1. GPX: Interactive Exploration of Time-series Microarray Data
Daxin Jiang, Jian Pei, and Aidong Zhang
Motivations
Specific features of time-series microarray data
Special requirements from the domain of biology
Most clustering algorithms may not be effective to address the above problems

2. Time-series Microarray Data
Gene expression levels are monitored at different time points during a time series.

3. Co-expressed Genes and Coherent Patterns
Parallel coordinates for Iyer’s data
Examples of co-expressed genes and coherent patterns in gene expression data
[1] Iyer, V.R. et al. The transcriptional program in the response of human fibroblasts to serum. Science, 283:83–87, 1999.

4. Example – Cell Cycle
S phase
Early G1 phase
The cell cycle
Expression patterns of cell-cycle regulated genes of yeast reported by Spellman et al.
G2 phase
Late G1 phase
[2] Spellman et al., (1998).  Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization.  Molecular Biology of the Cell 9,
M phase

5. Cluster Analysis Partition the data set into several disjoint clusters
Each cluster is a group of co-expressed genes.
The centroid of the cluster is the coherent pattern.
Various of clustering methods
Partition-based approaches
Hierarchical approaches
Density-based approaches ……

6. What the Data Look Like
L. Zhang et al. Enhanced Visualization of Time Series through Higher Fourier Harmonics. BIOKDD 2003

7. High Connectivity of the Dataga gb
Two genes with complete different patterns connected by a “bridge”

8. Hierarchies of Co-expressed Genes and Coherent Patterns
The interpretation of co-expressed genes and coherent patterns mainly depends on the domain knowledge

9. To Split or Not Dependent on “domain knowledge” group A1 group A2

10. Which Split Option to Choose
Dependent on “domain knowledge”
Various split options may correspond to different hypotheses regarding gene function.

11. What is a “Good” Clustering Algorithm
Form a hierarchical structure
Flexible and convenient to derive clusters
Support users’ domain knowledge
Handle the high connectivity effectively

12. Partition-based Approaches
Form a hierarchical structure?
Yes, if we use it as the split strategy in the divisive approach
Flexible and convenient to derive clusters?
No, since the parameters are hard to determine
Handle the high connectivity effectively?
No, since it partitions the data set by force

13. Cut cluster borders by force

14. Hierarchical Approaches
Form a hierarchical structure?
Sure
Flexible and convenient to derive clusters?
Global threshold: convenient but not flexible
Handle the high connectivity effectively?
Depends on which inter-cluster measure is used
e.g., complete-link may be better than single-link

15. Density-based Approaches
Form a hierarchical structure?
Not explicitly
Possible if we adjust the parameters level by level
Flexible and convenient to derive clusters?
DBSCAN and DENCLUE use global thresholds
not flexible
OPTICS plots cluster structure
both flexible and convenient

16. Density-based Approaches
Handle the high connectivity effectively?
DBSCAN and OPTICS are not effective
“indirectly density-reachable” forms a chain
DENCLUE cuts the cluster border by force
center-defined clusters
a local maximum of density is the “center” of a cluster
other objects in the cluster are “attracted” to the local maximum

17. Our Solution– An Interactive Approach
Adopt a divisive approach to form a hierarchical structure
Users can choose whether to split or not
Still need one parameter
robust
easy to determine
Plot the cluster structure of the data set
Users can explore the data set by “drill down” and “roll up” operations based on their domain knowledge
Apply a novel strategy to handle the high connectivity.
Users can determine the cluster border

18. Pattern-based Strategy
coherent pattern
To find co-expressed genes and coherent expression patterns
Cluster-based strategy
First find clusters as co-expressed genes
Then use centroids as coherent expression patterns
Pattern-based strategy
First find coherent expression patterns
Then determine the co-expressed genes conforming to the pattern
Similarity
Genes …
0.94
gene g i6
gene g i5
0.95
gene g i4
0.98
gene g i3
gene g i2
0.99
gene g i1
-0.55
gene g in
-0.45
gene g in-1
-0.44
gene g in-2
  
Pattern-based strategy

19. Distance Measure Users are interested in overall shape
Euclidean distance does not work well
Normalize each data object O to O’ with a mean of 0 and a variance of 1
An object
After normalization
Shifting patterns
m is the number of attributes,  and  are the mean and the standard deviation of O, respectively.
Scaling patterns

20. Distance Measure Similarity and Distance between two genes (objects)
The similarity and distance measure defined above are consistent
Given objects O1, O2, O3 and O4,
Similarity(O1,O2)≥Similarity(O3,O4)
if and only if Distance(O1,O2)  Distance(O3,O4)

21. A Density-based Model A group of co-expressed genes form a dense area;
Genes at the core area have high density, while genes at the boundary area have low density;
Genes at the boundary area are “attracted” towards the local maximum level by level.

22. Density Measures Radius-based density KNN-based density
DENCLUE density

23. Definition of Density We modify the density definition by Denclue[3]
The influence function (attraction function)
Given a data set D
d(Oi,Oj) is the distance between Oi and Oj, and  is a parameter
is the estimated average similarity within a cluster
[3] Hinneburg, A. et al. An efficient approach to clustering in large multimedia database with noise. Proc. 4th Int. Con. on Knowledge discovery and data mining, 1998.

24. Attraction Tree
The “attractor” of object O is its nearest neighbor with a higher density than O.
Denoted by O  Attractor(O).
We can derive an attraction tree based on the “attractor” relationship
The weight for each edge e(Oi,Oj) on the attraction tree is defined as the similarity between Oi and Oj.
Use Pearson’s correlation coefficient as similarity measure.

25. An Example of Attraction Tree
An example data set
The attraction tree
Three features of attraction tree:
self-closed: a group of objects conforming to the same coherent pattern forms an attraction subtree.
robust to intermediate genes (noise)
three levels of edge weights

26. Index List Serialization of the attraction tree
Search the attraction tree based on the edge weight.
Order the genes in the “index list”.
The attraction tree
The index list

27. Index list
Similarity curve for
Iyer’sdata set

28. Coherent Pattern Index Graph
Compute the “coherent pattern index (CPI)” for each gene.
p is a parameter, Sim(gi) is the similarity between gi and its parent gj on the attraction tree
The index list
The coherent pattern index graph

30. M phase
S phase
Early G1 phase
Late G1 phase
G2 phase

31. Validation Measure P1 C1 P2 C2 P3 C3 P4 C4 … … Pn Cm
Ground truth patterns
Reported patterns
P1 is matched by C4 with similarity (suppose Sim(P1,C4)=0.95)
P2 is matched by C1 with similarity (supposeSim(P2,C1)=0.9)

32. Comparison With Other Approaches
Pattern
GPX (10)
Kmeans (10)
SOM (10)
SOTA (50)
Adapt(11)
CLICK(7)
CAST (9) 1
0.998
0.973
0.983
0.962
0.956
0.884
0.955 2
0.996
0.950
0.992
0.936
0.911
0.991
0.887 3
0.993
0.910
0.872
0.947
0.994
0.997 4
0.995
0.989
0.984
0.883
0.968 5
0.964
0.882
0.716
0.868
0.855 6
0.940
0.965
0.764
0.972
0.970 7
0.880
0.892
0.988
0.976
0.990
0.719 8
0.963
0.917
0.958
0.914
0.999 9
0.907
0.848
0.824
0.844
0.800 10
0.987
0.930
0.960
0.981
The similarity between the pattern reported by different approaches and the corresponding pattern in the ground truth (if any)

33. Comparison With Other Approaches
Pattern
GPX (7)
Kmeans (5)
SOM (5)
SOTA (99)
Adapt(21)
CLICK(9)
CAST (19) 1
0.901
0.928
0.194
0.938
0.884
0.855
0.900 2
0.970
0.976
0.972
0.968
0.978 3
0.980
0.950
0.552
0.940
0.953
0.888 4
0.773
0.437
0.961
0.796
0.984 5
0.945
0.965
0.964
0.956
0.962

34. Comparison with Optics
Iyer’s data set
Spellman’s data set

35. Effects of Parameters
Spellman’s data set
Iyer’s data set

36. Scalability The algorithm scales well with large data sets.
The computation time is dominated by the distance calculation.