def test_predict():
(I, J, K) = (5, 3, 2)
R = numpy.array(
[[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15]],
dtype=float)
M = numpy.ones((I, J))
K = 3
U = numpy.array([[125., 126.], [126., 126.], [126., 126.], [126., 126.],
[126., 126.]])
V = numpy.array([[84., 84.], [84., 84.], [84., 84.]])
M_test = numpy.array([[0, 0, 1], [0, 1, 0], [0, 0, 0], [1, 1, 0],
[0, 0,
0]]) #R->3,5,10,11, R_pred->21084,21168,21168,21168
MSE = (444408561. + 447872569. + 447660964. + 447618649) / 4.
R2 = 1. - (444408561. + 447872569. + 447660964. + 447618649) / (
4.25**2 + 2.25**2 + 2.75**2 + 3.75**2) #mean=7.25
Rp = 357. / (
math.sqrt(44.75) * math.sqrt(5292.)
) #mean=7.25,var=44.75, mean_pred=21147,var_pred=5292, corr=(-4.25*-63 + -2.25*21 + 2.75*21 + 3.75*21)
nmf = NMF(R, M, K)
nmf.U = U
nmf.V = V
performances = nmf.predict(M_test)
assert performances['MSE'] == MSE
assert performances['R^2'] == R2
assert performances['Rp'] == Rp
def test_run():
# Data generated from W = [[1,2],[3,4]], H = [[4,3],[2,1]]
R = [[8, 5], [20, 13]]
M = [[1, 1], [1, 0]]
K = 2
U = numpy.array([[10, 9], [8, 7]], dtype='f') #2x2
V = numpy.array([[6, 4], [5, 3]], dtype='f') #2x2
nmf = NMF(R, M, K)
# Check we get an Exception if W, H are undefined
with pytest.raises(AssertionError) as error:
nmf.run(0)
assert str(
error.value
) == "U and V have not been initialised - please run NMF.initialise() first."
# Then check for 1 iteration whether the updates work - heck just the first entry of U
nmf.U = U
nmf.V = V
nmf.run(1)
U_00 = 10 * (6 * 8 / 96.0 + 5 * 5 / 77.0) / (5.0 + 6.0) #0.74970484061
assert abs(U_00 - nmf.U[0][0]) < 0.000001
def test_compute_statistics():
R = numpy.array([[1,2],[3,4]],dtype=float)
M = numpy.array([[1,1],[0,1]])
(I,J,K) = 2, 2, 3
nmf = NMF(R,M,K)
R_pred = numpy.array([[500,550],[1220,1342]],dtype=float)
M_pred = numpy.array([[0,0],[1,1]])
MSE_pred = (1217**2 + 1338**2) / 2.0
R2_pred = 1. - (1217**2+1338**2)/(0.5**2+0.5**2) #mean=3.5
Rp_pred = 61. / ( math.sqrt(.5) * math.sqrt(7442.) ) #mean=3.5,var=0.5,mean_pred=1281,var_pred=7442,cov=61
assert MSE_pred == nmf.compute_MSE(M_pred,R,R_pred)
assert R2_pred == nmf.compute_R2(M_pred,R,R_pred)
assert Rp_pred == nmf.compute_Rp(M_pred,R,R_pred)
def test_compute_I_div():
R = [[1, 2, 0, 4], [5, 0, 7, 0]]
M = [[1, 1, 0, 1], [1, 0, 1, 0]]
K = 2
U = numpy.array([[1, 2], [3, 4]], dtype='f') #2x2
V = numpy.array([[5, 7, 9, 11], [6, 8, 10, 12]], dtype='f').T #4x2
#R_pred = [[17,23,29,35],[39,53,67,81]]
expected_I_div = sum([
1.0 * math.log(1.0 / 17.0) - 1.0 + 17.0,
2.0 * math.log(2.0 / 23.0) - 2.0 + 23.0,
4.0 * math.log(4.0 / 35.0) - 4.0 + 35.0,
5.0 * math.log(5.0 / 39.0) - 5.0 + 39.0,
7.0 * math.log(7.0 / 67.0) - 7.0 + 67.0
])
nmf = NMF(R, M, K)
nmf.U = U
nmf.V = V
I_div = nmf.compute_I_div()
assert abs(I_div - expected_I_div) < 0.0000001
def test_init():
# Test getting an exception when R and M are different sizes, and when R is not a 2D array
R1 = numpy.ones(3)
M = numpy.ones((2, 3))
K = 0
with pytest.raises(AssertionError) as error:
NMF(R1, M, K)
assert str(
error.value
) == "Input matrix R is not a two-dimensional array, but instead 1-dimensional."
R2 = numpy.ones((4, 3, 2))
with pytest.raises(AssertionError) as error:
NMF(R2, M, K)
assert str(
error.value
) == "Input matrix R is not a two-dimensional array, but instead 3-dimensional."
R3 = numpy.ones((3, 2))
with pytest.raises(AssertionError) as error:
NMF(R3, M, K)
assert str(
error.value
) == "Input matrix R is not of the same size as the indicator matrix M: (3, 2) and (2, 3) respectively."
# Test getting an exception if a row or column is entirely unknown
R = numpy.ones((2, 3))
M1 = [[1, 1, 1], [0, 0, 0]]
M2 = [[1, 1, 0], [1, 0, 0]]
with pytest.raises(AssertionError) as error:
NMF(R, M1, K)
assert str(error.value) == "Fully unobserved row in R, row 1."
with pytest.raises(AssertionError) as error:
NMF(R, M2, K)
assert str(error.value) == "Fully unobserved column in R, column 2."
# Test whether we made a copy of R with 1's at unknown values
I, J = 2, 4
R = [[1, 2, 0, 4], [5, 0, 7, 0]]
M = [[1, 1, 0, 1], [1, 0, 1, 0]]
K = 2
R_excl_unknown = [[1, 2, 1, 4], [5, 1, 7, 1]]
nmf = NMF(R, M, K)
assert numpy.array_equal(R, nmf.R)
assert numpy.array_equal(M, nmf.M)
assert nmf.I == I
assert nmf.J == J
assert nmf.K == K
assert numpy.array_equal(R_excl_unknown, nmf.R_excl_unknown)
def test_initialisation():
I, J = 2, 3
R = numpy.ones((I, J))
M = numpy.ones((I, J))
K = 4
# Init ones
init_UV = 'ones'
nmf = NMF(R, M, K)
nmf.initialise(init_UV)
assert numpy.array_equal(numpy.ones((2, 4)), nmf.U)
assert numpy.array_equal(numpy.ones((3, 4)), nmf.V)
# Init random
init_UV = 'random'
nmf = NMF(R, M, K)
nmf.initialise(init_UV)
for (i, k) in itertools.product(range(0, I), range(0, K)):
assert nmf.U[i, k] > 0 and nmf.U[i, k] < 1
for (j, k) in itertools.product(range(0, J), range(0, K)):
assert nmf.V[j, k] > 0 and nmf.V[j, k] < 1
def test_update():
I, J = 2, 4
R = [[1, 2, 0, 4], [5, 0, 7, 0]]
M = [[1, 1, 0, 1], [1, 0, 1, 0]]
K = 2
U = numpy.array([[1, 2], [3, 4]], dtype='f') #2x2
V = numpy.array([[5, 6], [7, 8], [9, 10], [11, 12]], dtype='f') #4x2
new_U = [[
1 * (1 * 5 / 17.0 + 2 * 7 / 23.0 + 4 * 11 / 35.0) / float(5 + 7 + 11),
2 * (1 * 6 / 17.0 + 2 * 8 / 23.0 + 4 * 12 / 35.0) / float(6 + 8 + 12)
],
[
3 * (5 * 5 / 39.0 + 7 * 9 / 67.0) / float(5 + 9),
4 * (5 * 6 / 39.0 + 7 * 10 / 67.0) / float(6 + 10)
]]
new_V = [[
5 * (1 * 1 / 17.0 + 3 * 5 / 39.0) / float(1 + 3),
6 * (2 * 1 / 17.0 + 4 * 5 / 39.0) / float(2 + 4)
], [7 * (1 * 2 / 23.0) / float(1), 8 * (2 * 2 / 23.0) / float(2)],
[9 * (3 * 7 / 67.0) / float(3), 10 * (4 * 7 / 67.0) / float(4)],
[11 * (1 * 4 / 35.0) / float(1), 12 * (2 * 4 / 35.0) / float(2)]]
nmf = NMF(R, M, K)
def reset():
nmf.U = numpy.copy(U)
nmf.V = numpy.copy(V)
for k in range(0, K):
reset()
nmf.update_U(k)
for i in range(0, I):
assert abs(new_U[i][k] - nmf.U[i, k]) < 0.00001
for k in range(0, K):
reset()
nmf.update_V(k)
for j in range(0, J):
assert abs(new_V[j][k] - nmf.V[j, k]) < 0.00001
# Also if I = J
I, J, K = 2, 2, 3
R = [[1, 2], [3, 4]]
M = [[1, 1], [0, 1]]
U = numpy.array([[1, 2, 3], [4, 5, 6]], dtype='f') #2x3
V = numpy.array([[7, 8, 9], [10, 11, 12]], dtype='f') #2x3
R_pred = numpy.array([[50, 68], [122, 167]], dtype='f') #2x2
nmf = NMF(R, M, K)
def reset_2():
nmf.U = numpy.copy(U)
nmf.V = numpy.copy(V)
for k in range(0, K):
reset_2()
nmf.update_U(k)
for i in range(0, I):
new_Uik = U[i][k] * sum( [V[j][k] * R[i][j] / R_pred[i,j] for j in range(0,J) if M[i][j] ]) \
/ sum( [V[j][k] for j in range(0,J) if M[i][j] ])
assert abs(new_Uik - nmf.U[i, k]) < 0.00001
for k in range(0, K):
reset_2()
nmf.update_V(k)
for j in range(0, J):
new_Vjk = V[j][k] * sum( [U[i][k] * R[i][j] / R_pred[i,j] for i in range(0,I) if M[i][j] ]) \
/ sum( [U[i][k] for i in range(0,I) if M[i][j] ])
assert abs(new_Vjk - nmf.V[j, k]) < 0.00001
check_empty_rows_columns(M, fraction)
# We now run the VB algorithm on each of the M's for each fraction.
all_performances = {metric: [] for metric in metrics}
average_performances = {metric: []
for metric in metrics} # averaged over repeats
for (fraction, Ms, Ms_test) in zip(fractions_unknown, all_Ms, all_Ms_test):
print "Trying fraction %s." % fraction
# Run the algorithm <repeats> times and store all the performances
for metric in metrics:
all_performances[metric].append([])
for (repeat, M, M_test) in zip(range(0, repeats), Ms, Ms_test):
print "Repeat %s of fraction %s." % (repeat + 1, fraction)
nmf = NMF(R, M, K)
nmf.initialise(init_UV, expo_prior)
nmf.run(iterations)
# Measure the performances
performances = nmf.predict(M_test)
for metric in metrics:
# Add this metric's performance to the list of <repeat> performances for this fraction
all_performances[metric][-1].append(performances[metric])
# Compute the average across attempts
for metric in metrics:
average_performances[metric].append(
sum(all_performances[metric][-1]) / repeats)
# Load in data
R = numpy.loadtxt(input_folder + "R.txt")
M = numpy.ones((I, J))
# Run the VB algorithm, <repeats> times
times_repeats = []
performances_repeats = []
for i in range(0, repeats):
# Set all the seeds
numpy.random.seed(0)
random.seed(0)
scipy.random.seed(0)
# Run the classifier
nmf = NMF(R, M, K)
nmf.initialise(init_UV, expo_prior)
nmf.run(iterations)
# Extract the performances and timestamps across all iterations
times_repeats.append(nmf.all_times)
performances_repeats.append(nmf.all_performances)
# Check whether seed worked: all performances should be the same
assert all([numpy.array_equal(performances, performances_repeats[0]) for performances in performances_repeats]), \
"Seed went wrong - performances not the same across repeats!"
# Print out the performances, and the average times
all_times_average = list(numpy.average(times_repeats, axis=0))
all_performances = performances_repeats[0]
print "np_all_times_average = %s" % all_times_average