Applied Machine Learning: Unsupervised Learning¶
- Unsupervised learning involves tasks that operate on datasets without labeled repsonses or target values
- Instead, the goal is to capture interesting structure or information
Applications of unsupervised learning:
- Visualize structure of a complex dataset
- Density estimation to predict probabilities of events
- Compress and summarize the data
- Extract features for supervised learning
- Discover important clusters or outliers
Two major types of unsupervised learning methods:
- Transformations
- Processes that extract or compute information
- Clustering
- Find groups in the data
- Assign every point in the dataset to one of the groups
Preamble and Datasets¶
%matplotlib notebook
import numpy as np
import pandas as pd
import seaborn as sn
import matplotlib.pyplot as plt
from sklearn.datasets import load_breast_cancer
# Breast cancer dataset
cancer = load_breast_cancer()
(X_cancer, y_cancer) = load_breast_cancer(return_X_y = True)
# Our sample fruits dataset
fruits = pd.read_table('fruit_data_with_colors.txt')
X_fruits = fruits[['mass','width','height', 'color_score']]
y_fruits = fruits[['fruit_label']] - 1
Dimensionality Reduction and Manifold Learning¶
The transformation category are known as dimensionality reduction algorithms. One every common need for dimensionality reduction arises when first exploring a dataset to understand how the samples may be grouped or related to each other by visualizing it using a two-dimensional scatterplot. One very important form of dimensionality reduction is called principal component analysis (PCA). Intuitively, what PCA does is take your cloud of original data points and finds a rotation of it, so the dimensions are statistically uncorrelated, PCA then typically drops all but the most informative initial dimensions that capture most of the variation in the original datset.
Principal Components Analysis (PCA)¶
Using PCA to find the first two principal components of the breast cancer dataset¶
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.datasets import load_breast_cancer
cancer = load_breast_cancer()
(X_cancer, y_cancer) = load_breast_cancer(return_X_y = True)
# Before applying PCA, each feature should be centered (zero mean) and with unit variance
X_normalized = StandardScaler().fit(X_cancer).transform(X_cancer)
pca = PCA(n_components = 2).fit(X_normalized)
X_pca = pca.transform(X_normalized)
print(X_cancer.shape, X_pca.shape)
Plotting the PCA-transformed version of the breast cancer dataset¶
from adspy_shared_utilities import plot_labelled_scatter
plot_labelled_scatter(X_pca, y_cancer, ['malignant', 'benign'])
plt.xlabel('First principal component')
plt.ylabel('Second principal component')
plt.title('Breast Cancer Dataset PCA (n_components = 2)');
Plotting the magnitude of each feature value for the first two principal components¶
fig = plt.figure(figsize=(8, 4))
plt.imshow(pca.components_, interpolation = 'none', cmap = 'plasma')
feature_names = list(cancer.feature_names)
plt.gca().set_xticks(np.arange(-.5, len(feature_names)));
plt.gca().set_yticks(np.arange(0.5, 2));
plt.gca().set_xticklabels(feature_names, rotation=90, ha='left', fontsize=12);
plt.gca().set_yticklabels(['First PC', 'Second PC'], va='bottom', fontsize=12);
plt.colorbar(orientation='horizontal', ticks=[pca.components_.min(), 0,
pca.components_.max()], pad=0.65);
PCA on the fruit dataset (for comparison)¶
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
# each feature should be centered (zero mean) and with unit variance
X_normalized = StandardScaler().fit(X_fruits).transform(X_fruits)
pca = PCA(n_components = 2).fit(X_normalized)
X_pca = pca.transform(X_normalized)
from adspy_shared_utilities import plot_labelled_scatter
plot_labelled_scatter(X_pca, y_fruits, ['apple','mandarin','orange','lemon'])
plt.xlabel('First principal component')
plt.ylabel('Second principal component')
plt.title('Fruits Dataset PCA (n_components = 2)');
Manifold learning methods¶
Multidimensional scaling (MDS) on the fruit dataset¶
from adspy_shared_utilities import plot_labelled_scatter
from sklearn.preprocessing import StandardScaler
from sklearn.manifold import MDS
# each feature should be centered (zero mean) and with unit variance
X_fruits_normalized = StandardScaler().fit(X_fruits).transform(X_fruits)
mds = MDS(n_components = 2)
X_fruits_mds = mds.fit_transform(X_fruits_normalized)
plot_labelled_scatter(X_fruits_mds, y_fruits, ['apple', 'mandarin', 'orange', 'lemon'])
plt.xlabel('First MDS feature')
plt.ylabel('Second MDS feature')
plt.title('Fruit sample dataset MDS');
Multidimensional scaling (MDS) on the breast cancer dataset¶
(This example is not covered in the lecture video, but is included here so you can compare it to the results from PCA.)
from sklearn.preprocessing import StandardScaler
from sklearn.manifold import MDS
from sklearn.datasets import load_breast_cancer
cancer = load_breast_cancer()
(X_cancer, y_cancer) = load_breast_cancer(return_X_y = True)
# each feature should be centered (zero mean) and with unit variance
X_normalized = StandardScaler().fit(X_cancer).transform(X_cancer)
mds = MDS(n_components = 2)
X_mds = mds.fit_transform(X_normalized)
from adspy_shared_utilities import plot_labelled_scatter
plot_labelled_scatter(X_mds, y_cancer, ['malignant', 'benign'])
plt.xlabel('First MDS dimension')
plt.ylabel('Second MDS dimension')
plt.title('Breast Cancer Dataset MDS (n_components = 2)');
t-SNE on the fruit dataset¶
(This example from the lecture video is included so that you can see how some dimensionality reduction methods may be less successful on some datasets. Here, it doesn't work as well at finding structure in the small fruits dataset, compared to other methods like MDS.)
from sklearn.manifold import TSNE
tsne = TSNE(random_state = 0)
X_tsne = tsne.fit_transform(X_fruits_normalized)
plot_labelled_scatter(X_tsne, y_fruits,
['apple', 'mandarin', 'orange', 'lemon'])
plt.xlabel('First t-SNE feature')
plt.ylabel('Second t-SNE feature')
plt.title('Fruits dataset t-SNE');
t-SNE on the breast cancer dataset¶
Although not shown in the lecture video, this example is included for comparison, showing the results of running t-SNE on the breast cancer dataset. See the reading "How to Use t-SNE effectively" for further details on how the visualizations from t-SNE are affected by specific parameter settings.
tsne = TSNE(random_state = 0)
X_tsne = tsne.fit_transform(X_normalized)
plot_labelled_scatter(X_tsne, y_cancer,
['malignant', 'benign'])
plt.xlabel('First t-SNE feature')
plt.ylabel('Second t-SNE feature')
plt.title('Breast cancer dataset t-SNE');
Clustering¶
K-means¶
This example from the lecture video creates an artificial dataset with make_blobs, then applies k-means to find 3 clusters, and plots the points in each cluster identified by a corresponding color.
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
from adspy_shared_utilities import plot_labelled_scatter
X, y = make_blobs(random_state = 10)
kmeans = KMeans(n_clusters = 3)
kmeans.fit(X)
plot_labelled_scatter(X, kmeans.labels_, ['Cluster 1', 'Cluster 2', 'Cluster 3'])
Example showing k-means used to find 4 clusters in the fruits dataset. Note that in general, it's important to scale the individual features before applying k-means clustering.
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
from adspy_shared_utilities import plot_labelled_scatter
from sklearn.preprocessing import MinMaxScaler
fruits = pd.read_table('fruit_data_with_colors.txt')
X_fruits = fruits[['mass','width','height', 'color_score']].as_matrix()
y_fruits = fruits[['fruit_label']] - 1
X_fruits_normalized = MinMaxScaler().fit(X_fruits).transform(X_fruits)
kmeans = KMeans(n_clusters = 4, random_state = 0)
kmeans.fit(X_fruits_normalized)
plot_labelled_scatter(X_fruits_normalized, kmeans.labels_,
['Cluster 1', 'Cluster 2', 'Cluster 3', 'Cluster 4'])
Agglomerative clustering¶
from sklearn.datasets import make_blobs
from sklearn.cluster import AgglomerativeClustering
from adspy_shared_utilities import plot_labelled_scatter
X, y = make_blobs(random_state = 10)
cls = AgglomerativeClustering(n_clusters = 3)
cls_assignment = cls.fit_predict(X)
plot_labelled_scatter(X, cls_assignment,
['Cluster 1', 'Cluster 2', 'Cluster 3'])
Creating a dendrogram (using scipy)¶
This dendrogram plot is based on the dataset created in the previous step with make_blobs, but for clarity, only 10 samples have been selected for this example, as plotted here:
X, y = make_blobs(random_state = 10, n_samples = 10)
plot_labelled_scatter(X, y,
['Cluster 1', 'Cluster 2', 'Cluster 3'])
print(X)
And here's the dendrogram corresponding to agglomerative clustering of the 10 points above using Ward's method. The index 0..9 of the points corresponds to the index of the points in the X array above. For example, point 0 (5.69, -9.47) and point 9 (5.43, -9.76) are the closest two points and are clustered first.
from scipy.cluster.hierarchy import ward, dendrogram
plt.figure()
dendrogram(ward(X))
plt.show()
DBSCAN clustering¶
from sklearn.cluster import DBSCAN
from sklearn.datasets import make_blobs
X, y = make_blobs(random_state = 9, n_samples = 25)
dbscan = DBSCAN(eps = 2, min_samples = 2)
cls = dbscan.fit_predict(X)
print("Cluster membership values:\n{}".format(cls))
plot_labelled_scatter(X, cls + 1,
['Noise', 'Cluster 0', 'Cluster 1', 'Cluster 2'])
