Mining and Visualization of Flow Cytometry Data ANGELA CHIN UNIVERSITY OF HOUSTON RESEARCH EXPERIENCE FOR UNDERGRADUATES JULY 3,

Contents 1.Introduction to Flow Cytometry 2.The Problem 3.Current Approaches & Results 4.Future Work 2

Flow Cytometry MEDICAL TECHNIQUE USED FOR CELL COUNTING AND CELL SORTING 3

How it Works Picture from: Abcam 4

Flow Cytometry Application  Determine whether a person has b-cell lymphoma  Based on the number of clusters that result from flow cytometry Two clusters : cancer patient Three clusters : healthy individual 5

Example: Flow Cytometry Results 6 Cancer PatientHealthy Patient

Problems with Current Methods  The process for determining if there are two or three clusters is manual  Doctors’ time could be better spent on other tasks 7

The Problem CREATING AN AUTOMATED METHOD TO DETERMINING THE NUMBER OF CLUSTERS 8

Past Approaches  Many ways to determine number of clusters Most need to know the number of clusters ahead of time  Most popular is k-means, but there are some problems Need to give the algorithm the number of clusters beforehand Has difficulty when clusters are close, different sizes, etc. 9

Further Defining the Problem We want to be able to determine the number of clusters when:  The distance between clusters is very small  The ratio of cluster sizes is large (100:1 to 1000:1) We decided to further constrain the problem such that we could determine:  1 cluster vs 2 clusters when the size ratio was up to 1000:1 10

Current Approaches & Results 11

Two Approaches Approach #1: Transformation  Find the center of the data  Take each point and find its angle from the horizontal line located at the center (new x-value) and distance from the center (new y-value)  Use transformed data to determine number of clusters Approach #2: Testing Normal Fit  Project 2D data onto line to create 1D data  Apply normal distribution fit  Compare the Bayesian Information Criterion (BIC) of the fit to a cut-off limit  If the BIC is above the limit, there are two clusters; otherwise, there is one 12

Approach #1: Transformation 13

Approach #1: Transformation 14

Approach #1: Transformation Process 15

Approach #1: Transformation 16

Approach #2: Testing Normal Fit 17

Approach #2: Testing Normal Fit 3 standard deviations apart, ratio 1:99 ONE CLUSTER BEST FITSTWO CLUSTER BEST FITS 18

Approach #2: Testing Normal Fit  Comparing BIC of the one cluster versus two clusters  All data was generated using points and the same standard deviations  The ratios between clusters and distance between two clusters (if applicable) was varied Ratios: 199:1 to 63:1 Distance: 1.5 to 5 Standard Deviations apart 19

Approach #2: Testing Normal Fit 20  Comparing BIC of the one cluster versus two clusters  All data was generated using points and the same standard deviations  The ratios between clusters and distance between two clusters (if applicable) was varied Ratios: 199:1 to 63:1 Distance: 1.5 to 5 Standard Deviations apart

Future Work 21

Future Work  Approach #1: Determine if there is a way to detect the second cluster in the transformation  Approach #2: Use real data to see if a cut-off can be determined  Overall: After figuring out how to distinguish one and two clusters, extend the method to two versus three clusters 22

Limitations  Assume the data will have Gaussian distribution  Number of clusters limited to two or three 23

Acknowledgements I would like to thank my research advisor, Dr. Stephen Huang, and Mitch Shih for their guidance on this project. I would also like to thank the University of Houston Computer Science Department and the National Science Foundation for providing me with the opportunity to participate in the REU. 24