Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a...

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Cluster analysis

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Transcript of Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a...

Page 1: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Cluster analysis

Page 2: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

• Partition MethodsDivide data into disjoint clusters

• Hierarchical Methods

Build a hierarchy of the observations and deduce the clusters from it.

Page 3: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

K-means

Page 4: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Criteria

Page 5: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Same criteria with multivariate data:

Page 6: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Justifying the criteria• Anova: decomposition of the variance.

Univariate:

SST=SSW+SSB

Multivariate:

Minimizing the withing clusters variance is equivalent to maximize the between clusters variance (the difference between clusters).

Page 7: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

K-means algorithm

Page 8: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Number of clusters

Page 9: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Consequences of standardization

Page 10: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Ruspini example

Page 11: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 12: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 13: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 14: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 15: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Problems of k-means

• Very sensitive to outliers

• Euclidean distances not appropriate for eliptical clusters

• It does not give the number of clusters.

Page 16: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Hierarchical Algoritms

Page 17: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Agglomerative algorithms

Page 18: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Nearest neighbour distance

Page 19: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Farthest neighbour distance

Page 20: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Average distance

Page 21: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Centroid method distance

Page 22: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Ward’s method distance

Page 23: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Dendograms

Page 24: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Example

Page 25: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 26: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 27: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 28: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 29: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 30: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 31: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 32: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Problems of hierarchical cluster

• If n is large, slow. Each time n(n-1)/2 comparisons.

• Euclidean distances not always appropriate

• If n is large, dendogram difficult to interpret

Page 33: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Clustering by variables

Page 34: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 35: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Distances between quantitative variables

Page 36: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Distances between qualitative variables

Page 37: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Similarity between attributes

Page 38: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.
Page 39: Cluster analysis. Partition Methods Divide data into disjoint clusters Hierarchical Methods Build a hierarchy of the observations and deduce the clusters.

Clusters and clusters strategies

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Metallic Clusters, Metallic Clusters, MesoscopicMesoscopic ... Presentations3/Zachariah AFOSR Workshop 21 January 2015.pdfMetallic Clusters, Metallic Clusters, MesoscopicMesoscopic

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Pennsylvania’s Industry Clusters Industry Clusters... · 1 Pennsylvania’s Industry Clusters Since 2004, Pennsylvania has defined industry clusters in the commonwealth to serve

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PDS: Deduce Elder Privacy from Smart Homes

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Chapter 6 Similarity, Neighbors, and Clusters. Similarity, Neighbors, Clusters Similarity underlies many data science methods and solutions to business.

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USM Core Thematic Clusters: Descriptions, courses ... Clusters... · 10 USM Core Thematic Clusters: Descriptions, courses, prerequisites (updated July 20 2015) Thematic clusters provide

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rmgsc.cr.usgs.gov · 2008-04-01 · Appendix A .3. wc deduce the solution = u — satisfies Solstng We deduce The asymptotic norlliitli(y of requires x, but need assump- tinn that

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Disordered Materials Professor Richard Welberry · This group combines diffuse X-ray scattering methods with computer simulation to deduce ... simulation to observed X-ray diffraction

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A SYNTHESIS OF RECENT ADVANCES IN THE METHOD OF … · 2011. 11. 15. · Kouba [1970] and Ying Chung-Chi [1970] one can deduce that the group and sequential methods are mathematical

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SSHRC Clusters Mid-term Report Form Part 1 SSHRC Clusters … · Form V2 (2006) STRATEGIC KNOWLEDGE CLUSTERS (CLUSTERS) MID-TERM REPORT _____ CLUSTERS MID-TERM REPORT As stated in

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Efficient Monomer-Based Quantum Chemistry Methods for … · 2013-11-06 · CHAPTER TWO Efficient Monomer-Based Quantum Chemistry Methods for Molecular and Ionic Clusters Leif D.

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Disordered Materials Professor Richard Welberry · 2004-05-27 · his group combines diffuse X-ray scattering methods with computer simulation to deduce the arrangement of atoms and

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