1. Faithful Sampling for Spectral Clustering to Analyze High Throughput Flow Cytometry Data
Parisa Shooshtari
School of Computing Science, Simon Fraser University, Burnaby
Brinkman’s Lab, Terry Fox Laboratory, BC Cancer Agency, Vancouver

2. Outline: Flow Cytometry (FCM) Data Clustering of FCM data
Spectral Clustering
Faithful Sampling for Spectral Clustering
Result
Summary

3. Basics of Flow Cytometry Technique
Sample
Int-1
MHC-II
MHC-II
Intensity
MHC-II
CD-11c
Wave Length
CD-11c
Intensity
Int-2
MHC-II
Int-2
Int-1
MHC-II
CD-11c
Wave Length

4. Cell Population Identification in Flow Cytometry (FCM)
Parameter 2
Parameter 1 X%
Parameter 3
Parameter 4
Now think that this cell is just one of thousands of cells flowing pass through a tube one cell at a time. These cells can be differentiated using the fluorescence intensity indicating, for example, presence or absence of a particular cell surface protein. CLICK Here each dot represent individual cell. Axes indicate intensity at different wavelengths. A gate can then be drawn to select a particular subset of cell population with common intensities.
Further sub-setting can be done based on 1-D and 2-D projections of data
Adapted from the Science Creative Quarterly (2)

5. Importance of FCM Data Clustering
Manual Gating is
Subjective
Error-prone
Time-Consuming
It ignores the multi-variation nature of the data
Analyzing large size FCM data sets (with up to 19 dimensions and 1000,000 points) is impractical without the aim of automated techniques

6. Which Clustering Algorithm Is Suitable?
Model-Based algorithms like FlowClust, FlowMerge and FLAME are not suitable for non-elliptical shape clusters.
A Good Clustering
FlowMerge
GFP

7. Our Motivation for Using Spectral Clustering
Spectral clustering does not require any priori assumption on cluster size, shape or distribution
It is not sensitive to outliers, noise and shape of clusters

8. Spectral Clustering in One Slide
Represent data sets by a similarity graph
Construct the Graph:
Vertices: data points p1, p2, …, pn
Weights of edges: similarity values Si, j as
Clustering: Find a cut through the graph
Define a cut objective function
Solve it

9. The Bottleneck of Spectral Clustering
Serious empirical barriers when applying this algorithm to large datasets
Time complexity: O(n3) ---- > 2 years for 300,000 data points (cells)
Required memory: O(n2) ---- > 5 terabytes for 300,000 data points (cells)

10. Faithful Sampling: Our Solution for Applying Spectral Clustering to Large Data
Uniform Sampling:
Low density populations close to dense ones may not remain distinguishable
Faithful Sampling:
Tends to choose more samples from non-dense parts of the data.

11. How Does Our Faithful Sampling Preserve Information?
Space Uniform Sampling: It preserves low-density parts of the data by selecting more samples from them compared to the uniform sampling.
Keeping the list of points in neighbourhood of samples: This will be used to define similarities between communities.

12. Clustering Result
Low density populations surrounded by dense ones

13. Clustering Result Populations with Non-elliptical Shapes
Subpopulations of a major population
SamSPECTRAL
flowMerge
FLAME

14. Dependency of SamSPECTRAL Results to Scaling Factor (σ)
Monocytes
Dendritic Cells
σ = 100
σ = 200
B Cells
σ = 300
σ = 400

15. Block Diagram of Clustering Ensemble Methodσ1 σ2 σr
SamSPECTRAL
SamSPECTRAL
SamSPECTRAL
Build New Feature Vectors
Compute Similarities Between Categorical Feature Vectors
SamSPECTRAL for Categorical Data
Final Results

16. Results After Applying Clustering Ensemble Method
CD14
MHC-II
Final Result after Applying Clustering Ensemble Method
Manual Gating
Monocytes
Monocytes
CD14
B Cells
B Cells
Dendritic Cells
Dendritic Cells
MHC-II

17. Advantages of Using Clustering Ensemble Method
No need for manual setting of initial parameters
Higher quality and stability of clustering results
F-measure between manual gating and original SamSPECTRAL is in average 0.77 (sd=0.07)
F-measure between manual gating and our clustering ensemble method is 0.91

18. Summary
Spectral clustering can now be applied to large size data by our proposed Faithful (Information Preserving) sampling.
This sampling method can be used in combination with other graph-based clustering algorithms with different objective functions to reduce size of the data.
We have shown that SamSPECTRAL has advantage over model-based clusterings in identification of
Cell populations with non-elliptical shapes
Low-density populations surrounded by dense ones
Sub-populations of a major population

19. Acknowledgement Committee: Co-authors on SamSPECTRAL Data Providers
Dr. Arvind Gupta
Dr. Ryan Brinkman
Dr. Tobias Kollman
Co-authors on SamSPECTRAL
Habil Zare
Data Providers
Connie Eaves
Peter Landsdrop
Keith Humphries

20. Thanks for Your Attention!

21. Cell Population Identification in Flow Cytometry (FCM)
Parameter 2
Parameter 1 X%
Parameter 3
Parameter 4
Now think that this cell is just one of thousands of cells flowing pass through a tube one cell at a time. These cells can be differentiated using the fluorescence intensity indicating, for example, presence or absence of a particular cell surface protein. CLICK Here each dot represent individual cell. Axes indicate intensity at different wavelengths. A gate can then be drawn to select a particular subset of cell population with common intensities.
Further sub-setting can be done based on 1-D and 2-D projections of data
Adapted from the Science Creative Quarterly (2)

22. SamSPECTRAL Algorithm

23. SamSPECTRAL Algorithm