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from __future__ import print_function, division
import numpy as np
from mlfromscratch.utils import Plot, euclidean_distance, normalize
class DBSCAN():
"""A density based clustering method that expands clusters from
samples that have more neighbors within a radius specified by eps
than the value min_samples.
Parameters:
-----------
eps: float
The radius within which samples are considered neighbors
min_samples: int
The number of neighbors required for the sample to be a core point.
"""
def __init__(self, eps=1, min_samples=5):
self.eps = eps
self.min_samples = min_samples
def _get_neighbors(self, sample_i):
""" Return a list of indexes of neighboring samples
A sample_2 is considered a neighbor of sample_1 if the distance between
them is smaller than epsilon """
neighbors = []
idxs = np.arange(len(self.X))
for i, _sample in enumerate(self.X[idxs != sample_i]):
distance = euclidean_distance(self.X[sample_i], _sample)
if distance < self.eps:
neighbors.append(i)
return np.array(neighbors)
def _expand_cluster(self, sample_i, neighbors):
""" Recursive method which expands the cluster until we have reached the border
of the dense area (density determined by eps and min_samples) """
cluster = [sample_i]
# Iterate through neighbors
for neighbor_i in neighbors:
if not neighbor_i in self.visited_samples:
self.visited_samples.append(neighbor_i)
# Fetch the sample's distant neighbors (neighbors of neighbor)
self.neighbors[neighbor_i] = self._get_neighbors(neighbor_i)
# Make sure the neighbor's neighbors are more than min_samples
# (If this is true the neighbor is a core point)
if len(self.neighbors[neighbor_i]) >= self.min_samples:
# Expand the cluster from the neighbor
expanded_cluster = self._expand_cluster(
neighbor_i, self.neighbors[neighbor_i])
# Add expanded cluster to this cluster
cluster = cluster + expanded_cluster
else:
# If the neighbor is not a core point we only add the neighbor point
cluster.append(neighbor_i)
return cluster
def _get_cluster_labels(self):
""" Return the samples labels as the index of the cluster in which they are
contained """
# Set default value to number of clusters
# Will make sure all outliers have same cluster label
labels = np.full(shape=self.X.shape[0], fill_value=len(self.clusters))
for cluster_i, cluster in enumerate(self.clusters):
for sample_i in cluster:
labels[sample_i] = cluster_i
return labels
# DBSCAN
def predict(self, X):
self.X = X
self.clusters = []
self.visited_samples = []
self.neighbors = {}
n_samples = np.shape(self.X)[0]
# Iterate through samples and expand clusters from them
# if they have more neighbors than self.min_samples
for sample_i in range(n_samples):
if sample_i in self.visited_samples:
continue
self.neighbors[sample_i] = self._get_neighbors(sample_i)
if len(self.neighbors[sample_i]) >= self.min_samples:
# If core point => mark as visited
self.visited_samples.append(sample_i)
# Sample has more neighbors than self.min_samples => expand
# cluster from sample
new_cluster = self._expand_cluster(
sample_i, self.neighbors[sample_i])
# Add cluster to list of clusters
self.clusters.append(new_cluster)
# Get the resulting cluster labels
cluster_labels = self._get_cluster_labels()
return cluster_labels
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