Optimization for Radiology and Social Media

Ken GoldbergIEOR (EECS, School of Information, BCNM)

UC Berkeley College of Engineering Research Council, May 2010

Outline

• IEOR Dept, BCNM• Radiology• Social Media

UC Berkeley IEOR Department• The only IEOR department in the UC system

• Ranked #3 in USA

• 55 BS, 10 BA, 30 MS, 5-8 PhD degrees per year

IEOR Faculty:Ilan AdlerAlper AtamturkJon BurgstoneYing-Ju ChenLaurent El Ghaoui Ken GoldbergXin GuoDorit S. HochbaumRichard Karp Philip M. KaminskyRobert C. LeachmanAndrew LimShmuel S. OrenChristos PapadimitriouRhonda L. Righter (Chair)Lee W. SchrubenZuo-Jun "Max" ShenIkhlaq SidhuCandace Yano

Mission

To critically analyze and shape developments in new media from trans-disciplinary and global perspectives that emphasize humanities and the public interest.

bcnm.berkeley.edu

New Media Initiative

Art/Design

Humanities

Technology

Rhetoric

Philosophy

BAMPFA

Art History

Film Studies

EECS

IEOR

Public Health

Journalism

Architecture

Music

Art Practice

iSchool

ME

BioE

Theater

Education

CITRIS

Radiology

Ken Goldberg, Alper Atamturk, Laurent El Ghaoui (IEOR) James O’Brien, Jonathan Shewchuck (EECS)

I.-C. Hsu, MD, J. Pouliot, PhD (UCSF)

8

Prostate Cancer

1 in 6 men will be diagnosed with prostate cancer

over 230,000 cases each year in the USone death every 16 minutes

High Dose Rate Brachytherapy

http://www.prostatebrachytherapyinfo.net/PCT21.html

http://automation.berkeley.edu/projects/needlesteering/

Robot Motion Planning

• Theorem (Completeness): A sensorless plan exists for any polygonal part.• Theorem (Complexity): For a polygon of n sides, the algorithm runs in time

O(n2) and finds plans of length O(n).

• Extensions:• Stochastically Optimal Plans• Extension to Non-Zero Friction • Geometric Eccentricity / constant time complexity• Part Fixturing and Holding

Dosimetry: Inverse Planning

Color Dose

Blue < 75%

Cyan 75% - 100%

Green 100% - 120%

Yellow 120% - 150%

Orange 150% - 200%

Red > 200%

Index Requirement

VP100 > 90%

HI > 60%

VU120 < 0.1 cc

VR75 < 1.0 cc

VB75 < 1.0 ccDosimetric Criteria

Dose Distribution

Inverse Planning with Simulated Annealing (IPSA)

• Inverse planning software developed at UCSF by Pouliot group • FDA-approved: used clinically worldwide• Simulated annealing dose point penalty method

Inverse Planning with Linear Programming (IPLP)

• LP formulation (UC Berkeley)• Guarantees global optima• Optimization of HDR Brachytherapy Dose Distributions using Linear Programming with Penalty Costs.

Ron Alterovitz, Etienne Lessard, Jean Pouliot, I-Chow Joe Hsu, James F. O'Brien, and Ken Goldberg. Medical Physics, vol. 33, no. 11, pp. 4012-4019, Nov. 2006.

Limitations of Penalty Model

• Only specifies dosimetry at dose points, not to organs• Not equivalent to dosimetric indices

– Not intuitive for Physicians– Results not always clinically viable. – Results difficult to customize for special cases

• Dosimetric index: if dose at x > R, then x = 1, x = 0 otherwise• Discrete Variables

Inverse Planning with Integer Programming (IP2)

• Parameters:– Dsij: dose rate from j to s,i

– Rs: Dose threshold for s

– Ms: Max dose for points in s

– Ls: Lower bound for dosimetric s

– Us: Upper bound for dosimetric s

• Variables– tj: dwell time at j

– xsi: counting variable for s,i

• Model– Maximize Σ x0i

– Subject to:• Σ Dsij tj ≥ Rs xsi

• Σ Dsij tj ≤ Rs + (Ms – Rs) xsi

• Ls ≤ Σ xsi ≤ Us

• tj ≥ 0

• xsi є {0,1}

• Indices– s: organ– i: point in organ– j: dwell position

Initial Results: Comparing IPSA with IP2

• Average Runtime (sec):– IPSA: 5– IP2 (heuristic 1): 23– IP2 (heuristic 2): 900

• Compliance with all clinical criteria– IPSA: 0% of patients – IP2 (heuristic 1): 95% of patients– IP2 (heuristic 2): 100% of patients–

IP2 for Needle Reduction• Minimize number of needles

• Minimize trauma

• Speed Recovery

Possible Needles Optimal Needle Selection (example)

Future Work• Conic Optimization• Robust Optimization

Model uncertainties in:– Organ location, motion– Edema– Catheter displacement

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Tissue Simulation

http://graphics.cs.berkeley.edu/papers/Chentanez-ISN-2009-08/

Nuttapong Chentanez, Ron Alterovitz, Daniel Ritchie, Lita Cho, Kris K. Hauser, Ken Goldberg, Jonathan R. Shewchuk, and James F. O'Brien. "Interactive Simulation of Surgical Needle Insertion and Steering". In Proceedings of

ACM SIGGRAPH 2009, pages 88:1–10, Aug 2009.

Superhuman Performance of Surgical Tasks by Robots using Iterative Learning

from Human-Guided Demonstrations

Jur van den Berg, Stephen Miller, Daniel Duckworth, Humphrey Hu, Andrew Wan, Xiao-Yu Fu, Ken Goldberg, Pieter Abbeel

University of California, Berkeley

Method:

• 1. Robot learns surgical task from human demonstrations– Knot tying– Suturing

• 2. Robot learns to execute tasks with superhuman performance– Increase smoothness– Increase speed

Social Media

Ken Goldberg, Gail de Kosnik, Kimiko RyokaiAlec Ross, Katie Dowd (US State Dept)

… …

……

Collaborative

collaborative robot control:

MultiTasking

Batch

Motivation

Goals of Organization• Engage community• Understand community

– Solicit input– Understand the distribution of

viewpoints– Discover insightful comments

Goals of Community• Understand relationships to other

community members• Consider a diversity of viewpoints• Express ideas, and be heard

Motivation

Classical approaches: surveys, polls

Drawbacks: limited samples, slow, doesn’t increase engagement

Current approaches: online forums, comment lists

Drawbacks: data deluge, cyberpolarization, hard to discover insights

Related Work: Visualization

Clockwise, starting from top left:

Morningside Analytics, MusicBox, Starry Night

Related Work: Info Filtering

• K. Goldberg et al, 2001: Eigentaste

• E. Bitton, 2009: spatial model• Polikar, 2006: ensemble

learning

Six 50-minute Learning Object Modules, preparation materials, slides for in-class lectures, discussion ideas, hand-on activities, and homework assignments.

Canonical Correlation Analysis (CCA)

• Observed variables: x, y• Latent variable: z• Learn MLEs for low-rank

projections A and B• Equivalently, find inverse mapping

that maximizes correlation between A, B

zz

xx yyGraphical model for CCA

x = Az + εy = Bz + ε

z = A-1x = B-1y

zz

xx yy

Canonical Correlation Analysis (CCA)

zzxx

yy

CCA gives three posterior expectations E(z|x) E(z|y) E(z|x,y)

E(z|x,y) is used to visualize the opinion spaceTextual

Comment

Opinion Vector

Canonical Correlation Analysis (CCA)

Each point in the Canonical representation has an expected list of words associated to it.

A visualization of this list of words can be used to give users more information about their location

Opinion Space: Crowdsourcing InsightsScalability: n Participants, n Viewpointsn2 Peer to Peer ReviewsViewpoints are k-DimensionalDim. Reduction: 2D Map of Affinity/SimilarityInsight vs. Agreement: Nonlinear Scoring

Ken Goldberg, UC BerkeleyAlec Ross, U.S. State Dept

Optimization for Radiology and Social Media

Ken GoldbergIEOR (EECS, School of Information, BCNM)

UC Berkeley College of Engineering Research Council, May 2010

IP2 Heuristics• Capping

– Allocate dose budget to dose points that are likely to need it.

– :1. Solve LP relaxation

2. Analyze solution and impose new constraints on hottest dose points.

3. Resolve to feasible solution.

• Hard Cuts– Apply custom cuts so

that IP2 emphasizes dosimetric indices.

– :1. Solve LP relaxation.

2. Add cuts to incorrectly counted dose points.

3. Repeat until feasible for IP2

Hard Cutsx

dose

Hard cut

Constraints

Fractional Optimal Solution (cut off by Hard cut)

0

1

Dimensionality Reduction

Principal Component Analysis (PCA)• Assumes independence and linearity• Minimizes squared error• Scalable: compute position of new user in constant time

Approach: Visualization

Approach: Level the Playing Field

Approach: Wisdom of Crowds

“We’re moving from an Information Age to an Opinion Age.”- Warren Sack, UCSC

Berkeley Center for New Media (BCNM):

David Wong: EECS Undergraduate StudentTavi Nathanson: EECS Graduate StudentEphrat Bitton: IEOR Graduate StudentSiamak Faridani: IEOR Graduate StudentElizabeth Goodman: School of Information Graduate StudentAlex Sydell: EECS Undergraduate Student

Meghan Laslocky: Outside Consultant on ContentAri Wallach: Outside Consultant on Content and StrategySteve Weber: Outside Consultant on ContentPeter Feaver: Outside Consultant on Content

U.S. State Department:

Alec Ross: Senior Advisor for InnovationKatie Dowd: New Media DirectorDaniel Schaub: Director for Digital Communications

Multidimensional Scaling

• Goal: rearrange objects in low dim space so as to reproduce distances in higher dim

• Strategy: Rearrange & compare solns, maximizing goodness of fit:

• Can use any kind of similarity function• Pros

– Data need not be normal, relationships need not be linear

– Tends to yield fewer factors than FA• Con: slow, not scalable

dij f (ij ) 2i, j

δiji

j

diji

j

Kernel-based Nonlinear PCA

• Intuition: in general, can’t linearly separate n points in d < n dim, but can almost always do so in d ≥ n dim

• Method: compute covariance matrix after transforming data into higher dim space

• Kernel trick used to improve complexity• If Φ is the identity, Kernel PCA = PCA

C 1

m x j x j

T j1

m

Kernel-based Nonlinear PCA

• Pro: Good for finding clusters with arbitrary shape• Cons: Need to choose appropriate kernel (no unique

solution); does not preserve distance relationships

Input data KPCA output with Gaussian kernel

Stochastic Neighbor Embedding

• Converts Euclidean dists to conditional probabilities• pj|i = Pr(xi would pick xj as its neighbor | neighbors picked

according to their density under a Gaussian centered at xi)

• Compute similar prob qj|i in lower dim space

• Goal: minimize mismatch between pj|i and qj|i:

• Cons: tends to crowd points in center of map; difficult to optimize

C KL Pi Qi i

p j | i logp j | iq j | ij

i

Canonical Correlation Analysis (CCA)

CCA visualization with tag cloud for that location in the space. The tag cloud uses stemmed keywords.

Six 50-minute Learning Object Modules, preparation materials, slides for in-class lectures, discussion ideas, hand-on activities, and homework assignments.

Opinion SpaceWisdom of Crowds: Insights are RareScalable, Self-Organizing, Spatial Interface Visualize Diversity of ViewpointsIncorporate Position into Scoring Metrics

Ken GoldbergUC Berkeley

Metavid

http://newscenter.lbl.gov/feature-stories/2010/04/26/wanda/

Optimization for Radiology Treatment and Visualizing Public Opinion

Ken GoldbergAlec Ross, Director of Innovation, U.S. State Dept

Opinion Space: Crowdsourcing InsightsScalability: N Participants, N ViewpointsEach Viewpoint is n-DimensionalDim. Reduction: 2D Map of Affinity/SimilarityInsight vs. Agreement: Nonlinear ScoringN2 Peer to Peer Reviews

Ken Goldberg, UC BerkeleyAlec Ross, U.S. State Dept

66

Objective Function Improvement over IPSA

Statistically significant improvement (P = 1.5410-7)

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Patient Case

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Standard Dosimetric Indices

No significant improvement in any dosimetric index (P > 0.01)

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Pro

stat

eV

100

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stat

eV

150

Ure

thra

V10

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thra

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V50

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V50

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IPSA solutions LP solutions

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Prostate Dose Volume Histogram

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0 500 1000 1500 2000 2500 3000 3500

Dose (cGy)

Volu

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Desired

IPSA

LP

950 cGy

1425 cGy

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Isodose Curves

IPSA LP