_uup * n_vvp; termn = n_uun * n_vvn
if (termp >= termn):
w[i] = sqrt(s[i] * termp) * uup / n_uup
h[i] = sqrt(s[i] * termp) * vvp / n_vvp
else:
w[i] = sqrt(s[i] * termn) * uun / n_uun
h[i] = sqrt(s[i] * termn) * vvn / n_vvn
w = matrix_.nary_hstack(w)
h = matrix_.nary_vstack(h)
w.remove_small_values(0.0000000001)
h.remove_small_values(0.0000000001)
if (rank < self._reduced_dimension):
w = padd_zeros(w, 1, self._reduced_dimension - rank)
h = padd_zeros(h, 0, self._reduced_dimension - rank)
return w,h
def test_dense_lstsq_regression(self):
test_cases = self.pinv_test_cases
for m, m_inv in test_cases:
m1 = DenseMatrix(m)
id_ = DenseMatrix.identity(m1.shape[0])
res = Linalg.lstsq_regression(m1, id_)
np.testing.assert_array_almost_equal(res.mat, m_inv, 7)
def test_sparse_svd(self):
test_cases = self.svd_test_cases
for x, u_expected, s_expected, v_expected in test_cases:
for dim in [2, 3, 6]:
u, s, v = Linalg.svd(SparseMatrix(x), dim)
np.testing.assert_array_almost_equal(np.abs(u.mat.todense()),
np.abs(u_expected), 2)
np.testing.assert_array_almost_equal(np.abs(s),
np.abs(s_expected), 2)
np.testing.assert_array_almost_equal(np.abs(v.mat.todense()),
np.abs(v_expected), 2)
u, s, v = Linalg.svd(SparseMatrix(x), 1)
np.testing.assert_array_almost_equal(np.abs(u.mat.todense()),
np.abs(u_expected[:, 0:1]), 2)
np.testing.assert_array_almost_equal(np.abs(s),
np.abs(s_expected[0:1]), 2)
np.testing.assert_array_almost_equal(np.abs(v.mat.todense()),
np.abs(v_expected[:, 0:1]), 2)
def test_sparse_ridge_regression(self):
test_cases = self.pinv_test_cases
for m, m_inv in test_cases:
m1 = SparseMatrix(m)
id_ = SparseMatrix.identity(m1.shape[0])
res1 = Linalg.lstsq_regression(m1, id_)
np.testing.assert_array_almost_equal(res1.mat.todense(), m_inv, 7)
res2 = Linalg.ridge_regression(m1, id_, 1)[0]
error1 = (m1 * res1 - SparseMatrix(m_inv)).norm()
error2 = (m1 * res2 - SparseMatrix(m_inv)).norm()
#print "err", error1, error2
norm1 = error1 + res1.norm()
norm2 = error2 + res2.norm()
#print "norm", norm1, norm2
#THIS SHOULD HOLD, MAYBE ROUNDIGN ERROR?
#self.assertGreaterEqual(error2, error1)
self.assertGreaterEqual(norm1, norm2)
def test_sparse_ridge_regression(self):
test_cases = self.pinv_test_cases
for m, m_inv in test_cases:
m1 = SparseMatrix(m)
id_ = SparseMatrix.identity(m1.shape[0])
res1 = Linalg.lstsq_regression(m1, id_)
np.testing.assert_array_almost_equal(res1.mat.todense(), m_inv, 7)
res2 = Linalg.ridge_regression(m1, id_, 1)[0]
error1 = (m1 * res1 - SparseMatrix(m_inv)).norm()
error2 = (m1 * res2 - SparseMatrix(m_inv)).norm()
#print "err", error1, error2
norm1 = error1 + res1.norm()
norm2 = error2 + res2.norm()
#print "norm", norm1, norm2
#THIS SHOULD HOLD, MAYBE ROUNDIGN ERROR?
#self.assertGreaterEqual(error2, error1)
self.assertGreaterEqual(norm1, norm2)
def apply(self, matrix_):
u, s, v = Linalg.svd(matrix_, self._reduced_dimension)
return u.scale_columns(s), v
def train(self, matrix_a, matrix_b):
return Linalg.lstsq_regression(matrix_a, matrix_b, self._intercept)
def train(self, matrix_a, matrix_b=None):
"""
matrix_b is ignored
"""
W = Linalg.kronecker_product(matrix_a)
return W
def apply(self, matrix_):
u, s, v = Linalg.svd(matrix_, self._reduced_dimension)
return u.scale_columns(s), v
def train(self, matrix_a, matrix_b):
return Linalg.lstsq_regression(matrix_a, matrix_b, self._intercept)