Exploratory data analysis approaches unsupervised approaches. Steven Kiddle With thanks to Richard Dobson and Emanuele de Rinaldis

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1 Exploratory data analysis approaches unsupervised approaches Steven Kiddle With thanks to Richard Dobson and Emanuele de Rinaldis

2 Lecture overview Page 1 Ø Background Ø Revision Ø Other clustering methods

3 Background Page 2

4 Motivation Page 3 The most challenging task for a scientist is to make sense of lots of data The power of high-throughput analysis does not come from the analysis of single genes, but rather, from the analysis of many data points to identify patterns of gene expression Unsupervised learning allows unexpected patterns to be spotted

5 Supervised v.s. Unsupervised learning Page 4 Supervised Inputs Observations Observations Outputs

6 Supervised v.s. Unsupervised learning Page 5 Supervised Observations Inputs Unsupervised Unobserved, or not used in initial analysis Observations Observations Outputs

7 Clustering Page 6 Finding a partition such that: - Distance between objects within partition is minimised - Distance between objects from different cluster is maximised

8 Applications Page 7 Biology finding similar organisms, sequences, molecular signatures Marketing identify groups of customers with similar preferences Earthquakes Predict epicentre based on recordings Images Image compression Many more

9 Revision Page 8

10 Hiearchical clustering revision Page 9 In R: hclust In MATLAB: clusterdata

11 Hiearchical clustering revision Page 10 In R: hclust In MATLAB: clusterdata

12 Hiearchical clustering revision Page 11 In R: hclust In MATLAB: clusterdata

13 Hiearchical clustering revision Page 12 In R: hclust In MATLAB: clusterdata

14 Page 13

15 Page 14

16 Page 15

17 Page 16

18 Screen Shot at Page 17

19 Page 18

20 Principal Components Analysis (PCA) revision Page 19 gettinggeneticsdone.blogspot.co.uk/ In R: prcomp In MATLAB: princomp

21 Principal Components Analysis (PCA) revision Page 20 gettinggeneticsdone.blogspot.co.uk/ In R: prcomp In MATLAB: princomp

22 Other clustering methods Page 21

23 Multidimensional scaling (MDS) Page 22 PCA is a special case of MDS. MDS can use non-linear transformations of data points. Aflalo et al 2013

24 Automatic identification of clusters Page 23 Standard approaches: Ø K-means Ø K-centre

25 K-means example Page 24 Li et al., (2010)

26 K-means algorithm Page 25 In R: kmeans In MATLAB: kmeans 1) k initial "means" (in this case k=3) are randomly generated within the data domain (shown in color). Wikimedia

27 K-means algorithm Page 26 2) k clusters are created by associating every observation with the nearest mean. Wikimedia

28 K-means algorithm Page 27 3) The centroid of each of the k clusters becomes the new mean. Wikimedia

29 K-means algorithm Page 28 4) Steps 2 and 3 are repeated until convergence has been reached. Wikimedia

30 K-means disadvantages Page 29 Assumes clusters have same variance as each other in all directions. Ø Expectation-Maximisation (EM) clustering Requires a distance measure with a defined mean, such as Euclidean distance (the Pythagoras/ordinary distance). Ø K-centres Wikimedia

31 Unusual distance measures Page 30 Flight time can be affected by wind, busy airports etc Wikimedia

32 K-centres (also called K-medians) Page 31 Same data points as we used for k-means In R: pam {cluster} In MATLAB: kcenters Wikimedia

33 K-centres (also called K-medians) Page 32 1) k data points selected at random. Wikimedia

34 K-centres (also called K-medians) Page 33 2) k clusters are created by associating every observation with the nearest centre/median. Wikimedia

35 K-centres (also called K-medians) Page 34 3) For each cluster, the observation with the shortest distance to the rest of the cluster is chosen as the new centre/median. Wikimedia

36 K-centres (also called K-medians) Page ) Steps 2 & 3 are repeated until convergence has been reached Wikimedia

37 Example of results Page 36 Wikimedia

38 Even more clustering methods Page 37 K-means style Ø Expectation Maximisation Ø Self Organising Maps Ø Neural Networks K-centres style Ø Affinity Propagation (Frey et al., 2007) Ø Simulated Annealing For time series Ø SplineCluster (Heard et al., 2006) Wikimedia

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