Source code for yellowbrick.cluster.silhouette

# yellowbrick.cluster.silhouette
# Implements visualizers using the silhouette metric for cluster evaluation.
#
# Author:   Benjamin Bengfort
# Author:   Rebecca Bilbro
# Created:  Mon Mar 27 10:09:24 2017 -0400
#
# Copyright (C) 2017 The scikit-yb developers
# For license information, see LICENSE.txt
#
# ID: silhouette.py [57b563b] benjamin@bengfort.com $

"""
Implements visualizers that use the silhouette metric for cluster evaluation.
"""

##########################################################################
## Imports
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import numpy as np
import matplotlib.ticker as ticker

from sklearn.metrics import silhouette_score, silhouette_samples

from yellowbrick.utils import check_fitted
from yellowbrick.style import resolve_colors
from yellowbrick.cluster.base import ClusteringScoreVisualizer

## Packages for export
__all__ = ["SilhouetteVisualizer", "silhouette_visualizer"]


##########################################################################
## Silhouette Method for K Selection
##########################################################################


[docs]class SilhouetteVisualizer(ClusteringScoreVisualizer): """ The Silhouette Visualizer displays the silhouette coefficient for each sample on a per-cluster basis, visually evaluating the density and separation between clusters. The score is calculated by averaging the silhouette coefficient for each sample, computed as the difference between the average intra-cluster distance and the mean nearest-cluster distance for each sample, normalized by the maximum value. This produces a score between -1 and +1, where scores near +1 indicate high separation and scores near -1 indicate that the samples may have been assigned to the wrong cluster. In SilhouetteVisualizer plots, clusters with higher scores have wider silhouettes, but clusters that are less cohesive will fall short of the average score across all clusters, which is plotted as a vertical dotted red line. This is particularly useful for determining cluster imbalance, or for selecting a value for K by comparing multiple visualizers. Parameters ---------- model : a Scikit-Learn clusterer Should be an instance of a centroidal clustering algorithm (``KMeans`` or ``MiniBatchKMeans``). If the estimator is not fitted, it is fit when the visualizer is fitted, unless otherwise specified by ``is_fitted``. ax : matplotlib Axes, default: None The axes to plot the figure on. If None is passed in the current axes will be used (or generated if required). colors : iterable or string, default: None A collection of colors to use for each cluster group. If there are fewer colors than cluster groups, colors will repeat. May also be a Yellowbrick or matplotlib colormap string. is_fitted : bool or str, default='auto' Specify if the wrapped estimator is already fitted. If False, the estimator will be fit when the visualizer is fit, otherwise, the estimator will not be modified. If 'auto' (default), a helper method will check if the estimator is fitted before fitting it again. kwargs : dict Keyword arguments that are passed to the base class and may influence the visualization as defined in other Visualizers. Attributes ---------- silhouette_score_ : float Mean Silhouette Coefficient for all samples. Computed via scikit-learn `sklearn.metrics.silhouette_score`. silhouette_samples_ : array, shape = [n_samples] Silhouette Coefficient for each samples. Computed via scikit-learn `sklearn.metrics.silhouette_samples`. n_samples_ : integer Number of total samples in the dataset (X.shape[0]) n_clusters_ : integer Number of clusters (e.g. n_clusters or k value) passed to internal scikit-learn model. y_tick_pos_ : array of shape (n_clusters,) The computed center positions of each cluster on the y-axis Examples -------- >>> from yellowbrick.cluster import SilhouetteVisualizer >>> from sklearn.cluster import KMeans >>> model = SilhouetteVisualizer(KMeans(10)) >>> model.fit(X) >>> model.show() """ def __init__(self, model, ax=None, colors=None, is_fitted="auto", **kwargs): # Initialize the visualizer bases super(SilhouetteVisualizer, self).__init__(model, ax=ax, **kwargs) # Visual Properties # Use colors if it is given, otherwise attempt to use colormap which # which will override colors. If neither is found, default to None. # The colormap may yet still be found in resolve_colors self.colors = colors if "colormap" in kwargs: self.colors = kwargs["colormap"]
[docs] def fit(self, X, y=None, **kwargs): """ Fits the model and generates the silhouette visualization. """ # TODO: decide to use this method or the score method to draw. # NOTE: Probably this would be better in score, but the standard score # is a little different and I'm not sure how it's used. if not check_fitted(self.estimator, is_fitted_by=self.is_fitted): # Fit the wrapped estimator self.estimator.fit(X, y, **kwargs) # Get the properties of the dataset self.n_samples_ = X.shape[0] self.n_clusters_ = self.estimator.n_clusters # Compute the scores of the cluster labels = self.estimator.predict(X) self.silhouette_score_ = silhouette_score(X, labels) self.silhouette_samples_ = silhouette_samples(X, labels) # Draw the silhouette figure self.draw(labels) # Return the estimator return self
[docs] def draw(self, labels): """ Draw the silhouettes for each sample and the average score. Parameters ---------- labels : array-like An array with the cluster label for each silhouette sample, usually computed with ``predict()``. Labels are not stored on the visualizer so that the figure can be redrawn with new data. """ # Track the positions of the lines being drawn y_lower = 10 # The bottom of the silhouette # Get the colors from the various properties color_kwargs = {"n_colors": self.n_clusters_} if self.colors is None: color_kwargs["colormap"] = "Set1" elif isinstance(self.colors, str): color_kwargs["colormap"] = self.colors else: color_kwargs["colors"] = self.colors colors = resolve_colors(**color_kwargs) # For each cluster, plot the silhouette scores self.y_tick_pos_ = [] for idx in range(self.n_clusters_): # Collect silhouette scores for samples in the current cluster . values = self.silhouette_samples_[labels == idx] values.sort() # Compute the size of the cluster and find upper limit size = values.shape[0] y_upper = y_lower + size color = colors[idx] self.ax.fill_betweenx( np.arange(y_lower, y_upper), 0, values, facecolor=color, edgecolor=color, alpha=0.5, ) # Collect the tick position for each cluster self.y_tick_pos_.append(y_lower + 0.5 * size) # Compute the new y_lower for next plot y_lower = y_upper + 10 # The vertical line for average silhouette score of all the values self.ax.axvline( x=self.silhouette_score_, color="red", linestyle="--", label="Average Silhouette Score", ) return self.ax
[docs] def finalize(self): """ Prepare the figure for rendering by setting the title and adjusting the limits on the axes, adding labels and a legend. """ # Set the title self.set_title( ("Silhouette Plot of {} Clustering for {} Samples in {} Centers").format( self.name, self.n_samples_, self.n_clusters_ ) ) # Set the X and Y limits # The silhouette coefficient can range from -1, 1; # but here we scale the plot according to our visualizations # l_xlim and u_xlim are lower and upper limits of the x-axis, # set according to our calculated max and min score with necessary padding l_xlim = max(-1, min(-0.1, round(min(self.silhouette_samples_) - 0.1, 1))) u_xlim = min(1, round(max(self.silhouette_samples_) + 0.1, 1)) self.ax.set_xlim([l_xlim, u_xlim]) # The (n_clusters_+1)*10 is for inserting blank space between # silhouette plots of individual clusters, to demarcate them clearly. self.ax.set_ylim([0, self.n_samples_ + (self.n_clusters_ + 1) * 10]) # Set the x and y labels self.ax.set_xlabel("silhouette coefficient values") self.ax.set_ylabel("cluster label") # Set the ticks on the axis object. self.ax.set_yticks(self.y_tick_pos_) self.ax.set_yticklabels(str(idx) for idx in range(self.n_clusters_)) # Set the ticks at multiples of 0.1 self.ax.xaxis.set_major_locator(ticker.MultipleLocator(0.1)) # Show legend (Average Silhouette Score axis) self.ax.legend(loc="best")
########################################################################## ## Quick Method ##########################################################################
[docs]def silhouette_visualizer( model, X, y=None, ax=None, colors=None, is_fitted="auto", show=True, **kwargs ): """Quick Method: The Silhouette Visualizer displays the silhouette coefficient for each sample on a per-cluster basis, visually evaluating the density and separation between clusters. The score is calculated by averaging the silhouette coefficient for each sample, computed as the difference between the average intra-cluster distance and the mean nearest-cluster distance for each sample, normalized by the maximum value. This produces a score between -1 and +1, where scores near +1 indicate high separation and scores near -1 indicate that the samples may have been assigned to the wrong cluster. Parameters ---------- model : a Scikit-Learn clusterer Should be an instance of a centroidal clustering algorithm (``KMeans`` or ``MiniBatchKMeans``). If the estimator is not fitted, it is fit when the visualizer is fitted, unless otherwise specified by ``is_fitted``. X : array-like of shape (n, m) A matrix or data frame with n instances and m features y : array-like of shape (n,), optional A vector or series representing the target for each instance ax : matplotlib Axes, default: None The axis to plot the figure on. If None is passed in the current axes will be used (or generated if required). colors : iterable or string, default: None A collection of colors to use for each cluster group. If there are fewer colors than cluster groups, colors will repeat. May also be a Yellowbrick or matplotlib colormap string. is_fitted : bool or str, default='auto' Specify if the wrapped estimator is already fitted. If False, the estimator will be fit when the visualizer is fit, otherwise, the estimator will not be modified. If 'auto' (default), a helper method will check if the estimator is fitted before fitting it again. show : bool, default: True If True, calls ``show()``, which in turn calls ``plt.show()`` however you cannot call ``plt.savefig`` from this signature, nor ``clear_figure``. If False, simply calls ``finalize()`` kwargs : dict Keyword arguments that are passed to the base class and may influence the visualization as defined in other Visualizers. Returns ------- viz : SilhouetteVisualizer The silhouette visualizer, fitted and finalized. """ oz = SilhouetteVisualizer( model, ax=ax, colors=colors, is_fitted=is_fitted, **kwargs ) oz.fit(X, y) if show: oz.show() else: oz.finalize() return oz