Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN 1

Remaining Lectures in 2009

1. Advanced Clustering and Outlier Detection 2. Advanced Classification and Prediction 3. Top Ten Data Mining Algorithms (short)4. Course Summary (short)5. Assignment5 Student Presentations

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN 2

Clustering Part2: Advanced Clustering and Outlier Detection

1. Hierarchical Clustering2. More on Density-based Clustering: DENCLUE 3. [EM Top10-DM-Alg]4. Cluster Evaluation Measures5. Outlier Detection

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

More on Clustering

1. Hierarchical Clustering to be discussed in Nov. 11

2. DBSCAN will be used in programming project

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

Hierarchical Clustering

Produces a set of nested clusters organized as a hierarchical tree

Can be visualized as a dendrogram– A tree like diagram that records the sequences of

merges or splits

1 3 2 5 4 60

0.05

0.1

0.15

0.2

1

2

3

4

5

6

1

23 4

5

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

Agglomerative Clustering Algorithm

More popular hierarchical clustering technique

Basic algorithm is straightforward1. Compute the proximity matrix

2. Let each data point be a cluster

3. Repeat

4. Merge the two closest clusters

5. Update the proximity matrix

6. Until only a single cluster remains

Key operation is the computation of the proximity of two clusters

– Different approaches to defining the distance between clusters distinguish the different algorithms

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

Starting Situation

Start with clusters of individual points and a proximity matrix

p1

p3

p5

p4

p2

p1 p2 p3 p4 p5 . . .

.

.

. Proximity Matrix

...p1 p2 p3 p4 p9 p10 p11 p12

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

Intermediate Situation

After some merging steps, we have some clusters

C1

C4

C2 C5

C3

C2C1

C1

C3

C5

C4

C2

C3 C4 C5

Proximity Matrix

...p1 p2 p3 p4 p9 p10 p11 p12

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

Intermediate Situation

We want to merge the two closest clusters (C2 and C5) and update the proximity matrix.

C1

C4

C2 C5

C3

C2C1

C1

C3

C5

C4

C2

C3 C4 C5

Proximity Matrix

...p1 p2 p3 p4 p9 p10 p11 p12

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

After Merging

The question is “How do we update the proximity matrix?”

C1

C4

C2 U C5

C3? ? ? ?

?

?

?

C2 U C5C1

C1

C3

C4

C2 U C5

C3 C4

Proximity Matrix

...p1 p2 p3 p4 p9 p10 p11 p12

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

How to Define Inter-Cluster Similarity

p1

p3

p5

p4

p2

p1 p2 p3 p4 p5 . . .

.

.

.

Similarity?

MIN MAX Group Average Distance Between Centroids Other methods driven by an objective

function– Ward’s Method uses squared error

Proximity Matrix

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

How to Define Inter-Cluster Similarity

p1

p3

p5

p4

p2

p1 p2 p3 p4 p5 . . .

.

.

.Proximity Matrix

MIN MAX Group Average Distance Between Centroids Other methods driven by an objective

function– Ward’s Method uses squared error

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

How to Define Inter-Cluster Similarity

p1

p3

p5

p4

p2

p1 p2 p3 p4 p5 . . .

.

.

.Proximity Matrix

MIN MAX Group Average Distance Between Centroids Other methods driven by an objective

function– Ward’s Method uses squared error

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

How to Define Inter-Cluster Similarity

p1

p3

p5

p4

p2

p1 p2 p3 p4 p5 . . .

.

.

.Proximity Matrix

MIN MAX Group Average Distance Between Centroids Other methods driven by an objective

function– Ward’s Method uses squared error

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

How to Define Inter-Cluster Similarity

p1

p3

p5

p4

p2

p1 p2 p3 p4 p5 . . .

.

.

.Proximity Matrix

MIN MAX Group Average Distance Between Centroids Other methods driven by an objective

function– Ward’s Method uses squared error

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

Cluster Similarity: Group Average

Proximity of two clusters is the average of pairwise proximity between points in the two clusters.

Need to use average connectivity for scalability since total proximity favors large clusters

||Cluster||Cluster

)p,pproximity(

)Cluster,Clusterproximity(ji

ClusterpClusterp

ji

jijjii

I1 I2 I3 I4 I5I1 1.00 0.90 0.10 0.65 0.20I2 0.90 1.00 0.70 0.60 0.50I3 0.10 0.70 1.00 0.40 0.30I4 0.65 0.60 0.40 1.00 0.80I5 0.20 0.50 0.30 0.80 1.00 1 2 3 4 5

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN 16

2009 Teaching of Clustering

Clustering Part1: Basics (September/October)1. What is Clustering?2. Partitioning/Representative-based Clustering

• K-means• K-medoids

3. Density Based Clustering centering on DBSCAN4. Region Discovery5. Grid-based Clustering 6. Similarity Assessment

Clustering Part2: Advanced Topics (November)

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

DBSCAN (http://www2.cs.uh.edu/~ceick/7363/Papers/dbscan.pdf )

DBSCAN is a density-based algorithm.– Density = number of points within a specified radius (Eps)

– Input parameter: MinPts and Eps

– A point is a core point if it has more than a specified number of points (MinPts) within Eps

These are points that are at the interior of a cluster

– A border point has fewer than MinPts within Eps, but is in the neighborhood of a core point

– A noise point is any point that is not a core point or a border point.

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

DBSCAN: Core, Border, and Noise Points

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

DBSCAN Algorithm (simplified view for teaching)

1. Create a graph whose nodes are the points to be clustered

2. For each core-point c create an edge from c to every point p in the -neighborhood of c

3. Set N to the nodes of the graph;

4. If N does not contain any core points terminate

5. Pick a core point c in N

6. Let X be the set of nodes that can be reached from c by going forward;

1. create a cluster containing X{c}

2. N=N/(X{c})

7. Continue with step 4Remarks: points that are not assigned to any cluster are outliers;http://www2.cs.uh.edu/~ceick/7363/Papers/dbscan.pdf gives a more efficient implementation by performing steps 2 and 6 in parallel

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

DBSCAN: Core, Border and Noise Points

Original Points Point types: core, border and noise

Eps = 10, MinPts = 4

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

When DBSCAN Works Well

Original Points Clusters

• Resistant to Noise

• Can handle clusters of different shapes and sizes

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

When DBSCAN Does NOT Work Well

Original Points

(MinPts=4, Eps=9.75).

(MinPts=4, Eps=9.12)

• Varying densities

• High-dimensional data

Problems with

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

Assignment 3 Dataset: Earthquake

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

Assignment3 Dataset: Complex9

http://www2.cs.uh.edu/~ml_kdd/Complex&Diamond/2DData.htm

K-Means in Weka DBSCAN in Weka

Dataset: http://www2.cs.uh.edu/~ml_kdd/Complex&Diamond/Complex9.txt

Ch. Eick: Introduction to Hierarchical Clustering and DBSCAN

DBSCAN: Determining EPS and MinPts

Idea is that for points in a cluster, their kth nearest neighbors are at roughly the same distance

Noise points have the kth nearest neighbor at farther distance

So, plot sorted distance of every point to its kth nearest neighbor

Non-Core-pointsCore-points

Run DBSCAN for Minp=4 and =5