[PDF] CSE601 Hierarchical Clustering PDF

Hierarchical Clustering / Dendrograms

The agglomerative hierarchical clustering algorithms available in this In this example we can compare our interpretation with an actual plot of the data ...

Dendrograms for hierarchical cluster analysis

stata.com cluster dendrogram — Dendrograms for hierarchical cluster analysis. Syntax. Menu. Description. Options. Remarks and examples. Reference. Also see.

Dendrograms for hierarchical cluster analysis

Remarks and examples. References. Also see. Description cluster dendrogram produces dendrograms (also called cluster trees) for a hierarchical clustering.

Chapter 7 Hierarchical cluster analysis

perhaps the easiest to understand – a dendrogram or tree – where the objects this chapter we demonstrate hierarchical clustering on a small example and ...

Hierarchical Clustering

28 févr. 2019 Hierarchical clustering is yet another technique for performing data ... For example to draw a dendrogram

Evaluating Hierarchical Clustering Methods for Corpora with

12 sept. 2021 Hierarchical clustering is popular in Digital Humanities to ... than what we would expect by chance (for example for small dendrograms).

Overlapping Hierarchical Clustering (OHC)

Reminder on classical agglomerative clustering: Figure: SLINK dendrogram obtained from the practical example. Ian Jeantet (IRISA).

Characterization Stability and Convergence of Hierarchical

We study hierarchical clustering schemes under an axiomatic view. by practicioners and statisticians see for example the dendrograms provided by the ...

Community Detection with Hierarchical Clustering Algorithms Feb 3

3 févr. 2017 This network is used to benchmark virtually every community detection algorithm. Example 2.3 The Zachary Karate Club network is named for ...

Hierarchical clustering

1 Introduction. 2 Principles of hierarchical clustering. 3 Example. 4 Partitioning algorithm : K-means. 5 Extras. 6 Characterizing classes of individuals.

[PDF] CSE601 Hierarchical Clustering

Dendrogram • A tree that shows how clusters are merged/split hierarchically • Each node on the tree is a cluster; each leaf node is a singleton cluster

[PDF] Hierarchical Clustering - csPrinceton

hierarchical clustering over flat approaches such as K-Means A dendrogram shows data items along one axis and distances along the other axis

[PDF] Hierarchical Clustering

Hierarchical Clustering • Produces a set of nested clusters organized as a hierarchical tree • Can be visualized as a dendrogram

(PDF) Hierarchical Clustering - ResearchGate

28 fév 2019 · The graphical representation of that tree that embeds the nodes on the plane is called a dendrogram To implement a hierarchical clustering

[PDF] 17 Hierarchical clustering - Stanford NLP Group

hierarchic clustering) outputs a hierarchy a structure that is more informative than the unstructured set of clusters returned by flat clustering 1

[PDF] Chapter 7 Hierarchical cluster analysis

perhaps the easiest to understand – a dendrogram or tree – where the objects this chapter we demonstrate hierarchical clustering on a small example and

[PDF] Hierarchical clustering 10601 Machine Learning

Hierarchical clustering 10601 Machine Learning We do not have a teacher that provides examples with their The number of dendrograms with n

[PDF] Hierarchical Clustering Techniques

7 fév 2019 · Agglomerative hierarchical clustering starts with every single object the dendrogram given in Figure 7 3 for example we have h12 = 1

[PDF] Hierarchical clustering - Duke University

Agglomerative clustering is monotonic ? The similarity between merged clusters is monotone decreasing with the level of the merge ? Dendrogram: Plot

[PDF] Hierarchical Clustering / Dendrograms - NCSS

The two outliers 6 and 13 are fused in rather arbitrarily at much higher distances This is the interpretation In this example we can compare our

How dendrogram is used in hierarchical clustering?
A dendrogram is a tree-structured graph used in heat maps to visualize the result of a hierarchical clustering calculation. The result of a clustering is presented either as the distance or the similarity between the clustered rows or columns depending on the selected distance measure.
What is dendrogram with an example?
A dendrogram is a branching diagram that represents the relationships of similarity among a group of entities. Each branch is called a clade. on. There is no limit to the number of leaves in a clade.
What is hierarchical clustering PDF?
A hierarchical clustering method is a set of simple (flat) clustering methods arranged in a tree structure. These methods create clusters by recursively partitioning the entities in a top-down or bottom-up manner. We examine and compare hierarchical clustering algorithms in this paper.
Hierarchical clustering involves creating clusters that have a predetermined ordering from top to bottom. For example, all files and folders on the hard disk are organized in a hierarchy. There are two types of hierarchical clustering, Divisive and Agglomerative.

Clustering

Lecture 3: Hierarchical Methods

Jing Gao

SUNY Buffalo

Outline

Basics

Motivation, definition, evaluation

Methods

Partitional

Hierarchical

Density-based

Mixture model

Spectral methods

Advanced topics

Clustering ensemble

Clustering in MapReduce

Semi-supervised clustering, subspace clustering, co-clustering, etc. 2 3

Hierarchical Clustering

Agglomerative approach

b d c e a a b d e c d e a b c d e

Step 0 Step 1 Step 2 Step 3 Step 4 bottom-up

Initialization:

Each object is a cluster

Iteration:

Merge two clusters which are

most similar to each other;

Until all objects are merged

into a single cluster 4

Hierarchical Clustering

Divisive Approaches

b d c e a a b d e c d e a b c d e

Step 4 Step 3 Step 2 Step 1 Step 0 Top-down

Initialization:

All objects stay in one cluster

Iteration:

Select a cluster and split it into

two sub clusters

Until each leaf cluster contains

only one object 5

Dendrogram

A tree that shows how clusters are merged/split

hierarchically Each node on the tree is a cluster; each leaf node is a singleton cluster 6

Dendrogram

A clustering of the data objects is obtained by cutting the dendrogram at the desired level, then each connected component forms a cluster

Agglomerative Clustering Algorithm

More popular hierarchical clustering technique

Basic algorithm is straightforward

1.Compute the distance matrix

2.Let each data point be a cluster

3.Repeat

4. Merge the two closest clusters

5. Update the distance matrix

6.Until only a single cluster remains

Key operation is the computation of the distance between two clusters Different approaches to defining the distance between clusters distinguish the different algorithms 7

Starting Situation

Start with clusters of individual points and a distance matrix p1 p3 p5 p4 p2 p1 p2 p3 p4 p5 . . . . Distance Matrix p1p2p3p4p9p10p11p128

Intermediate Situation

After some merging steps, we have some clusters

Choose two clusters that has the smallest

distance (largest similarity) to merge C1 C4 C2 C5 C3 C2 C1 C1 C3 C5 C4 C2

C3 C4 C5

Distance Matrix

p1p2p3p4p9p10p11p12 9

Intermediate Situation

We want to merge the two closest clusters (C2 and C5) and update the distance matrix. C1 C4 C2 C5 C3 C2 C1 C1 C3 C5 C4 C2

C3 C4 C5

Distance Matrix

p1p2p3p4p9p10p11p12 10

After Merging

C1 C4

C2 U C5

C3 C2 U C5 C1 C1 C3 C4

C2 U C5

C3 C4

Distance Matrix

p1p2p3p4p9p10p11p12 11

How to Define Inter-Cluster Distance

p1 p3 p5 p4 p2 p1 p2 p3 p4 p5 . . .

Distance?

YMIN YMAX

YGroup Average

YDistance Between Centroids

Distance Matrix

MIN or Single Link

Inter-cluster distance

The distance between two clusters is represented by the distance of the closest pair of data objects belonging to different clusters. Determined by one pair of points, i.e., by one link in the proximity graph ),(min),( ,minqpdCCd MIN

Nested Clusters Dendrogram

1 2 3 4 5 6 1 2 3 4 5

3625410

0.05 0.1 0.15 0.2 14

Strength of MIN

Original Points Two Clusters

ͻ Can handle non-elliptical shapes

Limitations of MIN

Original Points

Two Clusters

ͻ Sensitive to noise and outliers

MAX or Complete Link

Inter-cluster distance

The distance between two clusters is represented by the distance of the farthest pair of data objects belonging to different clusters ),(max),( ,minqpdCCd MAX

Nested Clusters Dendrogram

3641250

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 1 2 3 4 5 6 1 2 5 3 4 18

Strength of MAX

Original Points

Two Clusters

ͻ Less susceptible to noise and outliers

Limitations of MAX

Original Points

ͻTends to break large clusters

20 21

MIN (2 clusters) MAX (2 clusters)

Limitations of MAX

ͻBiased towards globular clusters

Group Average or Average Link

Inter-cluster distance

The distance between two clusters is represented by the average distance of all pairs of data objects belonging to different clusters Determined by all pairs of points in the two clusters ,minqpdavgCCd

Group Average

Nested Clusters Dendrogram

3641250

0.05 0.1 0.15 0.2 0.25 1 2 3 4 5 6 1 2 5 3 4 23

Group Average

Compromise between Single and Complete

Link

Strengths

Less susceptible to noise and outliers

Limitations

Biased towards globular clusters

Centroid Distance

Inter-cluster distance

The distance between two clusters is represented by the distance between the centers of the clusters

Determined by cluster centroids

),(),(jijimeanmmdCCd 25
Similarity of two clusters is based on the increase in squared error when two clusters are merged Similar to group average if distance between points is distance squared

Less susceptible to noise and outliers

Biased towards globular clusters

Hierarchical analogue of K-means

Can be used to initialize K-means

Comparison

Group Average

Ward's Method

1 2 3 4 5 6 1 2 5 3 4

MIN MAX

1 2 3 4 5 6 1 2 5 3 4 1 2 3 4 5 6 1 2 5 3 4 1 2 3 4 5 6 1 2 3 4 5 27

Time and Space Requirements

O(N2) space since it uses the distance matrix

N is the number of points

O(N3) time in many cases

There are N steps and at each step the size, N2,

distance matrix must be updated and searched

Complexity can be reduced to O(N2 log(N) ) time

for some approaches 28

Strengths

Do not have to assume any particular number

of clusters

Any desired number of clusters can be obtained

They may correspond to meaningful

taxonomies camera, ..), furniture, groceries 29

Problems and Limitations

Once a decision is made to combine two clusters, it cannot be undone

No objective function is directly minimized

Different schemes have problems with one or more of the following:

Sensitivity to noise and outliers

Difficulty handling different sized clusters and irregular shapes

Breaking large clusters

Take-away Message

Agglomerative and divisive hierarchical clustering

Several ways of defining inter-cluster distance

The properties of clusters outputted by different

approaches based on different inter-cluster distance definition

Pros and cons of hierarchical clustering

31
quotesdbs_dbs17.pdfusesText_23

[PDF] [PDF] CSE601 Hierarchical Clustering

How dendrogram is used in hierarchical clustering?

What is dendrogram with an example?

What is hierarchical clustering PDF?

Clustering

Lecture 3: Hierarchical Methods

Jing Gao

SUNY Buffalo

Outline

Basics

Motivation, definition, evaluation

Methods

Partitional

Hierarchical

Density-based

Mixture model

Spectral methods

Advanced topics

Clustering ensemble

Clustering in MapReduce

Hierarchical Clustering

Agglomerative approach

Step 0 Step 1 Step 2 Step 3 Step 4 bottom-up

Initialization:

Each object is a cluster

Iteration:

Merge two clusters which are

Until all objects are merged

Hierarchical Clustering

Divisive Approaches

Step 4 Step 3 Step 2 Step 1 Step 0 Top-down

Initialization:

All objects stay in one cluster

Iteration:

Select a cluster and split it into

Until each leaf cluster contains

Dendrogram

A tree that shows how clusters are merged/split

Dendrogram

Agglomerative Clustering Algorithm

More popular hierarchical clustering technique

Basic algorithm is straightforward

1.Compute the distance matrix

2.Let each data point be a cluster

3.Repeat

4. Merge the two closest clusters

5. Update the distance matrix

6.Until only a single cluster remains

Starting Situation

Intermediate Situation

After some merging steps, we have some clusters

Choose two clusters that has the smallest

C3 C4 C5

Distance Matrix

Intermediate Situation

C3 C4 C5

Distance Matrix

After Merging

C2 U C5

C2 U C5

Distance Matrix

How to Define Inter-Cluster Distance

Distance?

YGroup Average

YDistance Between Centroids

Distance Matrix

MIN or Single Link

Inter-cluster distance

Nested Clusters Dendrogram

3625410

Strength of MIN

Original Points Two Clusters

ͻ Can handle non-elliptical shapes

Limitations of MIN

Original Points

Two Clusters

ͻ Sensitive to noise and outliers

MAX or Complete Link

Inter-cluster distance

Nested Clusters Dendrogram