I am working creating a PCA combined with a Mahalanobis distance function to remove any outliers detected from the PCA transformation. I have come across this article which uses R: Mahalanobis output in R.
However, how do I implement the Mahalanobis with Python and get an ellipse to centre around the cluster.
Some sample data and plot:
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn.decomposition import PCA
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
from sklearn.preprocessing import StandardScaler
from sklearn.covariance import EmpiricalCovariance, MinCovDet
iris = datasets.load_iris()
X = iris.data
y = iris.target
target_names = iris.target_names
steps = [
("preprocessing", StandardScaler()),
("pca", PCA()),]
pipe = Pipeline(steps)
searchPCA = GridSearchCV(pipe, { "pca__n_components": [1, 2,3]}, n_jobs = 3)
searchPCA.fit(X)
DF = searchPCA.transform(X)
plt.figure()
colors = ["navy", "turquoise", "darkorange"]
lw = 2
for color, i, target_name in zip(colors, [0, 1, 2], target_names):
plt.scatter(
DF[y == i, 0], DF[y == i, 1], color=color, alpha=0.8, lw=lw, label=target_name
)
plt.legend(loc="best", shadow=False, scatterpoints=1)
plt.title("PCA of IRIS dataset")
xx, yy = np.meshgrid(
np.linspace(plt.xlim()[0], plt.xlim()[1], 100),
np.linspace(plt.ylim()[0], plt.ylim()[1], 100),)
zz = np.c_[xx.ravel(), yy.ravel()]
robust_cov = MinCovDet().fit(DF[y == i,0:2])
mahal_robust_cov = robust_cov.mahalanobis(zz)
mahal_robust_cov = mahal_robust_cov.reshape(xx.shape)
plt.contour(
xx, yy, np.sqrt(mahal_robust_cov), cmap=plt.cm.YlOrBr_r, linestyles="dashed", levels=[3])
EDIT:
This plots a contour and I managed to get all three ellipses for each cluster however I get part of the circle edge missing, how to fill these all in?
Please add plt.xlim() and plt.ylim():
plt.legend(loc="best", shadow=False, scatterpoints=1)
plt.title("PCA of IRIS dataset")
plt.xlim(-3,4) # ADD
plt.ylim(-3,3) # ADD
xx, yy = np.meshgrid(
np.linspace(plt.xlim()[0], plt.xlim()[1], 100),
np.linspace(plt.ylim()[0], plt.ylim()[1], 100),)
zz = np.c_[xx.ravel(), yy.ravel()]
How do I add legend to the plot over in my scenario? the parameter of text is the text = tfidf.transform(document) and the parameter of clusters are the unsupervised clusters ranging from 0 to 19 clusters and have their bag of words. How do I add the legend to the plots? It is indistinguishable that which color corresponds to which cluster.
def plot_tsne_pca(data, labels):
max_label = max(labels)
max_items = np.random.choice(range(data.shape[0]), size=3000, replace=False)
pca = PCA(n_components=2).fit_transform(data[max_items,:].todense())
tsne = TSNE().fit_transform(PCA(n_components=50).fit_transform(data[max_items,:].todense()))
idx = np.random.choice(range(pca.shape[0]), size=3000, replace=False)
label_subset = labels[max_items]
label_subset = [cm.hsv(i/max_label) for i in label_subset[idx]]
f, ax = plt.subplots(1, 2, figsize=(20, 6))
ax[0].scatter(pca[idx, 0], pca[idx, 1], c=label_subset)
ax[0].set_title('PCA Cluster Plot')
ax[1].scatter(tsne[idx, 0], tsne[idx, 1], c=label_subset)
ax[1].set_title('TSNE Cluster Plot')
plot_tsne_pca(text, clusters)
Here is the full example of the code: https://pastebin.com/3PABg7xh
You can use legend_elements() to automatically return the lists of artists/labels (or a subset thereof) for legend creation. See Automated legend creation for more details
import matplotlib.pyplot as plt
from matplotlib import offsetbox
from sklearn import (manifold, datasets)
digits = datasets.load_digits(n_class=6)
X = digits.data
y = digits.target
tsne = manifold.TSNE(n_components=2, init='pca', random_state=0)
X_tsne = tsne.fit_transform(X)
fig, ax = plt.subplots()
sc = ax.scatter(X_tsne[:,0], X_tsne[:,1], c=y, cmap='tab10')
ax.legend(*sc.legend_elements(), title='clusters')
EDIT
In your particular case, the code was not working because legend_elements() is meant to be used when you have a mapping between a numeric c= list and a colormap. But instead, you were passing a list of colors that you constructed by hand (label_subset = [cm.hsv(i/max_label) for i in label_subset[idx]]). If you remove that line and keep a numeric label_subset and map it to colors using cmap= then everything works as expected
def plot_tsne_pca(data, labels, sizelist, cmap='tab10'):
max_label = max(labels)
max_items = np.random.choice(range(data.shape[0]), sizelist, replace=False)
pca = PCA(n_components=2).fit_transform(data[max_items, :].todense())
tsne = TSNE().fit_transform(PCA(n_components=1).fit_transform(data[max_items, :].todense()))
idx = np.random.choice(range(pca.shape[0]), sizelist, replace=False)
label_subset = labels[max_items]
#label_subset = [cm.hsv(i / max_label) for i in label_subset[idx]]
f, ax = plt.subplots(1, 2, figsize=(20, 6))
ax[0].scatter(pca[idx, 0], pca[idx, 1], c=label_subset, cmap=cmap)
ax[0].set_title('PCA Cluster Plot')
sc = ax[1].scatter(tsne[idx, 0], tsne[idx, 1], c=label_subset, cmap=cmap)
ax[1].set_title('TSNE Cluster Plot')
ax[1].legend(*sc.legend_elements(), title='clusters')
plot_tsne_pca(text, clusters, sizelist)
I'm hoping to use k-means clustering to plot and return the position of each cluster's centroid. The following groups two sets of xy scatter points into 6 clusters.
Using the df below, the coordinates in A and B and C and D are plotted as a scatter. I'm hoping to plot and return the centroid of each cluster.
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from sklearn.cluster import KMeans
df = pd.DataFrame(np.random.randint(-50,50,size=(100, 4)), columns=list('ABCD'))
fig, ax = plt.subplots()
Y_sklearn = df[['A','B','C','D']].values
model = KMeans(n_clusters = 4)
model.fit(Y_sklearn)
plt.scatter(Y_sklearn[:,0],Y_sklearn[:,1], c = model.labels_);
plt.scatter(Y_sklearn[:,2],Y_sklearn[:,3], c = model.labels_);
plt.show()
Solution
When you make a plot from KMeans prediction, if the number of features are more than two, you can only select two of the features (in your case, say, columns A and B) as the x and y coordinates on the 2D plane of the scatterplot. A better way to properly represent your higher-dimensional data on a 2D-plane would be some form of dimension-reduction: such as PCA. However, to keep the scope of this answer manageable I am only resorting to using the first two columns of the data X_train or X_test below and NOT using PCA to get the most important two dimensions.
I tried writing this answer so that anyone could start from zero experience and still follow along the code and run it to see what it does. Yes, it is long, and hence I have broken it down into multiple sections, so you could skip them if needed.
⭐For your convenience you could get the entire code in this colab notebook:
🔥
⭐⭐⭐ Jump to Section G to see the code used to make the plots.
👉 👉 👉 Section A gives a summary and is useful if you are just interested in the code to add the cluster-centers to your scatterplot.
List of Sections
A. Identification of Clusters in Data using KMeans Method
B. Import Libraries
C. Dummy Data
D. Custom Functions
E. Calculate True Cluster Centers
F. Define, Fit and Predict using KMeans Model
F.1. Predict for y_train using X_train
F.2. Predict for y_test using X_test
G. Make Figure with train, test and prediction data
References
A. Identification of Clusters in Data using KMeans Method
We will use sklearn.cluster.KMeans to identify the clusters. The attribute model.cluster_centers_ will give us the predicted cluster centers. Say, we want to find out 5 clusters in our training data, X_train with shape: (n_samples, n_features) and labels, y_train with shape: (n_samples,). The following code block fits the model to the data (X_train) and then predicts y and saves the prediction in y_pred_train variable.
# Define model
model = KMeans(n_clusters = 5)
# Fit model to training data
model.fit(X_train)
# Make prediction on training data
y_pred_train = model.predict(X_train)
# Get predicted cluster centers
model.cluster_centers_ # shape: (n_cluster, n_features)
## Displaying cluster centers on a plot
# if you just want to add cluster centers
# to your existing scatter-plot,
# just do this --->>
cluster_centers = model.cluster_centers_
plt.scatter(cluster_centers[:, 0], cluster_centers[:, 1],
marker='s', color='orange', s = 100,
alpha=0.5, label='pred')
This is the result ⭐⭐⭐ Jump to section G to see the code used to make the plots.
B. Import Libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
import pprint
%matplotlib inline
%config InlineBackend.figure_format = 'svg' # 'svg', 'retina'
plt.style.use('seaborn-white')
C. Dummy Data
We will use data generated in the following code-block. By design we create a dataset with 5 clusters and the following specifications. And then split the data into train and test blocks using sklearn.model_selection.train_test_split.
## Creating data with
# n_samples = 2500
# n_features = 4
# Expected clusters = 5
# centers = 5
# cluster_std = [1.0, 2.5, 0.5, 1.5, 2.0]
NUM_SAMPLES = 2500
RANDOM_STATE = 42
NUM_FEATURES = 4
NUM_CLUSTERS = 5
CLUSTER_STD = [1.0, 2.5, 0.5, 1.5, 2.0]
TEST_SIZE = 0.20
def dummy_data():
## Creating data with
# n_samples = 2500
# n_features = 4
# Expected clusters = 5
# centers = 5
# cluster_std = [1.0, 2.5, 0.5, 1.5, 2.0]
X, y = make_blobs(
n_samples = NUM_SAMPLES,
random_state = RANDOM_STATE,
n_features = NUM_FEATURES,
centers = NUM_CLUSTERS,
cluster_std = CLUSTER_STD
)
return X, y
def test_dummy_data(X, y):
assert X.shape == (NUM_SAMPLES, NUM_FEATURES), "Shape mismatch for X"
assert set(y) == set(np.arange(NUM_CLUSTERS)), "NUM_CLUSTER mismatch for y"
## D. Create Dummy Data
X, y = dummy_data()
test_dummy_data(X, y)
## Create train-test-split
X_train, X_test, y_train, y_test = train_test_split(
X, y, test_size=TEST_SIZE, random_state=RANDOM_STATE)
D. Custom Functions
We will use the following 3 custom defined functions:
get_cluster_centers()
scatterplot()
add_cluster_centers()
def get_cluster_centers(X, y, num_clusters=None):
"""Returns the cluster-centers as numpy.array of
shape: (num_cluster, num_features).
"""
num_clusters = NUM_CLUSTERS if (num_clusters is None) else num_clusters
return np.stack([X[y==i].mean(axis=0) for i in range(NUM_CLUSTERS)])
def scatterplot(X, y,
cluster_centers=None,
alpha=0.5,
cmap='viridis',
legend_title="Classes",
legend_loc="upper left",
ax=None):
if ax is not None:
plt.sca(ax)
scatter = plt.scatter(X[:, 0], X[:, 1],
s=None, c=y, alpha=alpha, cmap=cmap)
legend = ax.legend(*scatter.legend_elements(),
loc=legend_loc, title=legend_title)
ax.add_artist(legend)
if cluster_centers is not None:
plt.scatter(cluster_centers[:, 0], cluster_centers[:, 1],
marker='o', color='red', alpha=1.0)
ax = plt.gca()
return ax
def add_cluster_centers(true_cluster_centers=None,
pred_cluster_centers=None,
markers=('o', 's'),
colors=('red, ''orange'),
s = (None, 200),
alphas = (1.0, 0.5),
center_labels = ('true', 'pred'),
legend_title = "Cluster Centers",
legend_loc = "upper right",
ax = None):
if ax is not None:
plt.sca(ax)
for idx, cluster_centers in enumerate([true_cluster_centers,
pred_cluster_centers]):
if cluster_centers is not None:
scatter = plt.scatter(
cluster_centers[:, 0], cluster_centers[:, 1],
marker = markers[idx],
color = colors[idx],
s = s[idx],
alpha = alphas[idx],
label = center_labels[idx]
)
legend = ax.legend(loc=legend_loc, title=legend_title)
ax.add_artist(legend)
return ax
E. Calculate True Cluster Centers
We will calculate the true cluster centers for train and test datasets and save the results to a dict: true_cluster_centers.
true_cluster_centers = {
'train': get_cluster_centers(X = X_train, y = y_train, num_clusters = NUM_CLUSTERS),
'test': get_cluster_centers(X = X_test, y = y_test, num_clusters = NUM_CLUSTERS)
}
# Show result
pprint.pprint(true_cluster_centers, indent=2)
Output:
{ 'test': array([[-2.44425795, 9.06004013, 4.7765817 , 2.02559904],
[-6.68967507, -7.09292101, -8.90860337, 7.16545582],
[ 1.99527271, 4.11374524, -9.62610383, 9.32625443],
[ 6.46362854, -5.90122349, -6.2972843 , -6.04963714],
[-4.07799392, 0.61599582, -1.82653858, -4.34758032]]),
'train': array([[-2.49685525, 9.08826 , 4.64928719, 2.01326914],
[-6.82913109, -6.86790673, -8.99780554, 7.39449295],
[ 2.04443863, 4.12623661, -9.64146529, 9.39444917],
[ 6.74707792, -5.83405806, -6.3480674 , -6.37184345],
[-3.98420601, 0.45335025, -1.23919526, -3.98642807]])}
F. Define, Fit and Predict using KMeans Model
model = KMeans(n_clusters = NUM_CLUSTERS, random_state = RANDOM_STATE)
model.fit(X_train)
## Output
# KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,
# n_clusters=5, n_init=10, n_jobs=None, precompute_distances='auto',
# random_state=42, tol=0.0001, verbose=0)
F.1. Predict for y_train using X_train
## Process Prediction: train data
y_pred_train = model.predict(X_train)
# get model predicted cluster-centers
pred_train_cluster_centers = model.cluster_centers_ # shape: (n_cluster, n_features)
# sanity check
assert all([
y_pred_train.shape == (NUM_SAMPLES * (1 - TEST_SIZE),),
set(y_pred_train) == set(y_train)
])
F.2. Predict for y_test using X_test
## Process Prediction: test data
y_pred_test = model.predict(X_test)
# get model predicted cluster-centers
pred_test_cluster_centers = model.cluster_centers_ # shape: (n_cluster, n_features)
# sanity check
assert all([
y_pred_test.shape == (NUM_SAMPLES * TEST_SIZE,),
set(y_pred_test) == set(y_test)
])
G. Make Figure with train, test and prediction data
fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(15, 6))
FONTSIZE = {'title': 16, 'suptitle': 20}
TITLE = {
'train': 'Train Data Clusters',
'test': 'Test Data Clusters',
'suptitle': 'Cluster Identification using KMeans Method',
}
CENTER_LEGEND_LABELS = ('true', 'pred')
LAGEND_PARAMS = {
'data': {'title': "Classes", 'loc': "upper left"},
'cluster_centers': {'title': "Cluster Centers", 'loc': "upper right"}
}
SCATTER_ALPHA = 0.4
CMAP = 'viridis'
CLUSTER_CENTER_PLOT_PARAMS = dict(
markers = ('o', 's'),
colors = ('red', 'orange'),
s = (None, 200),
alphas = (1.0, 0.5),
center_labels = CENTER_LEGEND_LABELS,
legend_title = LAGEND_PARAMS['cluster_centers']['title'],
legend_loc = LAGEND_PARAMS['cluster_centers']['loc']
)
SCATTER_PLOT_PARAMS = dict(
alpha = SCATTER_ALPHA,
cmap = CMAP,
legend_title = LAGEND_PARAMS['data']['title'],
legend_loc = LAGEND_PARAMS['data']['loc'],
)
## plot train data
data_label = 'train'
ax = axs[0]
plt.sca(ax)
ax = scatterplot(X = X_train, y = y_train,
cluster_centers = None,
ax = ax, **SCATTER_PLOT_PARAMS)
ax = add_cluster_centers(
true_cluster_centers = true_cluster_centers[data_label],
pred_cluster_centers = pred_train_cluster_centers,
ax = ax, **CLUSTER_CENTER_PLOT_PARAMS)
plt.title(TITLE[data_label], fontsize = FONTSIZE['title'])
## plot test data
data_label = 'test'
ax = axs[1]
plt.sca(ax)
ax = scatterplot(X = X_test, y = y_test,
cluster_centers = None,
ax = ax, **SCATTER_PLOT_PARAMS)
ax = add_cluster_centers(
true_cluster_centers = true_cluster_centers[data_label],
pred_cluster_centers = pred_test_cluster_centers,
ax = ax, **CLUSTER_CENTER_PLOT_PARAMS)
plt.title(TITLE[data_label], fontsize = FONTSIZE['title'])
plt.suptitle(TITLE['suptitle'],
fontsize = FONTSIZE['suptitle'])
plt.show()
# save figure
fig.savefig("kmeans_fit_result.png", dpi=300)
Result:
References
Documentation: sklearn.cluster.KMeans
Documnetation: sklearn.model_selection.train_test_split
Documentation: matplotlib.pyplot.legend
Documentation: sklearn.decomposition.PCA
Managing legend in scatterplot using matplotlib
Demo of KMeans Assumptions
Based on how you make the scatter plot, I guess A and B correspond to the xy coordinates of the first set of points, while C and D correspond to the xy coordinates of the second set of points. If so, you cannot apply Kmeans to the dataframe directly, since there are only two features, i.e., x and y coordinates. Finding the centroids is actually quite simple, all you need is model_zero.cluster_centers_.
Let's first construct a dataframe that will be better for visualization
import numpy as np
# set the seed for reproducible datasets
np.random.seed(365)
# cov matrix of a 2d gaussian
stds = np.eye(2)
# four cluster means
means_zero = np.random.randint(10,20,(4,2))
sizes_zero = np.array([20,30,15,35])
# four cluster means
means_one = np.random.randint(0,10,(4,2))
sizes_one = np.array([20,20,25,35])
points_zero = np.vstack([np.random.multivariate_normal(mean,stds,size=(size)) for mean,size in zip(means_zero,sizes_zero)])
points_one = np.vstack([np.random.multivariate_normal(mean,stds,size=(size)) for mean,size in zip(means_one,sizes_one)])
all_points = np.hstack((points_zero,points_one))
As you can see, the four clusters are constructed by sampling points from four Gaussians with different means. With this dataframe, here is how you can plot it
import matplotlib.patheffects as PathEffects
from sklearn.cluster import KMeans
df = pd.DataFrame(all_points, columns=list('ABCD'))
fig, ax = plt.subplots(figsize=(10,8))
scatter_zero = df[['A','B']].values
scatter_one = df[['C','D']].values
model_zero = KMeans(n_clusters=4)
model_zero.fit(scatter_zero)
model_one = KMeans(n_clusters=4)
model_one.fit(scatter_one)
plt.scatter(scatter_zero[:,0],scatter_zero[:,1],c=model_zero.labels_,cmap='bwr');
plt.scatter(scatter_one[:,0],scatter_one[:,1],c=model_one.labels_,cmap='bwr');
# plot the cluster centers
txts = []
for ind,pos in enumerate(model_zero.cluster_centers_):
txt = ax.text(pos[0],pos[1],
'cluster %i \n (%.1f,%.1f)' % (ind,pos[0],pos[1]),
fontsize=12,zorder=100)
txt.set_path_effects([PathEffects.Stroke(linewidth=5, foreground="aquamarine"),PathEffects.Normal()])
txts.append(txt)
for ind,pos in enumerate(model_one.cluster_centers_):
txt = ax.text(pos[0],pos[1],
'cluster %i \n (%.1f,%.1f)' % (ind,pos[0],pos[1]),
fontsize=12,zorder=100)
txt.set_path_effects([PathEffects.Stroke(linewidth=5, foreground="lime"),PathEffects.Normal()])
txts.append(txt)
zero_mean = np.mean(model_zero.cluster_centers_,axis=0)
one_mean = np.mean(model_one.cluster_centers_,axis=0)
txt = ax.text(zero_mean[0],zero_mean[1],
'point set zero',
fontsize=15)
txt.set_path_effects([PathEffects.Stroke(linewidth=5, foreground="violet"),PathEffects.Normal()])
txts.append(txt)
txt = ax.text(one_mean[0],one_mean[1],
'point set one',
fontsize=15)
txt.set_path_effects([PathEffects.Stroke(linewidth=5, foreground="violet"),PathEffects.Normal()])
txts.append(txt)
plt.show()
Running this code, you will get
k_model = KMeans(n_clusters = 3).fit(actor_w2vec)
cluster_dict = {i: np.where(k_model.labels_ == i)[0] for i in range(k_model.n_clusters)}
I have applied KMeans on word2vec vector (3411x128). cluster_dict contains the cluster label(i.e. 0,1,2) as key and index number(1,2,3,4,....3411) as value such that these values are distributed among three clusters.
Now i want to visualize these cluster so i used TSNE to reduce the 128 dimension vector to 2 dimension
node_embeddings = actor_w2vec
transform = TSNE #PCA
trans = transform(n_components=2)
node_embeddings_2d = trans.fit_transform(node_embeddings)
but i don't know how combine these two in order to create a graph or scatter plot where all the point belonging to one cluster are combined together
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.cluster import KMeans
import plotly.express as px
df = pd.DataFrame(np.random.randint(0,100,size=(100, 4)), columns=list('ABCD'))
#remember to scale your data if the ranges are too broad
scaler = StandardScaler()
scaled_features = scaler.fit_transform(df)
kmeans_model = KMeans(n_clusters=3, max_iter=500, random_state=42)
y_km = kmeans_model.fit_predict(scaled_features)
pca_model = PCA(n_components=2, random_state=42)
transformed = pca_model.fit_transform(scaled_features)
centers = pca_model.transform(kmeans_model.cluster_centers_)
fig = px.scatter(x=transformed[:, 0], y=transformed[:, 1], color=y_km)
fig.add_scatter(
x=centers[:, 0],
y=centers[:, 1],
marker=dict(size=20, color="LightSeaGreen"), name="Centers"
)
fig.show()
If you only do kmeans.fit(df), you could get the labels from kmeans.labels_
import numpy as np
import matplotlib.pyplot as plt
#import seaborn as sns; sns.set()
import pandas as pd
from sklearn.datasets import make_blobs
from sklearn.cluster import KMeans
plt.rcParams['figure.dpi'] = 150
# create dataset
X, y = make_blobs(
n_samples=150, n_features=2,
centers=3, cluster_std=0.5,
shuffle=True, random_state=0
)
# plot
plt.scatter(
X[:, 0], X[:, 1],
edgecolor='black', s=50
)
plt.show()
km = KMeans(
n_clusters=3, init='random',
n_init=10, max_iter=10000,
tol=1e-04, random_state=0
)
y_km = km.fit_predict(X)
plt.scatter(X[:,0], X[:,1], c=y_km, s=50, cmap=plt.cm.Paired, alpha=0.4)
plt.scatter(km.cluster_centers_[:, 0],km.cluster_centers_[:, 1],
s=250, marker='*', label='centroids',
edgecolor='black',
c=np.arange(0,3),cmap=plt.cm.Paired,)
The line import seaborn as sns; sns.set() is not necessary, it just makes a nicer style.
For plotting you can use matplotlib.pyplot . Furthermore you can look on the shape of your data with node_embeddings_2d.shape, so you can make sure that plt.scatter takes the right arguments.
Good luck! ;)