1. Lecture 10. Clustering Algorithms
The Chinese University of Hong Kong
CSCI3220 Algorithms for Bioinformatics

2. Lecture outline Numeric datasets and clustering
Some clustering algorithms
Hierarchical clustering
Dendrograms
K-means
Subspace and bi-clustering algorithms
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

3. Numeric Datasets and Clustering
Part 1
Numeric Datasets and Clustering

4. Numeric datasets in bioinformatics
So far we have mainly studied problems related to biological sequences
Sequences represent the static states of an organism
Program and data stored in hard disk
Numeric measurements represent the dynamic states
Program and data loaded into memory at run time
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

5. Gene expression
Protein abundance is the best way to measure activity of a protein coding gene
However, not much data is available due to difficult experiments
mRNA levels are not ideal indicators of gene activity
mRNA level and protein level are not very correlated due to mRNA degradation, translational efficiency, translation and post-translational modifications, and so on
However, it is very easy to measure mRNA levels
High-throughput experiments to measure the mRNA levels of many genes at a time: microarrays and RNA (cDNA) sequencing
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

6. RNA sequencing
RNA sequencing is becoming a standard technology for measuring mRNA levels
Convert RNAs back to cDNAs, sequence them, and identify which genes they correspond to
“Digital”: expression level represented by read counts
No need to have prior knowledge about the sequences
If a sequence is not unique to a gene, cannot determine which gene it comes from
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

7. RNA sequencing
Image credit: Wang et al., Nature Review Genetics 10(1):57-63, (2009)
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

8. Processing RNA-seq data
Many steps and we will not go into the details
Quality check
Read trimming and filtering
Read mapping (BWT, suffix array, etc.)
Data normalization
...
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

9. Gene expression data Final form of data from microarray or RNA-seq:
A matrix of real numbers
Each row corresponds to a gene
Each column corresponds to a sample/experiment:
A particular condition
A cell type (e.g., cancer)
Questions:
Are there genes that show similar changes to their expression levels across experiments?
The genes may have related functions
Are there samples with similar set of genes expressed?
The samples may be of the same type
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

10. Clustering of gene expression data
Clustering: Grouping of related objects into clusters
An object could be a gene or a sample
Usually clustering is done on both. When genes are the objects, each sample is an attribute. When samples are the objects, each gene is an attribute
Goals:
Similar objects are in the same cluster
Dissimilar objects are in different clusters
Could define a scoring function to evaluate how good a set of clusters is
Most clustering problems are NP hard
We will study heuristic algorithms
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

11. Heatmap and clustering results
Color: expression level
Clustering
Samples
Genes
Image credit: Borries and Wang, Computational Statistics & Data Analysis 53(12): , (2009); Alizadeh et al., Nature 403(6769): , (2000)
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

12. Some Clustering Algorithms
Part 2
Some Clustering Algorithms

13. Hierarchical clustering
One of the most commonly used clustering algorithms is agglomerative hierarchical clustering
Agglomerative: Merging
There are also divisive hierarchical clustering algorithms
The algorithm:
Treat each object as a cluster by itself
Compute the distance between every pair of clusters
Merge the two closest clusters
Re-compute distance values between the merged cluster and each other cluster
Repeat #3 and #4 until only one cluster is left
Same as UPGMA, but without the phylogenetic context
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

14. Hierarchical clustering
2D illustration:
Each point is a gene
The coordinate of a point indicates the expression value of the gene in two samples
Dendrogram
(similar to a phylogenetic tree)
Sample 1
Sample 2 A B C D E F A B C D E F
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

15. Representing a dendrogram
Since a dendrogram is essentially a tree, we can represent it using any tree format
For example, the Newick format:
(((A,B),(C,(D,E))),F);
We could use the Newick format to also specify how the leaves should be ordered in a visualization.
For example, for the Newick string (F,((B,A),((D,E),C))); from the same merge order of the clusters but with the leaves ordered differently, the corresponding dendrogram is: A B C D E F B A C D E F
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

16. More details Three questions:
How to compute the distance between two points?
How to compute the distance between two clusters?
How to efficiently perform these computations?
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

17. Distance Most common: Euclidean distance
xi1j is the expression level of the i1-th object (say, gene) and the j-th attribute (say, sample) and m is the total number of attributes
Need to normalize the attributes
Also common: (1 - Pearson correlation) / 2. Pearson correlation is a similarity measure with value between -1 and 1:
, where
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

18. Euclidean distance vs. correlation
Two points have small Euclidean distance if their attribute values are close (but not necessarily correlated)
Two points have large Pearson correlation if their attribute values have consistent trends (but not necessarily close)
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

19. Which one to use?
Sometimes absolute expression values are more important
Example: When there is a set of homogenous samples (e.g., all of a certain cancer type), and the goal is to find out genes that are all highly expressed or lowly expressed
Usually the increase-decrease trend is more important than absolute expression values
Example: When detecting changes between two sets of samples or across a number of time points
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

20. Similarity between two clusters
Several schemes (using Euclidean distance as example):
Average-link: average between all pairs of points (used by UPGMA)
Single-link: closest among all pairs of points
Complete-link: farthest among all pairs of points
Centroid-link: between the centroids
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

21. Similarity between two clusters
Average-link: equal vote by all members of the clusters, preferring to merge clusters liked by many
Single-link: merge two clusters even if just one pair likes it very much
Complete-link: not merge two clusters even if just one pair does not like it
Centroid-link: similar to average-link, but easier to compute
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

22. Similarity between two clusters
Suppose clusters C1 and C2 have already been formed
Average-link prefers to merge I and C2 next, as their points are close on average
Single-link prefers to merge C1 and E next, as C and E are very close
Complete-link prefers to merge I and C2 next, as I is not too far from F, G or H (as compared to A-E, C-H, E-H, etc.)
Centroid-link prefers to merge C1 and C2 next, as their centroids are close (and not so affected by the long distance between C and H) C1 C2 H A F G D B C I E
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

23. Updating
To determine which two clusters are most similar, we need to compute the distance between every pair of clusters
At the beginning, this involves O(n2) computations for n objects, followed by a way to find out the smallest value, either
Linear scan, which would take O(n2) time OR
Sorting, which would take O(n2 log n2) = O(n2 log n) time
After a merge, we need to remove the distances involving the two merging clusters, and add back the distances of the new cluster with all other clusters: O(n) between-cluster distance calculations (assuming that takes constant time for now – will come back to this topic later), followed by either
Linear scan of new list, which would take O(n2) time OR
Re-sorting, which would take O(n2 log n) time OR
Binary search and removing/inserting distances, which would take O(n log n2) = O(n log n) time
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

24. Updating Summary: At the beginning After each merge In total,
Linear scan: O(n2) time OR
Sorting: O(n2 log n) time
After each merge
Re-sorting: O(n2 log n) time OR
Binary search and removing/inserting distances: O(n log n) time
In total,
Linear scan: O(n3) time
Maintaining a sorted list: O(n2 log n) time
Can these be done faster?
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

25. Heap
A heap (also called a priority queue) is for maintaining the minimum value of a list of numbers without sorting
Ideas:
Build a binary tree structure with each node storing one of the numbers, and the root of a sub-tree is always smaller than all other nodes in the sub-tree
Store the tree in an array that allows efficient updates
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

26. Heap
Example: tree representation (each node is the distance between two clusters)
Corresponding array representation (notice that the array is not entirely sorted)
If first entry has index 0, then the children of node at entry i are at entries 2i+1 and 2i+2
Smallest value always at the first entry of the array 1 4 9 5 6 10 13 12 8 11 1 4 9 5 6 10 13 12 8 11 2 3 7
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

27. Constructing a heap Staring with any input array
From node at entry N/2 down to node at entry 1, swap with smallest child iteratively if it is smaller than the current node
N is the total number of nodes, which is equal to n(n-1)/2, the number of pairs for n clusters
Example input: 13, 5, 10, 4, 11, 1, 9, 12, 8, 6 13 5 10 4 11 1 9 12 8 6
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

28. Constructing a heap 13 5 10 4 11 1 9 12 8 6 13 5 10 4 6 1 9 12 8 11 13 5 10 4 6 1 9 12 8 11 13 5 10 4 6 1 9 12 8 11 13 5 1 4 6 10 9 12 8 11 13 5 1 4 6 10 9 12 8 11 13 4 1 5 6 10 9 12 8 11 13 4 1 5 6 10 9 12 8 11 1 4 9 5 6 10 13 12 8 11
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

29. Constructing a heap Input: Output: 13 5 10 13 5 10 4 11 1 9 12 8 6 4
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

30. Constructing a heap Time needed:
Apparently, for each of the O(N) nodes, up to O(log N) swaps are needed, so O(N log N) time in total
Same as sorting
However, by doing a careful amortized analysis, actually only O(N) time is needed
Why?
Because only one node could have log N swaps, two nodes could have log N - 1 swaps, etc.
For example, for 15 nodes:
N log N = 15 log2 15  15(3) = 45
3 + 2(2) + 4(1) + 8(0) = 11
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

31. Deleting a value
For many applications of heaps, deletion is done to remove the value at the root only
In our clustering application, for each cluster we maintain the entries corresponding to the distances related to it, so after the cluster is merged we remove all these distance values from the heap
In both cases, deletion is done by moving the last value to the deleted entry, then re- “heapify”
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

32. Deleting a value Example: deleting 4 Each deletion takes O(log N) time
After each merge of two clusters, need to remove O(n) distances from heap – O(n log N) = O(n log n) time in total 1 1 11 9 5 6 10 13 12 8 1 5 9 8 6 10 13 12 11 4 9 5 6 10 13 12 8 11 1 4 9 5 6 10 13 12 8 11
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

33. Inserting a new value Add to the end
Iteratively swap with parent until larger than parent
Example: Adding value 3
Each insertion takes O(log N) time
After each merge of two clusters, need to insert O(n) distances to heap – O(n log N) = O(n log n) time in total 1 1 3 9 8 5 10 13 12 11 6 5 9 8 6 10 13 12 11 3 1 5 9 8 6 10 13 12 11 3
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

34. Total time and space O(N) = O(n2) space
Initial construction: O(N) = O(n2) time
After each merge: O(n log n) time
O(n) merges in total
Therefore in total O(n2 log n) time is needed
Now we study another structure that needs O(n2) space but only O(n2) time in total
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

35. Quad tree
Proposed in Eppstein, Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms , (1998)
Main idea: Group the objects iteratively to form a tree, with the minimum distance between all objects stored at the root of the sub-tree
Example: Distances between 9 objects
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

36. Quad tree 1 6 6 5 15 17 11 14 10 16 12 13 9 20 8 1 2 3 4 7 18 2 5 10 3 15 16 12 4 17 12 20 17 5 11 13 8 4 17 6 11 13 8 4 18 1 7 14 9 16 14 4 13 14 8 11 6 13 12 7 11 12 3 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 12 11 1 2 3 4 5 6 7 8
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

37. Updating the quad tree After a merge, the algorithm needs to
Delete distance values in two rows and two columns
Add back distance values into a row and a column
If we do not want to compact the tree, simply fill in  to the other row and column
Re-compute minimum values at upper levels
Example: Merging clusters 5 and 6
Suppose new distance between this merged cluster and other clusters are: 1 2 3 4 7 8 11 13 17 14 12
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

38. Merging clusters 5 and 6 1 6 6 5 15 17 11  14 10 16 12 13 9 20 8 1 2 3 4
5,6 7 2 5 10
Distances with new cluster: 3 15 16 12 1 2 3 4 7 8 11 13 17 14 12 4 17 12 20 17 5 11 13 8 4 17 6 11 13 8 4 18 1 7 14 9 16 14 4 13 14 8 11 6 13 12 7 11 12 3 1 2 3 4 5 6 7 6 5 15 17 11  14 10 16 12 13 9 20 8 1 2 3 4
5,6 7 1 2 3 4
5,6 7 8 5 12 11 17 6 1 2 3 4
5,6 7 8 5
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

39. Space and time analysis
Space needed: O(n2)
Initial construction: O(n2 + n2/4 + n2/ ) = O(n2) time
After each merge, number of values to update: O(2n + 2n/2 + 2n/ ) = O(n), each taking a constant amount of time
Time needed for the whole clustering process = O(n2)
More efficient than using a heap
There are data structures that require less space but more time
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

40. Computing within-cluster distances
If Ci and Cj are merged, how to compute d(CiCj,Ck) based on d(Ci,Ck) and d(Cj,Ck)?
Single-link: d(CiCj,Ck) = min{d(Ci,Ck), d(Cj,Ck)}
Complete-link: d(CiCj,Ck) = max{d(Ci,Ck), d(Cj,Ck)}
Average-link: d(CiCj,Ck) = [d(Ci,Ck)|Ci||Ck| + d(Cj,Ck)|Cj||Ck|] / [(|Ci|+|Cj|)|Ck|]
Centroid-link: Cen(CiCj) = [Cen(Ci)|Ci| + Cen(Cj)|Cj|] / (|Ci|+|Cj|)
All can be performed in constant time
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

41. A minor issue
What if the number of rows/columns in the distance matrix is not a power of 2?
Just add extra rows to the quad tree and fill them with 
Or just ignore these rows, which can save some space as compared to the above solution
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

42. A minor issue 1 6 6 5 15 17 11 14  10 16 12 13 9 20 8 1 2 3 4 7 18 2 5 10 3 15 16 12 4 17 12 20 17 5 11 13 8 4 17 6 11 13 8 4 18 1 7 14 9 16 14 4 13 14 8         1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 12 11 9 14 1 2 3 4 5 6 7 8
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

43. K-means K-means is another classical clustering algorithm
MacQueen, Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability , (1967)
Instead of hierarchically merging clusters, k-means iteratively partitions the objects into k clusters by repeating two steps until stabilized:
Determining cluster representatives
Randomly determined initially
Centroids of current members in subsequent iterations
Assigning each object to the cluster with the closest representative
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

44. Example (k=2) C1 A B C D E F I G H E G A B C D E F I G H A F C2 H B D
Random initial representatives C1
Assignment A B C D E F I G H E G
Re-determining
representatives A B C D E F I G H A F C2 H B D I C
Assignment A B C D E F I G H C1 C2
Assignment A B C D E F I G H C1
Re-determining
representatives A B C D E F I G H C2
Re-determining
representatives A B C D E F I G H
Assignment A B C D E F I G H C2 C1
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

45. Hierarchical clustering vs. k-means
Advantages
Providing the whole clustering tree (dendrogram), can cut to get any number of clusters
No need to pre-determine k
Fast
Low memory consumption
An object can move to another cluster
Disadvantages
Slow
High memory consumption
Once assigned, an object always stays in a cluster
Providing only final clusters
Need to pre-determine k
There are hundreds of other clustering algorithms proposed:
More efficient
Allowing other data types
Considering domain knowledge
Model-based
Finding clusters in subspaces (coming up next)
Density approach
...
Less sensitive to outliers
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

46. Embedded clusters
Euclidean distance and Pearson correlation consider all attributes equally
It is possible that for each cluster, only some attributes are relevant
Image credit: Pomeroy et al., Nature 415(6870): , (2002)
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

47. Finding clusters in a subspace
One way is not to distinguish between objects and attributes, but to find a subset of rows and a subset of columns (a bicluster) so that the values inside the bicluster exhibit some coherent patterns
Here we study one bi-clustering algorithm
Cheng and Church, 8th Annual International Conference on Intelligent Systems for Molecular Biology, , (2000)
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

48. Cheng and Church biclustering
Notations:
I is a subset of the rows
J is a subset of the columns
(I, J) defines a bicluster
Model: Each value aij (at row i and column j) in a cluster is influenced by:
Background of the whole cluster
Effect of the i-th row
Effect of the j-th column
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

49. Cheng and Church biclustering
Assumption:
In the ideal case, aij = aiJ + aIj – aIJ, where
is the mean of values in the cluster at row i
is the mean of values in the cluster at column j
is the mean of all values in the cluster
Goal of the algorithm is to find I and J such that the following mean squared residue score is minimized:
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

50. Example
Suppose the values in a cluster are generated according to the following row and column effects:
Then the corresponding averages values are:
a11 – a1J – aI1 + aIJ = 12 – 12.5 – = 0
You can verify for other i’s and j’s
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

51. Why this model?
Assuming the expression level of a gene in a particular sample is determined by three additive effects:
The cluster background
E.g., the activity of the whole functional pathway
The gene
E.g., some genes are intrinsically more active
The sample
E.g., in some samples, all the genes in the cluster are activated
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

52. Algorithm
How to find out clusters (i.e., (I, J)) that have small H values?
It is proved that finding the largest cluster with H less than a fixed threshold  is NP hard
Heuristic method:
Randomly determine I and J
Try all possible addition/deletion of one row/column, and accept the one that results in smallest H
Some variations involve addition or deletion only, or allowing addition or deletion of multiple rows/columns
Repeat #2 until H does not decrease or it is smaller than threshold 
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

53. More details
Obviously, if the cluster contains only one row and one column, the residue H must be 0
Could limit the minimum number of rows/columns
A cluster containing genes that do not change their expression values across different samples may not be interesting
Could use the variance of expression values across samples as a secondary score
How to find more than one cluster?
After finding a cluster, replace it with random values before calling the algorithm again
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

54. Some clusters found
Each line is a gene. The horizontal axis represents different time points
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

55. Case Study, Summary and Further Readings
Epilogue
Case Study, Summary and Further Readings

56. Case study: Successful stories
Clustering of gene expression data has led to the discovery of disease subtypes and key genes to some biological processes
Example 1: Automatic identification of cancer subtypes acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL) without prior knowledge of these classes
2 clusters
4 clusters
Image credit: Golub et al., Science 286(5439): , (1999)
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

57. Case study: Successful stories
Example 2: Identification of genes involved in the response to external stress
Each triangle: multiple time points after producing an environmental change, such as heat shock or amino acid starvation
Image credit: Gasch et al., Molecular Biology of the Cell 11(12): , (2000)
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

58. Case study: Successful stories
Example 3: Segmentation of the human genome into distinct region classes
Image credit: The ENCODE Project Consortium, Nature 489(7414):57-74, (2012)
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

59. Summary
Clustering is the process to group similar things into clusters
Many applications in bioinformatics, the most well-known one is on gene expression analysis
Classical clustering algorithms
Agglomerative hierarchical clustering
K-means
Subspace/bi-clustering algorithms
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017

60. Further readings
The book by Leonard Kaufman and Peter J. Rousseeuw, Finding Groups in Data: An Introduction to Cluster Analysis, Wiley Inter-Science 1990
A classical reference book on cluster analysis
Last update: 24-Aug-2017
CSCI3220 Algorithms for Bioinformatics | Kevin Yip-cse-cuhk | Fall 2017