This document proposes a method for clustering and labeling clusters using a double application of self-organizing maps (SOM). The method uses tensors to represent multi-aspect data and applies SOM first to cluster the data nonlinearly. It then applies SOM again to the cluster representation to visualize the main concepts within each cluster, which can then be used as potential cluster labels. The method is demonstrated on a case study of finding thematic research areas within a future cities laboratory by clustering researchers based on their interests and applying the double SOM to identify and label the main research clusters.

1. Cluster Labeling with Double
Application of SOM
http://www.ad-exchange.fr/
Vahid Moosavi
Researcher at Future Cities Laboratory
PhD Student at Chair for Computer Aided Architectural Design (CAAD), ETH Zurich,
Ludger Hovestadt
1 November 2013
SEC
svm@arch.ethz.ch

2. Outline
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How to explain clustering and clusters?
Cluster labeling problem
Current methods and the proposed method
The Case: Finding Thematic Research Areas within FCL

3. How to explain clustering and clusters?
• Conceptually Clusters are
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Meant to show temporal and evolving identities
To show emergent concepts from lower level concepts
Bottom up from instances Vs. external references
Decoupling identities from objects, things and instances and to
create new dimensions in between
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Brands,
Spoken languages and dialects
Academic disciplines
Genres of movies, music classes , ….
3

4. How to explain clustering and clusters?
• And Technically Clusters
– Show the direction of eigenvectors of data matrix
– Are the result of transformations, which can be linear or nonlinear
• And what is happening with new phenomena like Big Data and information
sharing is that externally defined (some times imposed!) references are not
sufficient any more.
– Academic disciplines
– Software industries : Google Android Vs. Microsoft windows XP!
The goal: How to make the process of clustering and concept generation,
computationally practical for individuals?
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5. Cluster labeling problem
• Topic Modeling in Natural Language
Processing
– Document Clustering
– Automatic Sentiment Analysis
• Market Segmentation and Customer
Clustering
– CRM data
– City Call center Data (Mood of the City)
• Enterprise Knowledge Modeling
Using Text Archives

6. Topic Modeling in Natural Language Processing
The Expression of Emotions in 20th Century Books
Alberto Acerbi, et. al. 2013
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7. Topic Modeling in Natural Language Processing
The Expression of Emotions in 20th Century Books
Alberto Acerbi, et. al. 2013
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8. Clustering and Cluster Labeling
In terms of Geography-Andre Skupin (2005)

9. Clustering and Cluster Labeling
A Semantic
Landscape of the
Last.fm Music

10. Current Methods
• Differential Cluster Labeling
– Mutual Information
– Chi-Squared Selection
• Cluster-Internal Labeling
– Centroid Labels
– Title Labels
– External knowledge labels

11. The Proposed Method
• Use of SOM as a nonlinear Data-Clustering (transformation)
and visualization technique
• Use of the concept of tensor to produce required data
matrices for SOM

12. The Proposed Method
Tensors
(multi-aspect data representation)

13. Aspect A Features
Objects
Objects
Aspect A Features
• Wavelet Decomposition
• One original object (one signal ) is
decomposed to several aspects (different
scales or frequencies)
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14. The Proposed Method
SOM
(as a nonlinear data transformation: here used for clustering and visualization)

15. SOM is a Generic Machine works normally with Matrices of
data
10 records, 100+ dimensions
200+ records, 100+ dimensions
But with clear clusters
200+ records, 100+ dimensions
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16. The Proposed Method
Features
Clusters Vector
Y
Tensor
Objects
Objects
X
SOM Clustering
Original Data set
A second Order Tensor
Clusters Vector
Features
Objects
Features
Z
SOM
Visualization of the
main concepts
(potential labels) within
each cluster

17. The Case: Finding Thematic Research Areas within FCL
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18. Finding Thematic Research Areas within FCL
Each row vector shows one
persons interest related to
those selected features
Objects
Features
X
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19. Finding Thematic Research Areas within FCL
First plot
(each curve is one person)
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20. Finding Thematic Research Areas within FCL
SOM
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21. Finding Thematic Research Areas within FCL
SOM + K means clustering
Now…
What are the main
concepts within
each cluster?
How to label these
clusters?
Objects
Clusters Vector
Y
5 clusters detected
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22. Finding Thematic Research Areas within FCL
Tensor based transformation
Y
Clusters Vector
Features
Objects
Clusters Vector
Objects
Features
X
Z
A simple visualization of each cluster
regarding to all the features
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23. Finding Thematic Research Areas within FCL
Tensor based transformation
+ another SOM
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24. Finding Thematic Research Areas within FCL
Tensor based transformation
+ another SOM
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25. Finding Thematic Research Areas within FCL
Tensor based transformation
+ another SOM
25

26. Finding Thematic Research Areas within FCL
Tensor based transformation
+ another SOM
26

27. Finding Thematic Research Areas within FCL
Tensor based transformation
+ another SOM
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28. Finding Thematic Research Areas within FCL
Tensor based transformation
+ another SOM
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29. Thanks!