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
Related
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()]
When performing classification, we may want to predict the class label, and also to obtain a probability, certainty or confidence around the respective label. Probabilities can be much more informative than labels. To convey likelihood, we need calibrated probabilities. In calibrated probabilities, the probability reflects the true likelihood. For instance, if 10 observations obtain a probability of 0.8 and probability is calibrated, we expect around 8 of those to belong to the positive class. If the probability is calibrated, we should see a match between the number of positive cases and the predicted probability.
Only binary classification is supported by sklearn. How can we extend sklearn's calibration_curve module for multi-class classification problems and plot a Probability Calibration Curve when len(np.unique(y_true)) > 2 ? Here is my code that plots it for binary classifications.
from sklearn.calibration import calibration_curve
import matplotlib.pyplot as plt
from matplotlib.ticker import (MultipleLocator, AutoMinorLocator)
import pathlib
from imblearn.pipeline import Pipeline
from sklearn.metrics import brier_score_loss
def __plot_calibration_curve_binary(clf, X_test, y_test, n_bins, strategy, **kwargs):
if 'probs' not in kwargs:
# score the test set
probs = clf.predict_proba(X_test)[:, 1]
fraction_of_positives, mean_predicted_value = calibration_curve(y_test, probs, n_bins=n_bins, strategy=strategy)
elif 'probs' in kwargs:
probs = kwargs['probs']
fraction_of_positives, mean_predicted_value = calibration_curve(y_test, probs, n_bins=n_bins, strategy=strategy)
else:
print("Please assign the probabilities(probs) or classifier to the function as shown in the example")
max_val = max(mean_predicted_value)
if 'fig_size' in kwargs and 'dpi' in kwargs:
fig, ax = plt.subplots(2, sharex=True, gridspec_kw={'height_ratios': [2, 1], 'hspace': 0.05}, figsize=kwargs['fig_size'], dpi=kwargs['dpi'], facecolor='white')
else:
fig, ax = plt.subplots(2, facecolor='white', sharex=True, gridspec_kw={'height_ratios': [2, 1], 'hspace': 0.05})
plt.rcParams["figure.facecolor"] = 'white'
plt.rcParams["axes.facecolor"] = 'white'
plt.rcParams["savefig.facecolor"] = 'white'
ax[0].xaxis.set_major_locator(MultipleLocator(0.1))
ax[1].xaxis.set_major_locator(MultipleLocator(0.1))
ax[0].xaxis.set_major_formatter('{x:.1f}')
ax[1].xaxis.set_major_formatter('{x:.1f}')
ax[0].yaxis.set_major_locator(MultipleLocator(0.1))
ax[0].yaxis.set_major_formatter('{x:.1f}')
ax[0].tick_params(which='both', width=1)
ax[0].tick_params(which='major', length=5)
ax[0].grid(True, zorder=0)
ax[1].grid(True, zorder=0)
if type(clf) == Pipeline:
estimator_name = type(clf['clf']).__name__
else:
estimator_name = type(clf).__name__
# print roc-auc
brier_score = ' (Brier Score : ' + str(round(brier_score_loss(y_test, probs), 4)) + ')'
#plot calibration curve
ax[0].plot(mean_predicted_value, fraction_of_positives, label = estimator_name + brier_score, zorder=2)
ax[0].scatter(mean_predicted_value, fraction_of_positives, zorder=3)
#plot perfect calibration line
ax[0].plot(np.linspace(0, max_val, n_bins), np.linspace(0, max_val, n_bins), linestyle='--', color='red', label='Perfect calibration', zorder=1)
#plot number of observation per prediction interval
ax[1].hist(probs, bins=n_bins, density=True, stacked=True, alpha=0.3, zorder=1)
#add labels and legends
ax[1].set_xlabel('Probability Predictions', fontsize=18)
ax[0].set_ylabel('Fraction of positive examples', fontsize=18)
ax[1].set_ylabel('Fraction of examples', fontsize=18)
if 'title' in kwargs:
ax[0].set_title(kwargs['title'], fontsize=18)
else:
ax[0].set_title('Probability Calibration Curve', fontsize=18)
ax[0].legend(loc='upper left')
ax[0].set_xlim([0.0, 1.0])
ax[1].set_xlim([0.0, 1.0])
ax[0].set_ylim([0.0, 1.0])
plt.show()
if 'save_fig_path' in kwargs:
path = pathlib.Path(kwargs['save_fig_path'])
path.parent.mkdir(parents=True, exist_ok=True)
if 'dpi' in kwargs:
fig.savefig(kwargs['save_fig_path'], dpi=kwargs['dpi'], facecolor=fig.get_facecolor(), edgecolor='none')
else:
fig.savefig(kwargs['save_fig_path'], facecolor=fig.get_facecolor(), edgecolor='none')
return fig, ax
def __plot_calibration_curve_multiclass(clf, X_test, y_test, n_bins, strategy, **kwargs):
print("Only binary classification is supported.")
def plot_calibration_curve(clf, X_test, y_test, n_bins=10, strategy='uniform', **kwargs):
"""
Plots probability calibration curve for the given model
Parameters
----------
clf : estimators to plot probability calibration curve
estimator instance (either sklearn.Pipeline, imblearn.Pipeline or a classifier)
PRE-FITTED classifier or a PRE-FITTED Pipeline in which the last estimator is a classifier.
X_test : pandas.DataFrame of shape (n_samples, n_features)
Test values.
y_test : pandas.Series of shape (n_samples,)
Target values.
n_bins: int, default=10
Number of bins to discretize the [0, 1] interval.
A bigger number requires more data.
Bins with no samples (i.e. without corresponding values in probs) will not be returned,
thus the returned arrays may have less than n_bins values.
strategy : {'uniform', 'quantile'}, default='uniform'
Strategy used to define the widths of the bins.
**kwargs : The following options are available with kwargs
probs: array-like of shape (n_samples,)
Probabilities of the positive class.
fig_size : tuple
Size (inches) of the plot.
dpi : int, default = 100
Image DPI.
title : str
The title of the plot.
save_fig_path : str
Full path where to save the plot. Will generate the folders if they don't exist already.
Returns
-------
fig : Matplotlib.pyplot.Figure
Figure from matplotlib
ax : Matplotlib.pyplot.Axe
Axe object from matplotlib
Example Syntax #1 : Plot calibration curve from estimator
-----------------
fig, ax = plot_calibration_curve(rf_pipe, X_test, y_test, n_bins=10, strategy='uniform',
fig_size=(12, 10), dpi=100,
save_fig_path="dir1/dir2/calibration_curve.png")
Example Syntax #2 : Plot the calibration curve using the calculated probabilities
-----------------
fig, ax = plot_calibration_curve(rf_pipe, X_test, y_test, n_bins=10, strategy='uniform',
probs=probs, fig_size=(12, 10), dpi=100,
save_fig_path="dir1/dir2/calibration_curve.png")
"""
if (len(y_test.unique()) == 2):
fig, ax = __plot_calibration_curve_binary(clf, X_test, y_test, n_bins=n_bins, strategy=strategy, **kwargs)
else:
fig, ax = __plot_calibration_curve_multiclass(clf, X_test, y_test, n_bins=n_bins, strategy=strategy, **kwargs)
return fig, ax
The output for the following syntax:
fig, ax = reporting.plot_calibration_curve(rf_pipe, X_test, y_test, n_bins=10, strategy='uniform',
probs=probs, fig_size=(12, 10), dpi=100,
save_fig_path="dir1/dir2/calibration_curve.png",
title='Probability Calibration Curve')
I'm new to Data Analytic
I've been working on the Regression Analysis Coding using matplotlib, numpy and pandas. However, I got some trouble with and try my best to find the way to resolve the problem via Stackoverflow and other websites, still, I could not.
Here's the code
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
Training_Dataset = pd.read_csv("https://raw.githubusercontent.com/kuroisep/Problem-1-Data-Analytic/main/A-train.csv?token=GHSAT0AAAAAABZ7O6G34ZTK4PMQGGZLRVS4Y2LAJSQ")
Training_Dataset = Training_Dataset.dropna()
X_train = np.array(Training_Dataset.iloc[:, :-1].values) # Independent Variable
y_train = np.array(Training_Dataset.iloc[:, 1].values) # Dependent Variable
Testing_Datatset = pd.read_csv("https://raw.githubusercontent.com/kuroisep/Problem-1-Data-Analytic/main/A-test.csv?token=GHSAT0AAAAAABZ7O6G2PRKTCT6YBKLZZSRWY2LAK2Q")
Testing_Dataset = Testing_Dataset.dropna()
X_test = np.array(Testing_Dataset.iloc[:, :-1].values) # Independent Variable
y_test = np.array(Testing_Dataset.iloc[:, 1].values) # Dependent Variable
from sklearn.linear_model import LinearRegression
regressor = LinearRegression()
regressor.fit(X_train, y_train)
accuracy = regressor.score(X_test, y_test)
print('Accuracy = '+ str(accuracy))
plt.style.use('seaborn')
plt.scatter(X_test, y_test, color = 'red', marker = 'o', s = 35, alpha = 0.5,
label = 'Test data')
plt.plot(X_train, regressor.predict(X_train), color = 'blue', label='Model Plot')
plt.title('Predicted Values vs Inputs')
plt.xlabel('Inputs')
plt.ylabel('Predicted Values')
plt.legend(loc = 'upper left')
plt.show()
And Here's the Syntax Error Detail
/usr/local/lib/python3.7/dist-packages/matplotlib/axes/_axes.py in scatter(self, x, y, s, c, marker, cmap, norm, vmin, vmax, alpha, linewidths, verts, edgecolors, plotnonfinite, **kwargs)
4389 y = np.ma.ravel(y)
4390 if x.size != y.size:
-> 4391 raise ValueError("x and y must be the same size")
4392
4393 if s is None:
ValueError: x and y must be the same size
my X_test value is (shape = (6,8))
array([[-2.474000e+01, -1.550000e+00, 9.105000e+01, 2.401980e+03,
-1.520000e+00, 1.360000e+01, 5.660000e+00, 1.059000e+01],
[ 1.075400e+02, -2.869000e+01, -8.259000e+01, 2.578915e+04,
5.290000e+00, -8.560000e+00, 1.490000e+00, -4.730000e+00],
[ 4.508000e+01, 9.662000e+01, 5.185000e+01, 1.280000e+00,
3.580000e+00, 5.200000e-01, -6.860000e+00, -7.800000e-01],
[-1.228100e+02, 1.779000e+01, -1.828500e+02, 2.928970e+03,
-1.210000e+00, -2.060000e+00, 9.680000e+00, -8.590000e+00],
[ 7.761000e+01, -7.230000e+01, 9.728000e+01, 1.917394e+04,
-9.290000e+00, 8.600000e-01, 7.060000e+00, -8.060000e+00],
[-4.401000e+01, 1.316500e+02, 6.988000e+01, 1.778310e+03,
-1.375000e+01, -1.475000e+01, -1.227000e+01, -8.300000e-01]])
my y_test value is (shape=(6,))
array([ -1.55, -28.69, 96.62, 17.79, -72.3 , 131.65])
I'm sorry if my question seems old.
Thank you for your kindness
plt.scatter requires the x and y points to have the shape of (n,). In your case the shapes of X_test, y_test are ((6, 8), (6,)), respectively. Considering the label of the first plot is Test data, you can use np.arange so that you can get y_test values over indexes:
plt.scatter(np.arange(len(y_test)), y_test, color = 'red', marker = 'o', s = 35, alpha = 0.5,
label = 'Test data')
Output:
For the second plot, regressor.predict(X_train) will give the predicted y_train values so again compare predicted values with actual values:
plt.plot(y_train, regressor.predict(X_train), color = 'blue', label='Model Plot')
Output:
By the way, your train-test split isn't right. You set x2 as the target variable but x2 is also included in the training set, that is the reason why the model has perfectly fitted and gives 100% accuracy, but that is the beyond the scope of this question.
X, t = make_swiss_roll(n_samples=1000, noise=0.2, random_state=42)
from sklearn.cluster import KMeans
kmeans = KMeans(n_clusters=3) # Number of clusters == 3
kmeans = kmeans.fit(X) # Fitting the input data
labels = kmeans.predict(X) # Getting the cluster labels
centroids = kmeans.cluster_centers_ # Centroid values
print("Centroids are:", centroids) # From sci-kit learn
fig = plt.figure(figsize=(20,10))
ax = fig.add_subplot(111, projection='3d')
x = np.array(labels==0)
y = np.array(labels==1)
z = np.array(labels==2)
ax.scatter(x,y,z, marker="s"[kmeans.labels_], s=40, cmap="RdBu")
I am trying to Plot the clusters in 3D by colouring all labels belonging to their class, and plot the centroids using a separate symbol. I managed to get the KMeans technique working, atleast I believe I did. But I'm stuck trying to plot it in 3D. I believe there can be a simple solution I'm just not seeing it. Does anyone have any idea what I need to change in my solution to achieve this?
import matplotlib.pyplot as plt
from sklearn.datasets import make_swiss_roll
from mpl_toolkits.mplot3d import Axes3D
X, t = make_swiss_roll(n_samples=1000, noise=0.2, random_state=42)
from sklearn.cluster import KMeans
kmeans = KMeans(n_clusters=3) # Number of clusters == 3
kmeans = kmeans.fit(X) # Fitting the input data
labels = kmeans.predict(X) # Getting the cluster labels
centroids = kmeans.cluster_centers_ # Centroid values
# print("Centroids are:", centroids) # From sci-kit learn
fig = plt.figure(figsize=(10,10))
ax = fig.gca(projection='3d')
x = np.array(labels==0)
y = np.array(labels==1)
z = np.array(labels==2)
ax.scatter(centroids[:,0],centroids[:,1],centroids[:,2],c="black",s=150,label="Centers",alpha=1)
ax.scatter(X[x,0],X[x,1],X[x,2],c="blue",s=40,label="C1")
ax.scatter(X[y,0],X[y,1],X[y,2],c="yellow",s=40,label="C2")
ax.scatter(X[z,0],X[z,1],X[z,2],c="red",s=40,label="C3")
Try with this, now the clusters are black X:
from sklearn.datasets import make_swiss_roll
X, t = make_swiss_roll(n_samples=1000, noise=0.2, random_state=42)
from sklearn.cluster import KMeans
kmeans = KMeans(n_clusters=3) # Number of clusters == 3
kmeans = kmeans.fit(X) # Fitting the input data
labels = kmeans.predict(X) # Getting the cluster labels
centroids = kmeans.cluster_centers_ # Centroid values
print("Centroids are:", centroids) # From sci-kit learn
fig = plt.figure(figsize=(20,10))
ax = fig.add_subplot(111, projection='3d')
x = np.array(labels==0)
y = np.array(labels==1)
z = np.array(labels==2)
ax.scatter(X[x][:, 0], X[x][:, 1], X[x][:, 2], color='red')
ax.scatter(X[y][:, 0], X[y][:, 1], X[y][:, 2], color='blue')
ax.scatter(X[z][:, 0], X[z][:, 1], X[z][:, 2], color='yellow')
ax.scatter(centroids[:, 0], centroids[:, 1], centroids[:, 2],
marker='x', s=169, linewidths=10,
color='black', zorder=50)
The Problem:
I'm having trouble plotting and interpreting the results from my TensorFlow model. I've created my own CSV of [x, y, color] where there is a plot of randomly scattered dots with a clear pattern in the color formation. I'm able to enter all the data into the model and train the neural network but can't seem to put it all together. I'm a bit new to this as a hobbyist.
Essentially I want the ML algorithm to pick up the pattern from 100 datapoints and use it on a test dataset of nodes to plot an approximation of the pattern.
The Code:
LABEL_COLUMN = "Color"
LABELS=[0,1]
def get_dataset(data_url, **kwargs):
dataset = tf.data.experimental.make_csv_dataset(
data_url,
batch_size=5,
label_name=LABEL_COLUMN,
na_value="?",
num_epochs=1,
ignore_errors=True,
**kwargs)
return dataset
project_data = get_dataset(data_url)
project_test_data = get_dataset(test_data_url)
def pack(features,label):
return tf.stack(list(features.values()), axis=-1), label
packed_data = project_data.map(pack)
packed_test_data = project_test_data.map(pack)
model2 = tf.keras.Sequential([
tf.keras.layers.Dense(128, activation="relu"),
tf.keras.layers.Dense(128, activation="relu"),
tf.keras.layers.Dense(1),
])
model2.compile(
loss = tf.keras.losses.BinaryCrossentropy(from_logits=True),
optimizer = "adam",
metrics = ["accuracy"]
)
model2.fit(packed_data, epochs=100)
model_output = model2.predict(packed_test_data)
model_output.plot()
Gives the below error:
AttributeError: 'numpy.ndarray' object has no attribute 'plot'
Perhaps this function can be adapted to solve your problem?
(From https://jonchar.net/notebooks/Artificial-Neural-Network-with-Keras/)
import matplotlib.pyplot as plt
def plot_decision_boundary(X, y, model, steps=1000, cmap='Paired'):
"""
Function to plot the decision boundary and data points of a model.
Data points are colored based on their actual label.
"""
cmap = plt.get_cmap(cmap)
# Define region of interest by data limits
xmin, xmax = X[:,0].min() - 1, X[:,0].max() + 1
ymin, ymax = X[:,1].min() - 1, X[:,1].max() + 1
steps = 1000
x_span = np.linspace(xmin, xmax, steps)
y_span = np.linspace(ymin, ymax, steps)
xx, yy = np.meshgrid(x_span, y_span)
# Make predictions across region of interest
labels = model.predict(np.c_[xx.ravel(), yy.ravel()])
# Plot decision boundary in region of interest
z = labels.reshape(xx.shape)
fig, ax = plt.subplots()
ax.contourf(xx, yy, z, cmap=cmap, alpha=0.5)
# Get predicted labels on training data and plot
train_labels = model.predict(X)
ax.scatter(X[:,0], X[:,1], c=y, cmap=cmap, lw=0)
return fig, ax
plot_decision_boundary(X, y, model, cmap='RdBu')