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synthetic_datasets_normal.py
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synthetic_datasets_normal.py
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#!/usr/bin/env python3
"""
Synthetic 2D Gaussians (normal) datasets
Usage:
python -m datasets.synthetic_datasets_normal
ls datasets/synthetic/
"""
import os
import random
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.transforms as transforms
from absl import app
from absl import flags
from scipy import stats
from matplotlib.patches import Ellipse
from datasets.normalization import calc_normalization, apply_normalization
from datasets.synthetic_datasets import save_data_file, sine, display_xy
FLAGS = flags.FLAGS
flags.DEFINE_boolean("plots_for_paper", False, "Save plots only, i.e., not the data files")
def confidence_ellipse(ax, mean=None, cov=None, x=None, y=None, n_std=2.0,
facecolor='none', **kwargs):
"""
Create a plot of the covariance confidence ellipse of *x* and *y*. Or,
optionally from mean/cov instead (if known/available) of estimated from
samples drawn from these distributions.
Based on:
https://matplotlib.org/stable/gallery/statistics/confidence_ellipse.html
https://carstenschelp.github.io/2018/09/14/Plot_Confidence_Ellipse_001.html
Parameters
----------
x, y : array-like, shape (n, )
Input data.
ax : matplotlib.axes.Axes
The axes object to draw the ellipse into.
n_std : float
The number of standard deviations to determine the ellipse's radiuses.
**kwargs
Forwarded to `~matplotlib.patches.Ellipse`
Returns
-------
matplotlib.patches.Ellipse
"""
# Sanity checks
if x is not None and y is not None:
based_on_xy = True
if x.size != y.size:
raise ValueError("x and y must be the same size")
elif mean is not None and cov is not None:
based_on_xy = False
if len(cov) != 2 or len(mean) != 2:
raise ValueError("mean/cov must be 2D")
else:
raise ValueError("Pass either mean/cov or x/y")
# Estimate covariance from data, if not given
if based_on_xy:
cov = np.cov(x, y)
# Calculate needed parameter
pearson = cov[0, 1]/np.sqrt(cov[0, 0] * cov[1, 1])
# Using a special case to obtain the eigenvalues of this
# two-dimensional dataset.
ell_radius_x = np.sqrt(1 + pearson)
ell_radius_y = np.sqrt(1 - pearson)
ellipse = Ellipse((0, 0), width=ell_radius_x * 2, height=ell_radius_y * 2,
facecolor=facecolor, **kwargs)
# Calculating the standard deviation of x from the squareroot of the
# variance and multiplying with the given number of standard deviations.
scale_x = np.sqrt(cov[0, 0]) * n_std
# Calculate mean from the data if not given
if based_on_xy:
mean_x = np.mean(x)
else:
mean_x = mean[0]
# Same for y
scale_y = np.sqrt(cov[1, 1]) * n_std
if based_on_xy:
mean_y = np.mean(y)
else:
mean_y = mean[1]
# Compute the ellipse
transf = transforms.Affine2D() \
.rotate_deg(45) \
.scale(scale_x, scale_y) \
.translate(mean_x, mean_y)
ellipse.set_transform(transf + ax.transData)
return ax.add_patch(ellipse)
def get_translate_rotate(translate, rotate, dimensions, rotation_per_class):
""" Generate how much / where to translate and rotate and the corresponding
covariance matrix for the rotated multivariate normal distributions """
translate_amount = translate/2 # half since +/-
translation = np.random.uniform(
-translate_amount, translate_amount, dimensions)
rotate_amount = rotate/2*rotation_per_class
rotation = np.random.uniform(-rotate_amount, rotate_amount)
# No rotation of the Gaussian
# rotation_conv = np.diag(np.ones((dimensions,)))
# Simple rotation matrix to rotate the Gaussian distribution (if not
# isotropic)
rotation_conv = np.array([
[np.cos(rotation), -np.sin(rotation)],
[np.sin(rotation), np.cos(rotation)]
])
return translation, rotation, rotation_conv
def get_near_psd(A):
"""
Gets rid of "covariance is not positive-semidefinite" warning
From: https://stackoverflow.com/a/63131309
"""
C = (A + A.T)/2
eigval, eigvec = np.linalg.eig(C)
eigval[eigval < 0] = 0
return eigvec.dot(np.diag(eigval)).dot(eigvec.T)
def make_domain(num_classes, center, radius, dimensions,
inter_domain_translate=0, inter_domain_rotate=0,
intra_domain_translate=0, intra_domain_rotate=0,
initial_cov=None):
"""
Make a domain, i.e. generate a list of mean/cov for each class
Returns:
[(class1 mean, class1 cov), (class2 mean, class2 cov), ...]
"""
results = []
# For now we only support 2D. There's some ways to do this in 3D, but
# it looks like higher dimensions get a bit more complicated. For now
# we'll start with 2D only.
assert dimensions == 2, ">2D not yet implemented"
# Evenly distribute classes around a circle
rotation_per_class = 2*np.pi / num_classes
# Calculate inter-domain shift
inter_translate, inter_rotate, inter_rotate_conv = get_translate_rotate(
inter_domain_translate, inter_domain_rotate, dimensions, rotation_per_class)
# Start with a particular "shaped" Gaussian - for now, isotropic
if initial_cov is None:
initial_cov = np.diag(np.ones((dimensions,)))
# Create distribution for each class
for i in range(num_classes):
# Intra-domain shift, i.e. shift each class differently
intra_translate, intra_rotate, intra_rotate_conv = get_translate_rotate(
intra_domain_translate, intra_domain_rotate, dimensions, rotation_per_class)
# Adjust mean of distributions around the circle
theta = i*rotation_per_class + inter_rotate + intra_rotate
mean = np.array([
center[0] + radius*np.cos(theta),
center[1] + radius*np.sin(theta),
])
# Initial covariance before rotation
cov = initial_cov
# Inter-domain shift, i.e. shift all classes the same
mean += inter_translate + intra_translate
# It's isotropic for now, so we don't need to rotate.
# cov = inter_rotate_conv.dot(cov)
# cov = intra_rotate_conv.dot(cov)
# Get close positive-semidefinite to this matrix - needed because of
# the rotation matrices
# print("Before:", cov)
# print("After:", get_near_psd(cov))
# cov = get_near_psd(cov)
results.append((mean, cov))
return results
def get_distribution_data(domain, num_points):
""" Create the multivariate normal distribution and draw a number of samples
from the distribution """
dists = []
data = []
labels = []
for i, (mean, cov) in enumerate(domain):
dist = stats.multivariate_normal(mean, cov)
dists.append(dist)
if num_points > 0:
data.append(dist.rvs(num_points))
labels.append([i]*num_points)
return dists, data, labels
def plot_domains(domains, num_points, draw_lines, from_data, normalized,
fig=None, ax=None, title=None):
""" Visualize a set of multivariate normal distributions, one for each
class of each domain. Optionally estimate from a sample of points drawn
from these distributions rather from the mean/covariance directly, and
optionally from the normalized samples instead. Optionally draw lines
from each domain's class distributions to the center/mean of that domain
for added clarity. """
if fig is None and ax is None:
fig, ax = plt.subplots(figsize=(5, 5))
if not FLAGS.plots_for_paper:
ax.axvline(c='grey', lw=1)
ax.axhline(c='grey', lw=1)
# https://matplotlib.org/stable/tutorials/colors/colors.html
colors = ['C0', 'C1', 'C2', 'C3', 'C4', 'C5', 'C6', 'C7', 'C8', 'C9']
# For each domain
for i, domain in enumerate(domains):
means = np.array([mean for mean, cov in domain])
domain_mean = np.mean(means, axis=0)
# Create distributions and draw samples (if desired) from these
# distributions
_, data, _ = get_distribution_data(domain, num_points)
# If desired, normalize the points
if normalized:
# Compute stats over entire data, not over just one class
all_data = np.vstack(data)
norm = calc_normalization(all_data, "meanstd")
# Then, normalize each class's data
normalized_data = []
for d in data:
normalized_data.append(apply_normalization(d, norm))
data = normalized_data
# Calculate means from data if desired
if from_data:
means = [np.mean(d, axis=0) for d in data]
domain_mean = np.mean(means, axis=0)
# For each class in that domain
for j, (mean, cov) in enumerate(domain):
# Get class color
color = colors[j%len(colors)]
# Label for each class
if i == 0:
label = "Class {}".format(j)
else:
label = None
# Plot some data from the distribution
if num_points > 0:
x1 = data[j][:, 0]
x2 = data[j][:, 1]
ax.scatter(x1, x2, s=1.0, alpha=0.5, c=color)
# Make sure they're numpy arrays
mean = np.array(mean)
cov = np.array(cov)
# Plot the ellipse for the multivariate normal distribution
if from_data:
assert num_points > 0, "if from_data, set num_points > 0"
confidence_ellipse(ax, x=x1, y=x2,
edgecolor=color, alpha=0.5, facecolor=color,
label=label)
# Also overwrite mean, so we use the means from the data
mean = means[j]
else:
confidence_ellipse(ax, mean=mean, cov=cov,
edgecolor=color, alpha=0.5, facecolor=color,
label=label)
# Annotate each center by which source/target it's from, note
# target is at the end
txt = "$T$" if i == len(domains)-1 else "$S_{"+str(i)+"}$"
ax.annotate(txt, (mean[0], mean[1]))
if draw_lines:
# Line from each class center to the domain mean - makes it easier
# to see how domains are translated/rotated
ax.plot([domain_mean[0], mean[0]], [domain_mean[1], mean[1]],
'r-', alpha=0.5)
if not FLAGS.plots_for_paper:
if title is None:
title = "MS-DA Distributions, n={}".format(len(domains)-1)
if from_data and normalized:
title += ", from normalized data"
elif from_data:
title += ", from data"
elif normalized:
title += ", normalized"
ax.set_title(title)
ax.legend()
if fig is None and ax is None:
plt.tight_layout()
def generate_msda_problems(num_sources, num_classes,
center=(0, 0), radius=5, inter_domain_translate=10, inter_domain_rotate=1,
intra_domain_translate=5, intra_domain_rotate=0.5,
dimensions=2, num_points=0, seed=42, draw_lines=False,
from_data=False, normalize=False, fig=None, ax=None, title=None):
""" Generate a single MS-DA problem, for a given value of n, L, radius,
amount of translation/rotation for inter/intra-domain shifts, etc. Plot
the result. """
# Make repeatable
random.seed(seed)
np.random.seed(seed)
# Create domains
target = make_domain(num_classes, center, radius, dimensions)
sources = []
for i in range(num_sources):
sources.append(make_domain(num_classes, center, radius, dimensions,
inter_domain_translate, inter_domain_rotate,
intra_domain_translate, intra_domain_rotate))
# Plot domains
assert dimensions == 2, "Can only plot domains for 2D data at the moment"
# Note: we depend on the target being last for labeling
plot_domains(sources + [target], num_points, draw_lines, from_data,
normalize, fig, ax, title)
return sources, target
def save_plot(name, out="normal_plots", extension="png"):
""" Rather than displaying the plot, save it to a file """
if not os.path.exists(out):
os.makedirs(out)
plt.savefig(os.path.join(out, name+"."+extension), bbox_inches='tight')
plt.close()
def all_problems(num_sources, num_classes, draw_lines=False, center=(25, 25),
inter_scaling=[1], intra_scaling=[1], raw=False,
base_params=None, display=False, suffix=None):
""" Generate all the MS-DA problems for a given value of n and L, varying
inter-domain and/or intra-domain scaling, putting all of these results into
one plot. Both the theoretical distribution (exact from mean/covariance) and
the distribution estimated from 1k normalized points are displayed, to make
clear what may happen when we normalize the data. """
subplot_index = 0
rows = len(inter_scaling) * len(intra_scaling)
cols = 2
# num_plots = rows * cols
if FLAGS.plots_for_paper:
subplots = False
plot_ext = "pdf"
else:
subplots = True
plot_ext = "png"
if subplots:
fig, axs = plt.subplots(rows, cols, figsize=(10, 5*rows))
fig.suptitle("MS-DA Distributions, n={}".format(num_sources))
# For some reason Matplotlib doesn't include the extra dimension if
# it's only 1 row. To make the code below work either way, add dim back.
if rows == 1:
axs = [axs]
# Save space
fig.tight_layout()
# top - make title above plots
# wspace - between columns
# hspace - between rows
plt.subplots_adjust(top=0.93, wspace=0.05*cols, hspace=0.07*rows)
# Which are we varying?
if inter_scaling == [1] and intra_scaling == [1]:
variation = "none"
elif inter_scaling == [1]:
variation = "intra"
elif intra_scaling == [1]:
variation = "inter"
else:
variation = "both"
# Output suffix
if suffix is None:
suffix = ""
else:
suffix = "_" + suffix
# Base inter/intra-domain shifts
if base_params is None:
base_params = [10, 1, 5, 0.5]
for inter_scale in inter_scaling:
for intra_scale in intra_scaling:
assert len(base_params) == 4, "wrong number of base_params"
inter_domain_translate = base_params[0]*inter_scale
inter_domain_rotate = base_params[1]*inter_scale
intra_domain_translate = base_params[2]*intra_scale
intra_domain_rotate = base_params[3]*intra_scale
# Get title
if variation == "none":
title = ""
elif variation == "intra":
title = "intra-scale {}".format(intra_scale)
elif variation == "inter":
title = "inter-scale {}".format(inter_scale)
else:
title = "inter-scale {}, intra-scale {}".format(inter_scale, intra_scale)
name = "normal_n{}_l{}_inter{}_intra{}{}".format(
num_sources, num_classes, inter_scale, intra_scale,
suffix)
# The left column is the un-normalized
if subplots:
ax = axs[subplot_index//cols][subplot_index%cols]
subplot_index += 1
else:
fig = None
ax = None
generate_msda_problems(num_sources, num_classes,
draw_lines=draw_lines, num_points=100, center=center,
inter_domain_translate=inter_domain_translate,
inter_domain_rotate=inter_domain_rotate,
intra_domain_translate=intra_domain_translate,
intra_domain_rotate=intra_domain_rotate,
fig=fig, ax=ax, title=title)
# Check that from data looks the same
# generate_msda_problems(num_sources, num_classes,
# draw_lines=draw_lines, num_points=1000, from_data=True)
# The right column is the from_data/normalized
if subplots:
ax = axs[subplot_index//cols][subplot_index%cols]
subplot_index += 1
else:
fig = None
ax = None
# We only want the normalized plots when we generate subfigures
if subplots:
# Also, check results if we normalize - note only applies when we use this
# data directly rather than generating sines of two frequencies (x1 and x2).
sources, target = generate_msda_problems(num_sources, num_classes,
draw_lines=draw_lines, num_points=1000, from_data=True, normalize=True,
center=center,
inter_domain_translate=inter_domain_translate,
inter_domain_rotate=inter_domain_rotate,
intra_domain_translate=intra_domain_translate,
intra_domain_rotate=intra_domain_rotate,
fig=fig, ax=ax, title=title)
# Generate actual data
if not FLAGS.plots_for_paper:
if raw:
save_data(sources, target, num_classes, name, raw=True,
display=display)
else:
save_data(sources, target, num_classes, name+"_sine",
display=display)
else:
save_plot(name, extension=plot_ext)
# Save plot
if subplots:
save_plot("normal_n{}_l{}_{}{}".format(num_sources, num_classes,
variation, suffix), extension=plot_ext)
def sanity_check_freqs(freqs, sample_freq):
""" Check that no frequencies are negative or over Nyquist sampling rate """
for i, freq in enumerate(freqs):
for j, f in enumerate(freq):
if f < 0 or f > sample_freq/2:
raise ValueError(
"Found frequency {}, which is either <0 or >{}".format(
f, sample_freq/2))
def generate_sine(data):
""" Generate a bunch of univariate time series signals (length matches that
of data) with two sine waves of particular frequencies each
Input format: [(ex1 freq1, ex1 freq2), (ex2 freq1, ex2 freq2), ...]
Outputs: x, y
- x is the time dimension, i.e. from 0 to duration (in seconds)
- y is the amplitude at each point in time, i.e. the signal to be used
for classification, having shape [time_steps, num_examples] where
time_steps = duration * sample_freq
"""
# Config
duration = 0.2 # seconds
sample_freq = 250 # Hz
amp_noise = 0.0 # slight amplitude noise
freq_noise = 0.0 # slight frequency noise
phase_shift = 0.0 # random phase shift
# Generate time series data
freqs = data # [num examples, 2 frequencies]
sanity_check_freqs(freqs, sample_freq)
amps = [1.0, 1.0]
x, y = sine(f=freqs, amps=amps, maxt=duration,
length=duration*sample_freq,
freq_noise=freq_noise, phase_shift=phase_shift)
if amp_noise is not None:
y += np.random.normal(0.0, amp_noise, (y.shape[0], len(data)))
return x, y
def save_single_domain_data(domain, num_points, filename, raw, display=False):
"""
Generate either raw or time series data for each one domain and save that
data (and optionally display a sample)
If raw=True, then write the raw data (2D points) rather than the time series
signals. Num points indicates how many examples to generate.
"""
_, data_by_class, labels_by_class = get_distribution_data(domain, num_points)
data = np.vstack(data_by_class)
labels = np.hstack(labels_by_class)
# Convert to sine waves
if not raw:
# Debugging
if display:
num = 10 # how many from each class to display
for i in range(len(data_by_class)):
x, y = generate_sine(data_by_class[i])
display_xy(x[:, :num], y[:, :num], show=False)
title = "Class {}".format(i)
print(title, data_by_class[i][:num])
plt.title(title)
plt.show()
# Generate data for all classes combined
x, y = generate_sine(data)
# Transpose so we have [examples, time_steps]
data = np.array(y, dtype=np.float32).T
# Expand so we have 1 feature: [examples, time_steps, num_features]
data = np.expand_dims(data, axis=-1)
# Write to file
save_data_file(data, labels, filename)
def save_data(sources, target, num_classes, name,
num_train_points=10000, num_test_points=1000,
out="datasets/synthetic", raw=False, display=False):
""" Save data for each source domain and the target domain """
if not os.path.exists(out):
os.makedirs(out)
# We want this many points total, but they're generated per-class
num_train_points = num_train_points // num_classes
num_test_points = num_test_points // num_classes
for i, source in enumerate(sources):
save_single_domain_data(source, num_train_points,
'{}/{}_s{}_TRAIN'.format(out, name, i), raw, display)
save_single_domain_data(source, num_test_points,
'{}/{}_s{}_TEST'.format(out, name, i), raw, display)
save_single_domain_data(target, num_train_points,
'{}/{}_t_TRAIN'.format(out, name), raw, display)
save_single_domain_data(target, num_test_points,
'{}/{}_t_TEST'.format(out, name), raw, display)
def main(argv):
# Test inter/intra translate/rotate each separately
# n=4, L=3
all_problems(num_sources=4, num_classes=3, draw_lines=True,
base_params=[5, 0, 0, 0], inter_scaling=[0, 1, 2],
suffix="5,0,0,0")
all_problems(num_sources=4, num_classes=3, draw_lines=True,
base_params=[0, 0.5, 0, 0], inter_scaling=[0, 1, 2],
suffix="0,0.5,0,0")
all_problems(num_sources=4, num_classes=3, draw_lines=True,
base_params=[0, 0, 5, 0], intra_scaling=[0, 1, 2],
suffix="0,0,5,0")
all_problems(num_sources=4, num_classes=3, draw_lines=True,
base_params=[0, 0, 0, 0.5], intra_scaling=[0, 1, 2],
suffix="0,0,0,0.5")
# n=12, L=3 -- so we have n=2, 4, 6, 8, 10 and 10 has 3 diff. sets available
all_problems(num_sources=12, num_classes=3, draw_lines=True,
base_params=[5, 0, 0, 0], inter_scaling=[0, 1, 2],
suffix="5,0,0,0")
all_problems(num_sources=12, num_classes=3, draw_lines=True,
base_params=[0, 0.5, 0, 0], inter_scaling=[0, 1, 2],
suffix="0,0.5,0,0")
all_problems(num_sources=12, num_classes=3, draw_lines=True,
base_params=[0, 0, 5, 0], intra_scaling=[0, 1, 2],
suffix="0,0,5,0")
all_problems(num_sources=12, num_classes=3, draw_lines=True,
base_params=[0, 0, 0, 0.5], intra_scaling=[0, 1, 2],
suffix="0,0,0,0.5")
if __name__ == "__main__":
app.run(main)