C LUSTERING S TRATEGY : SWIFT GMM clustering with Sampling for k [ K - - PowerPoint PPT Presentation

SWIFT: SCALABLE WEIGHTED ITERATIVE FLOW-CLUSTERING TECHNIQUE

Iftekhar Naim∗, Gaurav Sharma∗, Suprakash Datta†, James S. Cavenaugh∗, Jyh-Chiang E. Wang∗, Jonathan A. Rebhahn∗, Sally

• A. Quataert∗, and Tim R. Mosmann∗

∗University of Rochester, Rochester, NY †York University, Toronto, ON

FlowCAP Summit, 2010

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OUTLINE

1 INTRODUCTION Flow cytometry (FC) Data Analysis Automated Multivariate clustering of FC Data 2 SWIFT METHOD FOR FC DATA ANALYSIS SWIFT Algorithm Weighted Iterative Sampling based EM Bimodality Splitting Graph-based Merging 3 DOES IT WORK? Does It Work? How Do We Know It Works? 4 FLOWCAP CONTEST Results on FlowCAP Datasets Few Thoughts for FlowCAP II 5 CONCLUSION

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OUTLINE

1 INTRODUCTION Flow cytometry (FC) Data Analysis Automated Multivariate clustering of FC Data 2 SWIFT METHOD FOR FC DATA ANALYSIS SWIFT Algorithm Weighted Iterative Sampling based EM Bimodality Splitting Graph-based Merging 3 DOES IT WORK? Does It Work? How Do We Know It Works? 4 FLOWCAP CONTEST Results on FlowCAP Datasets Few Thoughts for FlowCAP II 5 CONCLUSION

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FLOW CYTOMETRY (FC) OVERVIEW

◮ Rapid multivariate analysis of individual cells.

◮ High throughput data generation (description of ∼ 1 million cells). ◮ High dimensionality (∼ 20 measurements per cell). Antigen Cell Antibody Fluorochrome

FIGURE: Flow cytometry system (Ref: http://probes.invitrogen.com)

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FC DATA ANALYSIS

◮ Traditionally FC data analyzed by Manual Gating

◮ Subjective, Scales poorly with increasing dimensions ◮ 1D/2D Projections may not represent full picture ◮ Inaccurate for overlapping clusters

(a) Two

• verlapping

clusters (b) Combined view (c) Manual gating

FIGURE: Manual gating for overlapping clusters.

◮ Automated multivariate clustering is desirable for FC Data

analysis .

◮ Repeatable, nonsubjective, comprehends multivariate structure.

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CHALLENGES OF AUTOMATED CLUSTERING OF FC DATA

◮ Challenges of Automated Clustering:

◮ Large FC datasets ◮ ∼ 1 million events ◮ High dimensionality ( 20 or more dimensions) ◮ Very small clusters that are important in immunological analysis

(100 − 200 cells out of millions)

◮ Overlapping clusters and background noise

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CHALLENGES OF AUTOMATED CLUSTERING OF FC DATA

◮ Challenges of Automated Clustering:

◮ Large FC datasets ◮ ∼ 1 million events ◮ High dimensionality ( 20 or more dimensions) ◮ Very small clusters that are important in immunological analysis

(100 − 200 cells out of millions)

◮ Overlapping clusters and background noise

◮ Our goal: Design automated clustering method capable of

addressing these challenges

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MANY DIFFERENT CLUSTERING METHODS

....

Patitional Clustering Hard Soft Clustering Clustering Spectral Based Grid Model Mixture Fuzzy K-means

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MANY DIFFERENT CLUSTERING METHODS

....

Patitional Clustering Hard Soft Clustering Clustering Spectral Based Grid Model Mixture Fuzzy K-means

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MODEL BASED CLUSTERING FOR FC DATA

◮ Model based clustering offers several advantages:

◮ Soft clustering- comprehends overlapping clusters, background

noise

◮ BUT, computationally expensive and choice of model imposes

limitation

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MODEL BASED CLUSTERING FOR FC DATA

◮ Model based clustering offers several advantages:

◮ Soft clustering- comprehends overlapping clusters, background

noise

◮ BUT, computationally expensive and choice of model imposes

limitation

◮ Recent proposals for statistical model based FC clustering (Chan

et al. [2008], Lo et al. [2008],Finak et al. [2009], Pyne et al. [2009])

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MODEL BASED CLUSTERING FOR FC DATA

◮ Model based clustering offers several advantages:

◮ Soft clustering- comprehends overlapping clusters, background

noise

◮ BUT, computationally expensive and choice of model imposes

limitation

◮ Recent proposals for statistical model based FC clustering (Chan

et al. [2008], Lo et al. [2008],Finak et al. [2009], Pyne et al. [2009])

◮ We propose computationally efficient model-based clustering

method SWIFT (Naim et al. [2010]) that offers two advantages:

◮ Scalability: Faster Computation + Less Memory Usage ◮ Detection of Small Populations: ∼ 100 cells out of 1 million

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OUTLINE

1 INTRODUCTION Flow cytometry (FC) Data Analysis Automated Multivariate clustering of FC Data 2 SWIFT METHOD FOR FC DATA ANALYSIS SWIFT Algorithm Weighted Iterative Sampling based EM Bimodality Splitting Graph-based Merging 3 DOES IT WORK? Does It Work? How Do We Know It Works? 4 FLOWCAP CONTEST Results on FlowCAP Datasets Few Thoughts for FlowCAP II 5 CONCLUSION

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SWIFT ALGORITHM FOR FC DATA CLUSTERING

SWIFT: a three stage algorithm:

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SWIFT ALGORITHM FOR FC DATA CLUSTERING

SWIFT: a three stage algorithm:

1 Weighted Iterative Sampling based EM : Gaussian mixture model

clustering + novel weighted iterative sampling

◮ Bayesian Information Criterion (BIC)

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SWIFT ALGORITHM FOR FC DATA CLUSTERING

SWIFT: a three stage algorithm:

1 Weighted Iterative Sampling based EM : Gaussian mixture model

clustering + novel weighted iterative sampling

◮ Bayesian Information Criterion (BIC)

2 Bimodality Splitting: Split any cluster that is,

◮ Bimodal in any dimensions or any principal components. ◮ Useful for clustering high dimensional data.

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SWIFT ALGORITHM FOR FC DATA CLUSTERING

SWIFT: a three stage algorithm:

1 Weighted Iterative Sampling based EM : Gaussian mixture model

clustering + novel weighted iterative sampling

◮ Bayesian Information Criterion (BIC)

2 Bimodality Splitting: Split any cluster that is,

◮ Bimodal in any dimensions or any principal components. ◮ Useful for clustering high dimensional data.

3 Graph-based Merging: Merge overlapping Gaussians ( Hennig

[2009], Finak et al. [2009], Baudry et al. [2010]).

◮ Allows representation of non-Gaussian clusters

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CLUSTERING STRATEGY: SWIFT

Soft clustering for Kentropy clusters Split Bimodal Clusters until Unimodal. GMM clustering with Sampling for k ∈ [Kmin, Kmax] BIC to decide number of Gaussians ( ˆ K) Graph-based Merging using Overlap/Entropy criteria Results in Kentropy Clusters Results in Ksplit Clusters

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STAGE 1: GAUSSIAN MIXTURE MODEL CLUSTERING

Soft clustering for Kentropy clusters Split Bimodal Clusters until Unimodal. GMM clustering with Sampling for k ∈ [Kmin, Kmax] BIC to decide number of Gaussians ( ˆ K) Graph-based Merging using Overlap/Entropy criteria Results in Kentropy Clusters Results in Ksplit Clusters

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STAGE 1: GAUSSIAN MIXTURE MODEL CLUSTERING

◮ Gaussian mixture model (GMM) clustering is chosen among the

model based methods

◮ Faster than other model based clustering methods ◮ Closed form solution

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STAGE 1: GAUSSIAN MIXTURE MODEL CLUSTERING

◮ Gaussian mixture model (GMM) clustering is chosen among the

model based methods

◮ Faster than other model based clustering methods ◮ Closed form solution

◮ Expectation Maximization (EM) algorithm for parameter

estimation

◮ Computational complexity of each iteration: O(Nkd2)

◮ N = the number of data-vectors in the dataset ◮ k = is the number of Gaussian components ◮ d = is the dimension of each data-vectors

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STAGE 1: SAMPLING FOR SCALABILITY

◮ Operate on smaller subsample of dataset for better computation

performance.

◮ Challenge: Poor representation of smaller clusters. (a) 4 Gaussians with 150K, 100K, 50K and 150 datapoints (b) After 10% sampling

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STAGE 1: SAMPLING FOR SCALABILITY

◮ Operate on smaller subsample of dataset for better computation

performance.

◮ Challenge: Poor representation of smaller clusters. (c) 4 Gaussians with 150K, 100K, 50K and 150 datapoints (d) After 10% sampling ◮ Solution: Weighted iterative sampling

◮ Faster computation ◮ Better detection of small clusters

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STAGE 1: WEIGHTED ITERATIVE SAMPLING BASED EM

FCS Dataset X Fix p largest clusters and add them to F. Initially F = ∅ Resample S from X with probability

• l∈F γ(i)

j

Subsample S from X GMM fitting to S using EM All the clusters fixed? Perform few EM iterations on X Output model parameters (θ) Yes No

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STAGE 1: WEIGHTED ITERATIVE SAMPLING BASED EM

FCS Dataset X Fix p largest clusters and add them to F. Initially F = ∅ Resample S from X with probability

• l∈F γ(i)

j

Subsample S from X GMM fitting to S using EM All the clusters fixed? Perform few EM iterations on X Output model parameters (θ) Yes No

F = set of clusters whose parameters are fixed.

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STAGE 1: WEIGHTED ITERATIVE SAMPLING BASED EM

FCS Dataset X Fix p largest clusters and add them to F. Initially F = ∅ Resample S from X with probability

• l∈F γ(i)

j

Subsample S from X GMM fitting to S using EM All the clusters fixed? Perform few EM iterations on X Output model parameters (θ) Yes No

F = set of clusters whose parameters are fixed. P(X(i) is selected in S) = ∑l∈F γ(i)

l

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STAGE 1: WEIGHTED ITERATIVE SAMPLING BASED EM

FIGURE: 4 Gaussian clusters with 150K, 100K, 50K and 150 datapoints

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WEIGHTED ITERATIVE SAMPLING: FIRST SAMPLE

(a) First sample (b) Clustering first sample ◮ Uniform random sampling

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WEIGHTED ITERATIVE SAMPLING: SECOND SAMPLE

(c) Second sample (d) Clustering second sample ◮ Sampling probability: (1−∑l∈{1} γ(i)

l )

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WEIGHTED ITERATIVE SAMPLING: THIRD SAMPLE

(e) Third sample (f) Clustering third sample ◮ Sampling probability: (1−∑l∈{1,2} γ(i)

l

)

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WEIGHTED ITERATIVE SAMPLING: LAST SAMPLE

(g) Last sample (h) Final clustering ◮ Sampling probability: (1−∑l∈{1,2,3} γ(i)

l )

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STAGE 2: BIMODALITY SPLITTING

Soft clustering for Kentropy clusters GMM clustering with Sampling for k ∈ [Kmin, Kmax] BIC to decide number of Gaussians ( ˆ K) Graph-based Merging using Overlap/Entropy criteria Results in Kentropy Clusters Results in Ksplit Clusters Split Bimodal Clusters until Unimodal.

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STAGE 2: BIMODALITY SPLITTING

◮ Motivated by Biology

◮ Separation along only one dimension can be significant

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STAGE 2: BIMODALITY SPLITTING

◮ Motivated by Biology

◮ Separation along only one dimension can be significant

◮ Clustering is challenging for high-dimensional data.

◮ Curse of Dimensionality. ◮ Discrimination in one dimension can be obfuscated by strong

similarity in other dimensions.

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STAGE 2: BIMODALITY SPLITTING

◮ Motivated by Biology

◮ Separation along only one dimension can be significant

◮ Clustering is challenging for high-dimensional data.

◮ Curse of Dimensionality. ◮ Discrimination in one dimension can be obfuscated by strong

similarity in other dimensions.

Problem:

◮ Gaussian mixture model for high dimensional data:

◮ Sometimes results in small clusters that are bimodal in one or two

dimensions

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STAGE 2: BIMODALITY SPLITTING

◮ Motivated by Biology

◮ Separation along only one dimension can be significant

◮ Clustering is challenging for high-dimensional data.

◮ Curse of Dimensionality. ◮ Discrimination in one dimension can be obfuscated by strong

similarity in other dimensions.

Problem:

◮ Gaussian mixture model for high dimensional data:

◮ Sometimes results in small clusters that are bimodal in one or two

dimensions

Solution:

◮ Detect bimodal clusters and split them.

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STAGE 2: BIMODALITY SPLITTING

◮ Bimodality Detection: detect clusters that are bimodal in

◮ Any given dimensions. ◮ Any principal components.

◮ Perform 1-D Kernel density estimation

◮ Compute number of modes.

−4 −2 2 4 6 8 10 5 10 15 20 25 30 35 40 45 −6 −4 −2 2 4 6 8 10 12 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

◮ Split each bimodal clusters until all subclusters are unimodal

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STAGE 3: GRAPH-BASED MERGING

Soft clustering for Kentropy clusters GMM clustering with Sampling for k ∈ [Kmin, Kmax] BIC to decide number of Gaussians ( ˆ K) Graph-based Merging using Overlap/Entropy criteria Results in Kentropy Clusters Results in Ksplit Clusters Split Bimodal Clusters until Unimodal.

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STAGE 3: GRAPH-BASED MERGING

◮ Merging of overlapping Gaussian components.

◮ Allows representing non-Gaussian clusers.

(k) After fitting 10 Gaussians (l) After merging down to 2 clusters

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STAGE 3: GRAPH-BASED MERGING

Merging Criterion: Normalized Overlap Measure (NO)

◮ ∼ Jaccard Index ◮ Ei = Ellipsoid approximating i-th Gaussian

NO(i,j) = Vol(Ei ∩ Ej) Vol(Ei ∪ Ej) (1) Merge (i′,j′) such that,

(i′,j′) = max(i,j)NO(i,j)

(2)

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STAGE 3: GRAPH-BASED MERGING

Merging Criterion: Normalized Overlap Measure (NO)

◮ ∼ Jaccard Index ◮ Ei = Ellipsoid approximating i-th Gaussian

NO(i,j) = Vol(Ei ∩ Ej) Vol(Ei ∪ Ej) (1) Merge (i′,j′) such that,

(i′,j′) = max(i,j)NO(i,j)

(2) Stopping Criterion: Merge until no significant changes in entropy (Finak et al. [2009], Baudry et al. [2010]). Ent(K) = −

n

∑

i=1 K

∑

j=1

γ(i)

j

log(γ(i)

j

)

(3)

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STAGE 3: GRAPH-BASED MERGING

◮ 5 Gaussian clusters

1 2 4 5 3

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STAGE 3: GRAPH-BASED MERGING

◮ 5 Gaussian clusters

1 2 4 5 3

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STAGE 3: GRAPH-BASED MERGING

◮ 5 Gaussian clusters

1 2 4 5 3

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STAGE 3: GRAPH-BASED MERGING

◮ 5 Gaussian clusters

1 2 4 5 3

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OUTLINE

1 INTRODUCTION Flow cytometry (FC) Data Analysis Automated Multivariate clustering of FC Data 2 SWIFT METHOD FOR FC DATA ANALYSIS SWIFT Algorithm Weighted Iterative Sampling based EM Bimodality Splitting Graph-based Merging 3 DOES IT WORK? Does It Work? How Do We Know It Works? 4 FLOWCAP CONTEST Results on FlowCAP Datasets Few Thoughts for FlowCAP II 5 CONCLUSION

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DOES IT WORK?

◮ Experiment: Cluster high-dimensional FC data ◮ Dataset:

◮ 544,000 Events ◮ 21 Dimensions

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DOES IT WORK?

◮ Experiment: Cluster high-dimensional FC data ◮ Dataset:

◮ 544,000 Events ◮ 21 Dimensions

◮ SWIFT Output:

◮ 191 Gaussians (Gaussian fitting + Bimodality Splitting) ◮ 143 Clusters (Post Merging)

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544,000 EVENTS, 21 DIMENSIONS, 143 CLUSTERS

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HOW DO WE KNOW IT WORKS?

◮ Experiments to produce datasets with ground truth

◮ Rochester Human Immunology Center

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HOW DO WE KNOW IT WORKS?

◮ Experiments to produce datasets with ground truth

◮ Rochester Human Immunology Center

◮ Electronic mixture of Human cells and Mouse cells

◮ Two datafiles: Human cells and Mouse cells only ◮ Human Datafile: 276,418 events ◮ Mouse Datafile: 267,582 events ◮ Total: 544,000 events ◮ Stained using both human and mouse antibodies. ◮ Human/mouse label is known for every cell.

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HOW DO WE KNOW IT WORKS?

◮ Experiments to produce datasets with ground truth

◮ Rochester Human Immunology Center

◮ Electronic mixture of Human cells and Mouse cells

◮ Two datafiles: Human cells and Mouse cells only ◮ Human Datafile: 276,418 events ◮ Mouse Datafile: 267,582 events ◮ Total: 544,000 events ◮ Stained using both human and mouse antibodies. ◮ Human/mouse label is known for every cell.

◮ Examine every clusters:

◮ Human only? Mouse only? or Both?

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FRACTIONAL MEMBERSHIP OF HUMAN AND MOUSE

20 40 60 80 100 120 140 0.2 0.4 0.6 0.8 1

Cluster Numbers Fractional Membership (Human or Mouse)

Human Mouse

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SMALL CLUSTER DETECTION

◮ Electronic human-mouse mixture

◮ Varying proportions of human cells. ◮ Five datasets: 50%, 25%, 10%, 1%, 0.1% Human cells.

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SMALL CLUSTER DETECTION

◮ Electronic human-mouse mixture

◮ Varying proportions of human cells. ◮ Five datasets: 50%, 25%, 10%, 1%, 0.1% Human cells.

◮ Sensitivity Analysis:

◮ Precision: Precision =

TP TP+FP

◮ Recall: Recall =

TP TP+FN

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SMALL CLUSTER DETECTION

◮ Electronic human-mouse mixture

◮ Varying proportions of human cells. ◮ Five datasets: 50%, 25%, 10%, 1%, 0.1% Human cells.

◮ Sensitivity Analysis:

◮ Precision: Precision =

TP TP+FP

◮ Recall: Recall =

TP TP+FN

% of Human cells Precision Recall Human Clusters 50% 99.8351% 99.902% 84 25% 99.5906% 99.728% 59 10% 98.8121% 99.405% 38 1% 96.0417% 92.2% 13 0.1% 71.8978% 98.5% 4

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ADVANTAGES OF SWIFT

◮ Scalable memory and computation time.

◮ Complexity of each EM iteration reduced from O(Nkd2) to

O(nkd2)

◮ n = Sample size

◮ Better resolution of small clusters ◮ Capable of detecting non-Gaussian clusters ◮ Works well for overlapping clusters (true for all model-based

methods)

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OUTLINE

1 INTRODUCTION Flow cytometry (FC) Data Analysis Automated Multivariate clustering of FC Data 2 SWIFT METHOD FOR FC DATA ANALYSIS SWIFT Algorithm Weighted Iterative Sampling based EM Bimodality Splitting Graph-based Merging 3 DOES IT WORK? Does It Work? How Do We Know It Works? 4 FLOWCAP CONTEST Results on FlowCAP Datasets Few Thoughts for FlowCAP II 5 CONCLUSION

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CLUSTERING RESULTS: GVHD DATASET

◮ GvHD Dataset: Data Sample 001.fcs

◮ 13831 Events ◮ 6 dimensions

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CLUSTERING RESULTS: GVHD DATASET

◮ GvHD Dataset: Data Sample 001.fcs

◮ 13831 Events ◮ 6 dimensions

◮ 13 Gaussians using BIC ◮ 11 Clusters after merging

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CLUSTERING RESULTS: GVHD DATASET

FL1.H FL2.H

100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000

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CLUSTERING RESULTS: GVHD DATASET

FL1.H FL2.H

100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000

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CLUSTERING RESULTS: GVHD DATASET

FSC.H SSC.H

100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000

FSC.H SSC.H

100 200 300 400 500 600 700 800 900 1000 50 100 150 200 250 300 350 400 450 500

FSC.H SSC.H

100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000

FSC.H SSC.H 200 400 600 800 1000 100 200 300 400 500 600 700 800 900 1000

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FEW THOUGHTS FOR FLOWCAP II

◮ FlowCAP-I datasets were relatively small

◮ Less than 100,000 events. ◮ Maximum 12 dimensions ◮ Number of clusters usually smaller than 25

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FEW THOUGHTS FOR FLOWCAP II

◮ FlowCAP-I datasets were relatively small

◮ Less than 100,000 events. ◮ Maximum 12 dimensions ◮ Number of clusters usually smaller than 25

◮ Introduction of larger datasets for FlowCAP II

◮ 1 millions events, 20 dimensions are common

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FEW THOUGHTS FOR FLOWCAP II

◮ FlowCAP-I datasets were relatively small

◮ Less than 100,000 events. ◮ Maximum 12 dimensions ◮ Number of clusters usually smaller than 25

◮ Introduction of larger datasets for FlowCAP II

◮ 1 millions events, 20 dimensions are common

◮ Introduction of different tasks and corresponding performance

measure

◮ Detection of very small clusters ◮ Detection of overlapping populations

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FEW THOUGHTS FOR FLOWCAP II

◮ FlowCAP-I datasets were relatively small

◮ Less than 100,000 events. ◮ Maximum 12 dimensions ◮ Number of clusters usually smaller than 25

◮ Introduction of larger datasets for FlowCAP II

◮ 1 millions events, 20 dimensions are common

◮ Introduction of different tasks and corresponding performance

measure

◮ Detection of very small clusters ◮ Detection of overlapping populations

◮ Gold standard for validation?

◮ Manual Gating: ◮ Focused rather than exhaustive ◮ Does not comprehend overlapping populations

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FEW THOUGHTS FOR FLOWCAP II

◮ FlowCAP-I datasets were relatively small

◮ Less than 100,000 events. ◮ Maximum 12 dimensions ◮ Number of clusters usually smaller than 25

◮ Introduction of larger datasets for FlowCAP II

◮ 1 millions events, 20 dimensions are common

◮ Introduction of different tasks and corresponding performance

measure

◮ Detection of very small clusters ◮ Detection of overlapping populations

◮ Gold standard for validation?

◮ Manual Gating: ◮ Focused rather than exhaustive ◮ Does not comprehend overlapping populations ◮ Electronically Mixed Datasets: for objective evaluation ◮ Human/Mouse dataset

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OUTLINE

1 INTRODUCTION Flow cytometry (FC) Data Analysis Automated Multivariate clustering of FC Data 2 SWIFT METHOD FOR FC DATA ANALYSIS SWIFT Algorithm Weighted Iterative Sampling based EM Bimodality Splitting Graph-based Merging 3 DOES IT WORK? Does It Work? How Do We Know It Works? 4 FLOWCAP CONTEST Results on FlowCAP Datasets Few Thoughts for FlowCAP II 5 CONCLUSION

45 / 48 SWIFT

CONCLUSION

◮ SWIFT: Scalable algorithm for FC data clustering

◮ Posterior sampling based EM + Bimodality Splitting +

Graph-based merging

◮ Advantages: lower computational complexity + better small cluster

resolution

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CONCLUSION

◮ SWIFT: Scalable algorithm for FC data clustering

◮ Posterior sampling based EM + Bimodality Splitting +

Graph-based merging

◮ Advantages: lower computational complexity + better small cluster

resolution

◮ Extensible to other soft clustering methods

◮ Mixture of t, skewed t distributions or fuzzy clustering

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CONCLUSION

◮ SWIFT: Scalable algorithm for FC data clustering

◮ Posterior sampling based EM + Bimodality Splitting +

Graph-based merging

◮ Advantages: lower computational complexity + better small cluster

resolution

◮ Extensible to other soft clustering methods

◮ Mixture of t, skewed t distributions or fuzzy clustering

◮ Further speed-up can be achieved by combining with

parallelization.

◮ Parallelization using GPU (Suchard et al. [2010],Espenshade

et al. [2009]).

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CONCLUSION

◮ SWIFT: Scalable algorithm for FC data clustering

◮ Posterior sampling based EM + Bimodality Splitting +

Graph-based merging

◮ Advantages: lower computational complexity + better small cluster

resolution

◮ Extensible to other soft clustering methods

◮ Mixture of t, skewed t distributions or fuzzy clustering

◮ Further speed-up can be achieved by combining with

parallelization.

◮ Parallelization using GPU (Suchard et al. [2010],Espenshade

et al. [2009]).

◮ Future work:

◮ Improve stability and robustness ◮ Cross-sample cluster matching for biological inference.

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COLLABORATORS

SWIFT

Naim, Sharma, Datta, Cavenaugh, Rebhahn, Wang, Mosmann

GAFF

Rebhahn, Cavenaugh, Naim, Sharma, Mosmann

Acceleration

Pangborn, Cavenaugh, von Laszewski

Rochester Human Immunology Center

Quataert, Mosmann

NYICE Influenza

Treanor, Topham, Sant, Kim, Whittaker, Mosmann

RPBIP Immunocompromised

Sanz, Looney, Mosmann, Ritchlin, Anolik, Quataert

ACE Autoimmunity

Sanz, Fowell, Looney, Quataert, Mosmann

Asthma

Georas, Looney, Mosmann

Lymphoma

Bernstein, Quataert

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REFERENCES

J.P . Baudry, A.E. Raftery, G. Celeux, K. Lo, and R. Gottardo. Combining mixture components for clustering. Journal of Computational and Graphical Statistics, 19 (2):332–353, 2010.

• C. Chan, F

. Feng, J. Ottinger, D. Foster, M. West, and T.B. Kepler. Statistical mixture modeling for cell subtype identification in flow cytometry. Cytometry Part A, (8), 2008.

• J. Espenshade, A. Pangborn, G. von Laszewski, D. Roberts, and J.S. Cavenaugh.

Accelerating Partitional Algorithms for Flow Cytometry on GPUs. pages 226–233, 2009.

• G. Finak, R. Gottardo, R. Brinkman, et al. Merging mixture components for cell

population identification in flow cytometry. Advances in Bioinformatics, 2009, 2009.

• C. Hennig. Methods for merging Gaussian mixture components. Advances in Data

Analysis and Classification, pages 1–32, 2009.

• K. Lo, R.R. Brinkman, and R. Gottardo. Automated gating of flow cytometry data via

robust model-based clustering. Cytometry Part A, 73:321–332, 2008. Iftekhar Naim, Suprakash Datta, Gaurav Sharma, James Cavenaugh, and Tim

• Mosmann. SWIFT: Scalable weighted iterative sampling for flow cytometry
• clustering. In Proc. IEEE Intl. Conf. Acoustics Speech and Sig. Proc., pages

509–512, Dallas, Texas, USA, Mar. 2010.

• S. Pyne et al. Automated high-dimensional flow cytometric data analysis. PNAS, 106

(21):8519, 2009. M.A. Suchard, Q. Wang, C. Chan, J. Frelinger, A. Cron, and M. West. Understanding

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