def time_exactIKPCA(data, kernel, num=5):
times = np.zeros((num, ))
for j in range(num):
start_time = time.time()
sfa = IKSFA(kernel, num_output_components=2)
for i in range(int(data.shape[0] / 100)):
sfa.ExactIKPCATrain(data[100 * i:100 * (i + 1)])
end_time = time.time()
times[j] = end_time - start_time
print("Average:", np.average(times), "+/-", np.std(times))
def test_greedyIKPCA_linear():
# make some test data (which is quadratic, but contains the linear piece)
num = 2000
v = np.linspace(0, 4 * np.pi, num)
x1 = np.sin(v) + np.cos(11 * v)**2
x2 = np.cos(11 * v)
data = np.c_[x1, x2, x1**2, x2**2, x1 * x2]
# Test my version of IKSFA
linearKernel = Kernel.LinearKernel
sfa = IKSFA(linearKernel, num_output_components=2)
sfa.GreedyIKPCA(data[:10])
sfa.GreedyIKPCA(data[10:20])
def test_greedyIKPCA_quadratic():
# # make some test data (which is quadratic)
num = 2000
v = np.linspace(0, 4 * np.pi, num)
x1 = np.sin(v) + np.cos(11 * v)**2
x2 = np.cos(11 * v)
# data = np.c_[x1, x2, x1 ** 2, x2 ** 2, x1 * x2]
data = np.c_[x1, x2]
# Test my version of IKPCA
quadraticKernel = Kernel.QuadraticKernel
sfa = IKSFA(quadraticKernel, num_output_components=2)
sfa2 = IKSFA(quadraticKernel, num_output_components=2)
# Compare doing IKPCA over everything at once to doing it in several pieces
total = sfa.GreedyIKPCA(data)
for i in range(int(num / 100)):
piecewise = sfa2.GreedyIKPCA(data[100 * i:100 * (i + 1)])
print("total:", total)
print("piecewise:", piecewise)
print(np.allclose(total, piecewise))
def test_exactIKPCA(name, data, kernel):
sfa = IKSFA(kernel, num_output_components=2)
sfa2 = IKSFA(kernel, num_output_components=2)
# Compare doing IKPCA over everything at once to doing it in several pieces
sfa.ExactIKPCATrain(data)
total = sfa.ExactIKPCATransform(data)
for i in range(int(data.shape[0] / 100)):
sfa2.ExactIKPCATrain(data[100 * i:100 * (i + 1)])
piecewise = sfa2.ExactIKPCATransform(data)
# Because the columns might be -1 * each other, we multiply by a correction
signs = total[0, :] / piecewise[0, :]
piecewise *= signs
if not np.allclose(total, piecewise):
print("Test Failed!")
print("total:", total)
print("piecewise:", piecewise)
else:
print("Test Passed ({})".format(name))
def test_linear():
# # make some test data (which is linear)
# num = 2000
# v = np.linspace(0, 4*np.pi, num)
# x1 = np.sin(v) + np.cos(11*v)
# x2 = np.cos(11*v)
# data = np.c_[x1, x2]
# make some test data (which is quadratic, but contains the linear piece)
num = 2000
v = np.linspace(0, 4 * np.pi, num)
x1 = np.sin(v) + np.cos(11 * v)**2
x2 = np.cos(11 * v)
data = np.c_[x1, x2, x1**2, x2**2, x1 * x2]
# Test my version of IKSFA
linearKernel = Kernel.LinearKernel
sfa = IKSFA(linearKernel, num_output_components=2)
sfa.BatchTrain(data)
result = sfa.BatchTransform(data)
# Use scaling to restore the results to a reasonable range
scaler = StandardScaler()
scaler.fit(result)
result = scaler.transform(result)
fig, (ax1, ax2, ax3, ax4) = plt.subplots(4, sharex=True, sharey=True)
# fig = plt.figure(figsize=(3, 12))
ax1.plot(v, x1, c="red")
ax1.set_ylabel(r"$x_1$", rotation=0, ha="right", va="center")
ax1.text(0.997,
0.98,
r"$\sin(v) + \cos(11v)$",
bbox={
'facecolor': 'w',
'alpha': 0.5,
'edgecolor': 'black',
'pad': 1
},
ha="right",
va="top",
transform=ax1.transAxes)
ax1.axhline(0, color="black", linestyle="--")
ax1.set_yticks([])
ax2.plot(v, x2, c="blue")
ax2.set_ylabel(r"$x_2$", rotation=0, ha="right", va="center")
ax2.text(0.997,
0.98,
r"$\cos(11v)$",
bbox={
'facecolor': 'w',
'alpha': 0.5,
'edgecolor': 'black',
'pad': 1
},
ha="right",
va="top",
transform=ax2.transAxes)
ax2.axhline(0, color="black", linestyle="--")
ax2.set_yticks([])
ax3.plot(v, result[:, 0], c="green")
ax3.set_ylabel(r"$SFA_0$", rotation=0, ha="right", va="center")
ax3.text(0.997,
0.98,
r"$\sim\alpha*\sin(v)$",
bbox={
'facecolor': 'w',
'alpha': 0.5,
'edgecolor': 'black',
'pad': 1
},
ha="right",
va="top",
transform=ax3.transAxes)
ax3.axhline(0, color="black", linestyle="--")
ax3.set_yticks([])
ax4.plot(v, result[:, 1], c="orange")
ax4.set_ylabel(r"$SFA_1$", rotation=0, ha="right", va="center")
ax4.text(0.997,
0.98,
r"$\sim\beta*\cos(11v)$",
bbox={
'facecolor': 'w',
'alpha': 0.5,
'edgecolor': 'black',
'pad': 1
},
ha="right",
va="top",
transform=ax4.transAxes)
ax4.axhline(0, color="black", linestyle="--")
ax4.set_yticks([])
plt.xlabel("v")
plt.xlim([0, 4 * np.pi])
plt.ylim([-2.2, 2.2])
plt.xticks([0, np.pi, 2 * np.pi, 3 * np.pi, 4 * np.pi],
["0", r"$\pi$", r"$2\pi$", r"$3\pi$", r"$4\pi$"])
fig.subplots_adjust(hspace=0)
plt.setp([a.get_xticklabels() for a in fig.axes[:-1]], visible=False)
fig.suptitle("Test Batch KSFA (Linear)")
filename = "../../plots/test-batchksfa-linear.png"
print("Saving to {}".format(filename))
plt.savefig(filename, dpi=300)
def test_IKPCARS(name, data, kernel):
sfa = IKSFA(kernel, num_output_components=2)
sfa_inc = IKSFA(kernel, num_output_components=2)
sfa2 = IKSFA(kernel,
num_output_components=2,
num_reduced_set_components=10,
RS_gradient_ascent_parallelization=(1, 1))
# Compare doing IKPCA over everything at once to doing it in several pieces
sfa.ExactIKPCATrain(data)
total = sfa.ExactIKPCATransform(data)
for i in range(int(data.shape[0] / 100)):
sfa3 = IKSFA(kernel, num_output_components=2)
sfa2.IKPCARSTrain(data[100 * i:100 * (i + 1)])
sfa3.IKPCARSTrain(data[:100 * (i + 1)])
sfa_inc.ExactIKPCATrain(data[100 * i:100 * (i + 1)])
piecewise = sfa2.IKPCARSTransform(data)
p3 = sfa3.IKPCARSTransform(data)
inc_out = sfa_inc.ExactIKPCATransform(data)
scaling = p3[0, :] / piecewise[0, :]
piecewise *= scaling
if not np.allclose(p3, piecewise):
print("Test %d Failed!" % i)
print("p3:", p3)
print("piecewise:", piecewise)
print("p3 - piece", p3 - piecewise)
scaling = inc_out[0, :] / piecewise[0, :]
piecewise *= scaling
if not np.allclose(inc_out, piecewise):
print("Test %d Failed!" % i)
print("inc_out:", inc_out)
print("piecewise:", piecewise)
print("inc - piece", inc_out - piecewise)
# sys.exit(-1)
else:
print(i)
piecewise = sfa2.IKPCARSTransform(data)
# Because the columns might be -1 * each other, we multiply by a correction
signs = total[0, :] / piecewise[0, :]
piecewise *= signs
if not np.allclose(total, piecewise):
print("Test Failed!")
print("total:", total)
print("piecewise:", piecewise)
else:
print("Test Passed ({})".format(name))