Lecture_3_k-mean-clustering.ppt

INTRODUCTION-
What is clustering?
 Clustering is the classification of objects into
different groups, or more precisely, the
partitioning of a data set into subsets
(clusters), so that the data in each subset
(ideally) share some common trait - often
according to some defined distance measure.

K-MEANS CLUSTERING
 The k-means algorithm is an algorithm to cluster
n objects based on attributes into k partitions,
where k < n.

 An algorithm for partitioning (or clustering) N
data points into K disjoint subsets Sj (k clusters)
containing data points so as to minimize the
sum-of-squares criterion
where xi is a vector representing the the nth data
point and cj is the geometric centroid of the data
points in Sj (kth cluster)
K-MEANS CLUSTERING

 Simply speaking k-means clustering is an
algorithm to classify or to group the objects
based on attributes/features into K number of
group.
 K is positive integer number.
 The grouping is done by minimizing the sum
of squares of distances between data and the
corresponding cluster centroid.
K-MEANS CLUSTERING

How the K-Mean Clustering
algorithm works?
 Initialization: once the number of groups, k has
been chosen, k centroids are established in the
data space, for instance, choosing them
randomly.
 Assignment of objects to the centroids: each
object of the data is assigned to its nearest
centroid.
 Centroids update: The position of the centroid
of each group is updated taking as the new
centroid the average position of the objects
belonging to said group.

 Step 1: Begin with a decision on the value of k =
number of clusters.
 Step 2: Put any initial partition that classifies the
data into k clusters. You may assign the training
samples randomly, or systematically as the following:
1. Take the first k training sample as single-element clusters
2. Assign each of the remaining (N-k) training sample to the
cluster with the nearest centroid. After each assignment,
recompute the centroid of the clusters.
K-MEANS CLUSTERING

 Step 3: Take each sample in sequence and
compute its distance from the centroid of
each of the clusters. If a sample is not
currently in the cluster with the closest
centroid, switch this sample to that cluster
and update the centroid of the cluster
gaining the new sample and the cluster
losing the sample.
 Step 4 . Repeat step 3 until convergence is
achieved, that is until a pass through the
training sample causes no new assignments.
K-MEANS CLUSTERING

A Simple example showing the
implementation of k-means algorithm
(using K=2)

Step 1:
Initialization: Randomly we choose following two centroids
(k=2) for two clusters.
In this case the 2 centroid are: m1 = (1.0,1.0) and m2 = (5.0,7.0)

Step 2:
 Thus, we obtain two clusters
containing:
{1,2,3} and {4,5,6,7}.
 Their new centroids are:
Individual Centroid 1 Centroid 2
1 0 7.21
2 1.12 6.10
3 3.61 3.61
4 7.21 0
5 4.72 2.5
6 5.31 2.06
7 4.30 2.92
Distance from individual
points to the two centroids

Step 3:
 Now using these centroids
we compute the Euclidean
distance of each object, as
shown in table.
 Therefore, the new
clusters are:
{1,2} and {3,4,5,6,7}
 Next centroids are:
m1=(1.25,1.5) and m2 =
(3.9,5.1)
1 1.57 5.38
2 0.47 4.28
3 2.04 1.78
4 5.64 1.84
5 3.15 0.73
6 3.78 0.54
7 2.74 1.08
Distance from individual
points to the two centroids

Step 4 :
The clusters obtained are:
{1,2} and {3,4,5,6,7}
 Therefore, there is no
change in the cluster.
 Thus, the algorithm comes
to a halt here and final
result consist of 2 clusters
{1,2} and {3,4,5,6,7}.
1 0.56 5.02
2 0.56 3.92
3 3.05 1.42
4 6.66 2.20
5 4.16 0.41
6 4.78 0.61
7 3.75 0.72

Elbow Method (choosing the
number of clusters)
Another Method - silhouette coefficient (self study)
Elbow Method

Weaknesses of K-Mean Clustering
1. When the numbers of data are not so many, initial
grouping will determine the cluster significantly.
2. The number of cluster, K, must be determined before
hand. Its disadvantage is that it does not yield the same
result with each run, since the resulting clusters depend
on the initial random assignments.
3. We never know the real cluster, using the same data,
because if it is inputted in a different order it may
produce different cluster if the number of data is few.
4. It is sensitive to initial condition. Different initial condition
may produce different result of cluster. The algorithm
may be trapped in the local optimum.

Applications of K-Mean
Clustering
 It is relatively efficient and fast.
 k-means clustering can be applied to machine
learning or data mining
 Used on acoustic data in speech understanding to
convert waveforms into one of k categories or
Image Segmentation.

Lecture_3_k-mean-clustering.ppt

Lecture_3_k-mean-clustering.ppt

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Lecture_3_k-mean-clustering.ppt