124 lines
4.6 KiB
Python
124 lines
4.6 KiB
Python
"""
|
|
=============================================
|
|
A demo of the Spectral Biclustering algorithm
|
|
=============================================
|
|
|
|
This example demonstrates how to generate a checkerboard dataset and bicluster
|
|
it using the :class:`~sklearn.cluster.SpectralBiclustering` algorithm. The
|
|
spectral biclustering algorithm is specifically designed to cluster data by
|
|
simultaneously considering both the rows (samples) and columns (features) of a
|
|
matrix. It aims to identify patterns not only between samples but also within
|
|
subsets of samples, allowing for the detection of localized structure within the
|
|
data. This makes spectral biclustering particularly well-suited for datasets
|
|
where the order or arrangement of features is fixed, such as in images, time
|
|
series, or genomes.
|
|
|
|
The data is generated, then shuffled and passed to the spectral biclustering
|
|
algorithm. The rows and columns of the shuffled matrix are then rearranged to
|
|
plot the biclusters found.
|
|
"""
|
|
|
|
# Author: Kemal Eren <kemal@kemaleren.com>
|
|
# License: BSD 3 clause
|
|
|
|
# %%
|
|
# Generate sample data
|
|
# --------------------
|
|
# We generate the sample data using the
|
|
# :func:`~sklearn.datasets.make_checkerboard` function. Each pixel within
|
|
# `shape=(300, 300)` represents with it's color a value from a uniform
|
|
# distribution. The noise is added from a normal distribution, where the value
|
|
# chosen for `noise` is the standard deviation.
|
|
#
|
|
# As you can see, the data is distributed over 12 cluster cells and is
|
|
# relatively well distinguishable.
|
|
from matplotlib import pyplot as plt
|
|
|
|
from sklearn.datasets import make_checkerboard
|
|
|
|
n_clusters = (4, 3)
|
|
data, rows, columns = make_checkerboard(
|
|
shape=(300, 300), n_clusters=n_clusters, noise=10, shuffle=False, random_state=42
|
|
)
|
|
|
|
plt.matshow(data, cmap=plt.cm.Blues)
|
|
plt.title("Original dataset")
|
|
_ = plt.show()
|
|
|
|
# %%
|
|
# We shuffle the data and the goal is to reconstruct it afterwards using
|
|
# :class:`~sklearn.cluster.SpectralBiclustering`.
|
|
import numpy as np
|
|
|
|
# Creating lists of shuffled row and column indices
|
|
rng = np.random.RandomState(0)
|
|
row_idx_shuffled = rng.permutation(data.shape[0])
|
|
col_idx_shuffled = rng.permutation(data.shape[1])
|
|
|
|
# %%
|
|
# We redefine the shuffled data and plot it. We observe that we lost the
|
|
# structure of original data matrix.
|
|
data = data[row_idx_shuffled][:, col_idx_shuffled]
|
|
|
|
plt.matshow(data, cmap=plt.cm.Blues)
|
|
plt.title("Shuffled dataset")
|
|
_ = plt.show()
|
|
|
|
# %%
|
|
# Fitting `SpectralBiclustering`
|
|
# ------------------------------
|
|
# We fit the model and compare the obtained clusters with the ground truth. Note
|
|
# that when creating the model we specify the same number of clusters that we
|
|
# used to create the dataset (`n_clusters = (4, 3)`), which will contribute to
|
|
# obtain a good result.
|
|
from sklearn.cluster import SpectralBiclustering
|
|
from sklearn.metrics import consensus_score
|
|
|
|
model = SpectralBiclustering(n_clusters=n_clusters, method="log", random_state=0)
|
|
model.fit(data)
|
|
|
|
# Compute the similarity of two sets of biclusters
|
|
score = consensus_score(
|
|
model.biclusters_, (rows[:, row_idx_shuffled], columns[:, col_idx_shuffled])
|
|
)
|
|
print(f"consensus score: {score:.1f}")
|
|
|
|
# %%
|
|
# The score is between 0 and 1, where 1 corresponds to a perfect matching. It
|
|
# shows the quality of the biclustering.
|
|
|
|
# %%
|
|
# Plotting results
|
|
# ----------------
|
|
# Now, we rearrange the data based on the row and column labels assigned by the
|
|
# :class:`~sklearn.cluster.SpectralBiclustering` model in ascending order and
|
|
# plot again. The `row_labels_` range from 0 to 3, while the `column_labels_`
|
|
# range from 0 to 2, representing a total of 4 clusters per row and 3 clusters
|
|
# per column.
|
|
|
|
# Reordering first the rows and then the columns.
|
|
reordered_rows = data[np.argsort(model.row_labels_)]
|
|
reordered_data = reordered_rows[:, np.argsort(model.column_labels_)]
|
|
|
|
plt.matshow(reordered_data, cmap=plt.cm.Blues)
|
|
plt.title("After biclustering; rearranged to show biclusters")
|
|
_ = plt.show()
|
|
|
|
# %%
|
|
# As a last step, we want to demonstrate the relationships between the row
|
|
# and column labels assigned by the model. Therefore, we create a grid with
|
|
# :func:`numpy.outer`, which takes the sorted `row_labels_` and `column_labels_`
|
|
# and adds 1 to each to ensure that the labels start from 1 instead of 0 for
|
|
# better visualization.
|
|
plt.matshow(
|
|
np.outer(np.sort(model.row_labels_) + 1, np.sort(model.column_labels_) + 1),
|
|
cmap=plt.cm.Blues,
|
|
)
|
|
plt.title("Checkerboard structure of rearranged data")
|
|
plt.show()
|
|
|
|
# %%
|
|
# The outer product of the row and column label vectors shows a representation
|
|
# of the checkerboard structure, where different combinations of row and column
|
|
# labels are represented by different shades of blue.
|