Sklearn : Mean Distance from Centroid of each cluster

Question

How can i find the mean distance from the centroid to all the data points in each cluster. I am able to find the euclidean distance of each point (in my dataset) from the centroid of each cluster. Now i want to find the mean distance from centroid to all the data points in each cluster. What is a good way of calculating mean distance from each centroid ? So far I have done this..

def k_means(self):
    data = pd.read_csv('hdl_gps_APPLE_20111220_130416.csv', delimiter=',')
    combined_data = data.iloc[0:, 0:4].dropna()
    #print combined_data
    array_convt = combined_data.values
    #print array_convt
    combined_data.head()


    t_data=PCA(n_components=2).fit_transform(array_convt)
    #print t_data
    k_means=KMeans()
    k_means.fit(t_data)
    #------------k means fit predict method for testing purpose-----------------
    clusters=k_means.fit_predict(t_data)
    #print clusters.shape
    cluster_0=np.where(clusters==0)
    print cluster_0

    X_cluster_0 = t_data[cluster_0]
    #print X_cluster_0


    distance = euclidean(X_cluster_0[0], k_means.cluster_centers_[0])
    print distance


    classified_data = k_means.labels_
    #print ('all rows forst column........')
    x_min = t_data[:, 0].min() - 5
    x_max = t_data[:, 0].max() - 1
    #print ('min is ')
    #print x_min
    #print ('max is ')
    #print x_max

    df_processed = data.copy()
    df_processed['Cluster Class'] = pd.Series(classified_data, index=df_processed.index)
    #print df_processed

    y_min, y_max = t_data[:, 1].min(), t_data[:, 1].max() + 5
    xx, yy = np.meshgrid(np.arange(x_min, x_max, 1), np.arange(y_min, y_max, 1))

    #print ('the mesh grid is: ')

    #print xx
    Z = k_means.predict(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)

    plt.figure(1)
    plt.clf()
    plt.imshow(Z, interpolation='nearest',
               extent=(xx.min(), xx.max(), yy.min(), yy.max()),
               cmap=plt.cm.Paired,
               aspect='auto', origin='lower')


    #print Z


    plt.plot(t_data[:, 0], t_data[:, 1], 'k.', markersize=20)
    centroids = k_means.cluster_centers_
    inert = k_means.inertia_
    plt.scatter(centroids[:, 0], centroids[:, 1],
                marker='x', s=169, linewidths=3,
                color='w', zorder=8)
    plt.xlim(x_min, x_max)
    plt.ylim(y_min, y_max)
    plt.xticks(())
    plt.yticks(())
    plt.show()

In short I want to calculate mean distance of all the data points in particular cluster from the centroid of that cluster as I need to clean my data on the basis of this mean distance

Answer 1

Here's one way. You can substitute another distance measure in the function for k_mean_distance() if you want another distance metric other than Euclidean.

Calculate distance between data points for each assigned cluster and cluster centers and return the mean value.

Function for distance calculation:

def k_mean_distance(data, cx, cy, i_centroid, cluster_labels):
    # Calculate Euclidean distance for each data point assigned to centroid 
    distances = [np.sqrt((x-cx)**2+(y-cy)**2) for (x, y) in data[cluster_labels == i_centroid]]
    # return the mean value
    return np.mean(distances)

And for each centroid, use the function to get the mean distance:

total_distance = []
for i, (cx, cy) in enumerate(centroids):
    # Function from above
    mean_distance = k_mean_distance(data, cx, cy, i, cluster_labels)
    total_dist.append(mean_distance)

So, in the context of your question:

def k_mean_distance(data, cx, cy, i_centroid, cluster_labels):
        distances = [np.sqrt((x-cx)**2+(y-cy)**2) for (x, y) in data[cluster_labels == i_centroid]]
        return np.mean(distances)

t_data=PCA(n_components=2).fit_transform(array_convt)
k_means=KMeans()
clusters=k_means.fit_predict(t_data)
centroids = km.cluster_centers_

c_mean_distances = []
for i, (cx, cy) in enumerate(centroids):
    mean_distance = k_mean_distance(t_data, cx, cy, i, clusters)
    c_mean_distances.append(mean_distance)

If you plot the results plt.plot(c_mean_distances) you should see something like this:

Answer 2

You can use following Attribute of KMeans:

cluster_centers_ : array, [n_clusters, n_features]

For every point, test to what cluster it belongs using predict(X) and after that calculate distance to cluster predict returns(it returns index).