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Efficient And Accurate Ranking of Multidimensional Drug Profiling Data by Graph-Based Algorithm Dorit S. Hochbaum Chun-nan Hsu Yan T. Yang

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Agenda Drug Ranking Problem Contributions Background and Problem Formulation Method Experiments Results Conclusions

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Agenda Drug Ranking Problem Contributions Background and Problem Formulation Method Experiments Results Conclusions

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Drug Ranking Problem

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Difficulties: Ranking of the intermediate ones 1 234

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Contributions Fractional Adjusted Bi-partitional Score FABS graph theoryHigh-throughput Screening Combinatorial Solution Photo credit: Oregon State University

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Background: High-throughput screening Recent innovation Robotics Software Speed & Quantity Design & Testing

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Background: High-throughput screening Recent innovation Robotics Software Speed & Quantity Design & Testing

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Background: High-throughput screening Recent innovation Robotics Software Speed & Quantity Design & Testing

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Background: High-throughput screening Recent innovation Robotics Software Speed & Quantity Design & Testing

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Background: High-throughput screening Recent innovation Robotics Software Speed & Quantity Design & Testing

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Background: High-throughput screening Recent innovation Robotics Software Speed & Quantity Design & Testing

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Background: High-throughput screening Recent innovation Robotics Software Speed & Quantity Design & Testing

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Problem Formulation

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1 234

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Two approaches: Generative Modeling: model everything X: input Y: output For each drug: Distributions of chemical components, reactions, distribution processes in the cell … Effectiveness distribution for each drug Compare parameters (e.g. mean) to obtain ranking

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Discriminative Learning Only focus on output, “Black box” X: input Y: output Criteria and/or training Input Output Little domain knowledge required Task-related criteria Direct optimization Drug ranking problem

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Method: Graph Formulation V

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E

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l Extreme Case 1 Extreme Case 2 Perfect EffectivenessZero effectiveness

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Method: Graph Formulation w How similar data point 1 is to data point 2 Inverse to the distance between two points. Euclidean distance Minkowski distance (generalized Euclidean) Mahalahobis distance (scaled Euclidean) City block distance (absolute value version of Euclidean) 1 2

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Method: Graph Formulation Encode : All possible pair-wise relationship. Compact & discrete Digitalized by matrix: Adjacency matrix w

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Method: Graph Cut w

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Method: Graph Cut w Cut

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Method: Graph Cut Graph cut: (Well studied problem) Criteria: Normalized Cut Prime [Hochbaum, 2010] Normalized Cut [Shi, Malik 2000] Minimum Cut Ratio Region [Cox, Rao, Zhong 1996]

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Method: Graph Cut Graph cut: (Well studied problem) Criteria: Normalized Cut’ Normalized Cut Minimum Cut Ratio Region P P NP-complete P

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Method: Graph Cut Graph cut: (Well studied problem) Goal: find a bi-partition Drug ranking: rank drugs Question: how to use partition algorithm?

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Method: FABS Question: how to use partition algorithm? Extreme 1Extreme 2 Zero EffectivenessPerfect Effectiveness Edges and edge weights are omitted

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Method: FABS Seeds: Force extreme cases in two separate partitions Extreme 1Extreme 2 Edges and edge weights are omitted Perfect Effectiveness Zero Effectiveness

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Method: FABS Seeds: Force extreme cases in two separate partitions Extreme 1Extreme 2 Edges and edge weights are omitted Bipartition: Perform any partition algorithm Zero EffectivenessPerfect Effectiveness

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Method: FABS Seeds: Force extreme cases in two separate partitions Edges and edge weights are omitted Bipartition: Perform any partition algorithm proportion: 1/3 proportion: 3/3 proportion: 0/3 Extreme 1Extreme 2 Zero EffectivenessPerfect Effectiveness

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Method: FABS Seeds: Force extreme cases in two separate partitions Edges and edge weights are omitted Bipartition: Perform any partition algorithm proportion: 1/3 proportion: 3/3 proportion: 0/ > 1/3 > 0

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Method: FABS Edges and edge weights are omitted Algorithm RankDrugs

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Method: FABS Edges and edge weights are omitted FABS

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Method: FABS – NC’ Edges and edge weights are omitted FABS Normalized Cut’ Blackbox: solves Normalized Cut’ criterion Normalized Cut’ criterion [Hochbaum 2010]: combinatorial & efficient solution good track record in various other fields

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Method: FABS – NC’ Edges and edge weights are omitted FABS Normalized Cut’ Advantages: FABS – NC’ FABS is one dimensional – ranks unambiguously; FABS is based on counts – diminishes effects of the outliers and noise; FABS-NC’ is obtained by a combinatorial algorithm FABS uses extreme cases for seeds – minimizes expert intervention; FABS uses individual points – avoids aggregating for each drug;

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Experiment: Mitochondria 937 mitochondria images Unknown drug rankings High resolutionComponents Effectiveness criterion: Toxicity (degree of fragmentation)

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Extreme cases [Lin et al. 2010] Intact Completely fragmented Intermediate cases

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Experiment: Mitochondria 937 mitochondria images Unknown drug rankings High resolutionComponents Effectiveness criterion: Toxicity (degree of fragmentation)

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Experiment: Mitochondria 937 mitochondria images Unknown drug rankings High resolutionComponents Extreme case 1 (Good) Extreme case 2 (Bad) Group 1 Effectiveness criterion: Toxicity (degree of fragmentation) Group 2 Group 3 Increasing fragmentation Intact Complete fragmentation Group 1 Group 2 Group 3 The Ground Truth

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Experiment: Evaluation Procedure Extreme CasesGroups Calculate Predication Accuracy 1000 runs Sample Extreme Points Sample Group Points Subsampling FABS-NC’ calculation Compare to the ground truth Ranking groups

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Experiment: Another Methods Used in practice: Center ranking: Find the centers for all groups and extreme cases; PCA ranking: Project onto the first principal component; Z-factor ranking: Calculate z-score for each group. [Zhang et al. 1999]

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Results:

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Artificial Noise/Outliers: Robustness Add noise/outliers to the ground truth: Calculate the mean and the standard deviation for a group Randomly generate a data point: If it is 3 standard deviation from the mean of the group, Accept as an outlier Otherwise, Reject Robustness: More robust method is less effected by the noise. Repeat

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Result with Noise

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FABS-SVM & Group Distance Measure Group 1Group 2Group 3Accuracy FABS-SVM % FABS-NC’ % How to measure the distance sensitivity of groups: FABS-SVM: Group Distance Measure (GDM) Algorithm calGDM

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Conclusions A new drug ranking framework FABS graph-based - producing a single scalar score; sidesteps many pitfalls of other traditional methods. mitochondria database FABS-NC′ better than three other methods; Robust when noise is introduced; Outperforms FABS-SVM. Group distance measure (GDM). In addition

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Future Directions 2. Expand our FABS application; 1. Assess other FABS implementation by GDM 3. Change Edge weight 4. Add node weight Thanks DHS Grant CBET UC Berkeley Information Sciences Institute

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