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**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

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**Outline: Flow Cytometry (FCM) Data Clustering of FCM data**

Spectral Clustering Faithful Sampling for Spectral Clustering Result Summary

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**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

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**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)

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**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

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**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

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**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

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**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

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**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)

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**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.

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**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.

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Clustering Result Low density populations surrounded by dense ones

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**Clustering Result Populations with Non-elliptical Shapes**

Subpopulations of a major population SamSPECTRAL flowMerge FLAME

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**Dependency of SamSPECTRAL Results to Scaling Factor (σ)**

Monocytes Dendritic Cells σ = 100 σ = 200 B Cells σ = 300 σ = 400

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**Block Diagram of Clustering Ensemble Method**

σ1 σ2 σr SamSPECTRAL SamSPECTRAL SamSPECTRAL Build New Feature Vectors Compute Similarities Between Categorical Feature Vectors SamSPECTRAL for Categorical Data Final Results

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**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

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**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

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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

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**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

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**Thanks for Your Attention!**

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**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)

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**SamSPECTRAL Algorithm**

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**SamSPECTRAL Algorithm**

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