def test_gls_and_weights(self):
assert_raises(ValueError, PCA, self.x, gls=True)
assert_raises(ValueError, PCA, self.x, weights=np.array([1.0, 1.0]))
# Pre-standardize to make comparison simple
x = (self.x - self.x.mean(0))
x = x / (x**2.0).mean(0)
pc_gls = PCA(x, ncomp=1, standardize=False, demean=False, gls=True)
pc = PCA(x, ncomp=1, standardize=False, demean=False)
errors = x - pc.projection
var = (errors**2.0).mean(0)
weights = 1.0 / var
weights = weights / np.sqrt((weights**2.0).mean())
assert_allclose(weights, pc_gls.weights)
assert_equal(x, pc_gls.data)
assert_equal(x, pc.data)
pc_weights = PCA(x,
ncomp=1,
standardize=False,
demean=False,
weights=weights)
assert_allclose(weights, pc_weights.weights)
assert_allclose(np.abs(pc_weights.factors), np.abs(pc_gls.factors))
def test_eig_svd_equiv(self):
"""
Test leading components since the tail end can differ
"""
pc_eig = PCA(self.x)
pc_svd = PCA(self.x, method='svd')
assert_allclose(pc_eig.projection, pc_svd.projection)
assert_allclose(np.abs(pc_eig.factors[:, :2]),
np.abs(pc_svd.factors[:, :2]))
assert_allclose(np.abs(pc_eig.coeff[:2, :]),
np.abs(pc_svd.coeff[:2, :]))
assert_allclose(pc_eig.eigenvals, pc_svd.eigenvals)
assert_allclose(np.abs(pc_eig.eigenvecs[:, :2]),
np.abs(pc_svd.eigenvecs[:, :2]))
pc_svd = PCA(self.x, method='svd', ncomp=2)
pc_nipals = PCA(self.x, method='nipals', ncomp=2)
assert_allclose(np.abs(pc_nipals.factors),
np.abs(pc_svd.factors),
atol=DECIMAL_5)
assert_allclose(np.abs(pc_nipals.coeff),
np.abs(pc_svd.coeff),
atol=DECIMAL_5)
assert_allclose(pc_nipals.eigenvals, pc_svd.eigenvals, atol=DECIMAL_5)
assert_allclose(np.abs(pc_nipals.eigenvecs),
np.abs(pc_svd.eigenvecs),
atol=DECIMAL_5)
# Check data for no changes
assert_equal(self.x, pc_svd.data)
# Check data for no changes
assert_equal(self.x, pc_eig.data)
# Check data for no changes
assert_equal(self.x, pc_nipals.data)
def test_wide(self):
pc = PCA(self.x_wide)
assert_equal(pc.factors.shape[1], self.x_wide.shape[0])
assert_equal(pc.eigenvecs.shape[1], min(np.array(self.x_wide.shape)))
pc = PCA(pd.DataFrame(self.x_wide))
assert_equal(pc.factors.shape[1], self.x_wide.shape[0])
assert_equal(pc.eigenvecs.shape[1], min(np.array(self.x_wide.shape)))
def test_rsquare(self):
x = self.x + 0.0
mu = x.mean(0)
x_demean = x - mu
std = np.std(x, 0)
x_std = x_demean / std
pc = PCA(self.x)
nvar = x.shape[1]
rsquare = np.zeros(nvar + 1)
tss = np.sum(x_std**2)
for i in range(nvar + 1):
errors = x_std - pc.project(i, transform=False, unweight=False)
rsquare[i] = 1.0 - np.sum(errors**2) / tss
assert_allclose(rsquare, pc.rsquare)
pc = PCA(self.x, standardize=False)
tss = np.sum(x_demean**2)
for i in range(nvar + 1):
errors = x_demean - pc.project(i, transform=False, unweight=False)
rsquare[i] = 1.0 - np.sum(errors**2) / tss
assert_allclose(rsquare, pc.rsquare)
pc = PCA(self.x, standardize=False, demean=False)
tss = np.sum(x**2)
for i in range(nvar + 1):
errors = x - pc.project(i, transform=False, unweight=False)
rsquare[i] = 1.0 - np.sum(errors**2) / tss
assert_allclose(rsquare, pc.rsquare)
def test_warnings_and_errors(self):
with warnings.catch_warnings(record=True) as w:
pc = PCA(self.x, ncomp=300)
assert_equal(len(w), 1)
with warnings.catch_warnings(record=True) as w:
rs = self.rs
x = rs.standard_normal((200, 1)) * np.ones(200)
pc = PCA(x, method='eig')
assert_equal(len(w), 1)
assert_raises(ValueError, PCA, self.x, method='unknown')
assert_raises(ValueError, PCA, self.x, missing='unknown')
assert_raises(ValueError, PCA, self.x, tol=2.0)
assert_raises(ValueError, PCA, np.nan * np.ones((200, 100)), tol=2.0)
def test_options(self):
pc = PCA(self.x)
pc_no_norm = PCA(self.x, normalize=False)
assert_allclose(pc.factors.dot(pc.coeff),
pc_no_norm.factors.dot(pc_no_norm.coeff))
princomp = pc.factors
assert_allclose(princomp.T.dot(princomp), np.eye(100), atol=1e-5)
weights = pc_no_norm.coeff
assert_allclose(weights.T.dot(weights), np.eye(100), atol=1e-5)
pc_10 = PCA(self.x, ncomp=10)
assert_allclose(pc.factors[:, :10], pc_10.factors)
assert_allclose(pc.coeff[:10, :], pc_10.coeff)
assert_allclose(pc.rsquare[:(10 + 1)], pc_10.rsquare)
assert_allclose(pc.eigenvals[:10], pc_10.eigenvals)
assert_allclose(pc.eigenvecs[:, :10], pc_10.eigenvecs)
pc = PCA(self.x, standardize=False, normalize=False)
mu = self.x.mean(0)
xdm = self.x - mu
xpx = xdm.T.dot(xdm)
val, vec = np.linalg.eigh(xpx)
ind = np.argsort(val)
ind = ind[::-1]
val = val[ind]
vec = vec[:, ind]
assert_allclose(xdm, pc.transformed_data)
assert_allclose(val, pc.eigenvals)
assert_allclose(np.abs(vec), np.abs(pc.eigenvecs))
assert_allclose(np.abs(pc.factors), np.abs(xdm.dot(vec)))
assert_allclose(pc.projection, xdm + mu)
pc = PCA(self.x, standardize=False, demean=False, normalize=False)
x = self.x
xpx = x.T.dot(x)
val, vec = np.linalg.eigh(xpx)
ind = np.argsort(val)
ind = ind[::-1]
val = val[ind]
vec = vec[:, ind]
assert_allclose(x, pc.transformed_data)
assert_allclose(val, pc.eigenvals)
assert_allclose(np.abs(vec), np.abs(pc.eigenvecs))
assert_allclose(np.abs(pc.factors), np.abs(x.dot(vec)))
def test_against_reference(self):
"""
Test against MATLAB, which by default demeans but does not standardize
"""
x = data.xo / 1000.0
pc = PCA(x, normalize=False, standardize=False)
ref = princomp1
assert_allclose(np.abs(pc.factors), np.abs(ref.factors))
assert_allclose(pc.factors.dot(pc.coeff) + x.mean(0), x)
assert_allclose(np.abs(pc.coeff), np.abs(ref.coef.T))
assert_allclose(pc.factors.dot(pc.coeff), ref.factors.dot(ref.coef.T))
pc = PCA(x[:20], normalize=False, standardize=False)
mu = x[:20].mean(0)
ref = princomp2
assert_allclose(np.abs(pc.factors), np.abs(ref.factors))
assert_allclose(pc.factors.dot(pc.coeff) + mu, x[:20])
assert_allclose(np.abs(pc.coeff), np.abs(ref.coef.T))
assert_allclose(pc.factors.dot(pc.coeff), ref.factors.dot(ref.coef.T))
def test_rsquare(self):
x = self.x + 0.0
mu = x.mean(0)
x_demean = x - mu
std = np.std(x, 0)
x_std = x_demean / std
pc = PCA(self.x)
nvar = x.shape[1]
rsquare = np.zeros(nvar + 1)
tss = np.sum(x_std ** 2)
for i in range(nvar + 1):
errors = x_std - pc.project(i, transform=False, unweight=False)
rsquare[i] = 1.0 - np.sum(errors ** 2) / tss
assert_allclose(rsquare, pc.rsquare)
pc = PCA(self.x, standardize=False)
tss = np.sum(x_demean ** 2)
for i in range(nvar + 1):
errors = x_demean - pc.project(i, transform=False, unweight=False)
rsquare[i] = 1.0 - np.sum(errors ** 2) / tss
assert_allclose(rsquare, pc.rsquare)
pc = PCA(self.x, standardize=False, demean=False)
tss = np.sum(x ** 2)
for i in range(nvar + 1):
errors = x - pc.project(i, transform=False, unweight=False)
rsquare[i] = 1.0 - np.sum(errors ** 2) / tss
assert_allclose(rsquare, pc.rsquare)
def test_pandas(self):
pc = PCA(pd.DataFrame(self.x))
pc1 = PCA(self.x)
assert_equal(pc.factors.values, pc1.factors)
fig = pc.plot_scree()
fig = pc.plot_scree(ncomp=10)
fig = pc.plot_scree(log_scale=False)
fig = pc.plot_rsquare()
fig = pc.plot_rsquare(ncomp=5)
proj = pc.project(2)
PCA(pd.DataFrame(self.x), ncomp=4, gls=True)
PCA(pd.DataFrame(self.x), ncomp=4, standardize=False)
def test_projection(self):
pc = PCA(self.x, ncomp=5)
mu = self.x.mean(0)
demean_x = self.x - mu
coef = np.linalg.pinv(pc.factors).dot(demean_x)
direct = pc.factors.dot(coef)
assert_allclose(pc.projection, direct + mu)
pc = PCA(self.x, standardize=False, ncomp=5)
coef = np.linalg.pinv(pc.factors).dot(demean_x)
direct = pc.factors.dot(coef)
assert_allclose(pc.projection, direct + mu)
pc = PCA(self.x, standardize=False, demean=False, ncomp=5)
coef = np.linalg.pinv(pc.factors).dot(self.x)
direct = pc.factors.dot(coef)
assert_allclose(pc.projection, direct)
pc = PCA(self.x, ncomp=5, gls=True)
mu = self.x.mean(0)
demean_x = self.x - mu
coef = np.linalg.pinv(pc.factors).dot(demean_x)
direct = pc.factors.dot(coef)
assert_allclose(pc.projection, direct + mu)
pc = PCA(self.x, standardize=False, ncomp=5)
coef = np.linalg.pinv(pc.factors).dot(demean_x)
direct = pc.factors.dot(coef)
assert_allclose(pc.projection, direct + mu)
pc = PCA(self.x, standardize=False, demean=False, ncomp=5, gls=True)
coef = np.linalg.pinv(pc.factors).dot(self.x)
direct = pc.factors.dot(coef)
assert_allclose(pc.projection, direct)
# Test error for too many factors
project = pc.project
assert_raises(ValueError, project, 6)
def test_smoke_plot_and_repr(self):
pc = PCA(self.x)
fig = pc.plot_scree()
fig = pc.plot_scree(ncomp=10)
fig = pc.plot_scree(log_scale=False)
fig = pc.plot_scree(cumulative=True)
fig = pc.plot_rsquare()
fig = pc.plot_rsquare(ncomp=5)
# Additional smoke test
pc.__repr__()
pc = PCA(self.x, standardize=False)
pc.__repr__()
pc = PCA(self.x, standardize=False, demean=False)
pc.__repr__()
# Check data for no changes
assert_equal(self.x, pc.data)
def test_smoke_plot_and_repr(self):
pc = PCA(self.x)
fig = pc.plot_scree()
fig = pc.plot_scree(ncomp=10)
fig = pc.plot_scree(log_scale=False)
fig = pc.plot_scree(cumulative=True)
fig = pc.plot_rsquare()
fig = pc.plot_rsquare(ncomp=5)
# Additional smoke test
pc.__repr__()
pc = PCA(self.x, standardize=False)
pc.__repr__()
pc = PCA(self.x, standardize=False, demean=False)
pc.__repr__()
# Check data for no changes
assert_equal(self.x, pc.data)
def test_replace_missing(self):
x = self.x.copy()
x[::5, ::7] = np.nan
pc = PCA(x, missing='drop-row')
x_dropped_row = x[np.logical_not(np.any(np.isnan(x), 1))]
pc_dropped = PCA(x_dropped_row)
assert_equal(pc.projection, pc_dropped.projection)
assert_equal(x, pc.data)
pc = PCA(x, missing='drop-col')
x_dropped_col = x[:, np.logical_not(np.any(np.isnan(x), 0))]
pc_dropped = PCA(x_dropped_col)
assert_equal(pc.projection, pc_dropped.projection)
assert_equal(x, pc.data)
pc = PCA(x, missing='drop-min')
if x_dropped_row.size > x_dropped_col.size:
x_dropped_min = x_dropped_row
else:
x_dropped_min = x_dropped_col
pc_dropped = PCA(x_dropped_min)
assert_equal(pc.projection, pc_dropped.projection)
assert_equal(x, pc.data)
pc = PCA(x, ncomp=3, missing='fill-em')
missing = np.isnan(x)
mu = nanmean(x, axis=0)
errors = x - mu
sigma = np.sqrt(nanmean(errors**2, axis=0))
x_std = errors / sigma
x_std[missing] = 0.0
last = x_std[missing]
delta = 1.0
count = 0
while delta > 5e-8:
pc_temp = PCA(x_std, ncomp=3, standardize=False, demean=False)
x_std[missing] = pc_temp.projection[missing]
current = x_std[missing]
diff = current - last
delta = np.sqrt(np.sum(diff**2)) / np.sqrt(np.sum(current**2))
last = current
count += 1
x = self.x + 0.0
projection = pc_temp.projection * sigma + mu
x[missing] = projection[missing]
assert_allclose(pc._adjusted_data, x)
# Check data for no changes
assert_equal(self.x, self.x_copy)
x = self.x
pc = PCA(x)
pc_dropped = PCA(x, missing='drop-row')
assert_allclose(pc.projection, pc_dropped.projection, atol=DECIMAL_5)
pc_dropped = PCA(x, missing='drop-col')
assert_allclose(pc.projection, pc_dropped.projection, atol=DECIMAL_5)
pc_dropped = PCA(x, missing='drop-min')
assert_allclose(pc.projection, pc_dropped.projection, atol=DECIMAL_5)
pc = PCA(x, ncomp=3)
pc_dropped = PCA(x, ncomp=3, missing='fill-em')
assert_allclose(pc.projection, pc_dropped.projection, atol=DECIMAL_5)
# Test too many missing for missing='fill-em'
x = self.x.copy()
x[:, :] = np.nan
assert_raises(ValueError, PCA, x, missing='drop-row')
assert_raises(ValueError, PCA, x, missing='drop-col')
assert_raises(ValueError, PCA, x, missing='drop-min')
assert_raises(ValueError, PCA, x, missing='fill-em')
def test_pandas(self):
pc = PCA(pd.DataFrame(self.x))
pc1 = PCA(self.x)
assert_equal(pc.factors.values, pc1.factors)
fig = pc.plot_scree()
fig = pc.plot_scree(ncomp=10)
fig = pc.plot_scree(log_scale=False)
fig = pc.plot_rsquare()
fig = pc.plot_rsquare(ncomp=5)
proj = pc.project(2)
PCA(pd.DataFrame(self.x), ncomp=4, gls=True)
PCA(pd.DataFrame(self.x), ncomp=4, standardize=False)