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Learning Classifiers for Computer Aided Diagnosis Using Local Correlations
Glenn Fung, Computer-Aided Diagnosis and TherapySiemens Medical Solutions, Inc.
Collaborators: Volkan Vural, Jennifer Dy [Northeastern University]Murat Dundar, Balaji Krishnapuram, Bharat Rao [Siemens]
Feb 13, 2008
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Outline Brief Overview of CAD systems Assumption in traditional classifier design are
Often, not valid in CAD problems Convex algorithms for Multiple Instance
Learning (MIL) Bayesian algorithms for Batch-wise
classification Faster, approximate algorithms via mathematical
programming
Summary / Conclusions
Page 3 Siemens Medical Solutions, Inc.
1D*: EKG
2D: X-ray, Mammo, Pap...
2D+Time: Echo
3D: CT, MRI, PET...
3D+Time: 4D Cardiac US/CT, Gated PET/CT, Dynamic MRI...
Imaging Data: Growing Possibilities, Growing Challenges
*signal acquired in time
Page 4 Siemens Medical Solutions, Inc.
Computer-Aided Intelligent Imaging InterpretatonThe Goal
For computer to “see” (or do) what medical experts see (or do)- To automate routine, mind-numbing, and time-consuming tasks;- To improve consistency (by reducing intra- and inter-expert variability);
Page 5 Siemens Medical Solutions, Inc.
For computer to “see” what doctors may miss - To improve sensitivity for disease detection and diagnosis;- To perform quantitative assessment not achievable by “eyeballing” or “guesstimate”;
Sensitivity = 3/5 = 60%Specificity = 3/4 = 75%
False Positive Rate (= 1 – specificity)
True Positive Rate (= Sensitivity)
Receiver operating characteristic (ROC) curve
Computer-Aided Intelligent Imaging InterpretatonThe Goal
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SegmentationSegmentation
“Segmentation is the partition of a digital image into multiple regions (sets of pixels), according to some criterion.” – wikipedia.org
At the low level, the criterion can be uniformity, which is determined according to pixel intensity, texture (repetitive patterns), etc.
At a semantic level, the criterion can be object(s) and the background.
In medical imaging, it usually refers to the delineation of different tissues or organs.
Computer-Aided Intelligent Imaging InterpretatonBasic Tools and Approaches
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DetectionDetection
Detection is the process of finding one or more object or region of interest.
In medical imaging, detection of abnormalities is often a primary goal. Examples include the detection of lung nodules, colon polyps, or breast lesions, all of which can be precursors to cancer; or the detection of abnormality of the brain (e.g., Alzheimer's disease) or pathological deformation of the heart (e.g., ventricular enlargement).
Computer-Aided Intelligent Imaging InterpretatonBasic Tools and Approaches
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ClassificationClassification
Classification is the separation of objects into different classes.
In medical imaging, classification is often performed on a tissue or organ to distinguish between its healthy and diseased state, or different stages of the disease.
A classifier is often trained using a training set, where one or more experts have assigned labels to a set of objects.
Computer-Aided Intelligent Imaging InterpretatonBasic Tools and Approaches
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• More and more data available,
• It is the prediction and early detection of diseases that saves most lives. However, “early” usually means more subtle signs and weaker signals in the images. Doctor often use a complex set of features that are often hard to formulate in computational forms;
• If doctors miss them, who will teach the computer?
• How do we know that we are doing better, if doctors do not agree among themselves?
• Regulatory challenges
Computer-Aided Intelligent Imaging InterpretatonChallenges
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CAD Algorithms
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CAD Workflow: Core Tasks
Collect individual
patient’s data
Feature extraction Inference
Decision support forphysician
Feature Extractionfrom free text
Feature Extractionfrom images
Feature Extractionfrom omics data
ImageRegistration
Segmentation& quantification
Combine info frommultiple sources
ModelOptimization
Causal prob.inference
Fusion &Classification
Evidentialinference
TemporalReasoning
Low-levelimage processing
Knowledge-basedmodeling
Predictivemodeling
Modeling /Candidate generation
Classification (forcandidate pruning)
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General Detection Examples
Vol 1Time 1
Detect /Analyze
Results1
Chest CT
Detect Nodules
Results
Colon CT
Detect Polyps
Results
Chest CT
Detect Emboli
Results
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Lung CAD
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Motivation
1. Lung cancer is the most commonly diagnosed cancer worldwide, accounting for 1.2 million new cases annually. Lung cancer is an exceptionally deadly disease: 6 out of 10 people will die within one year of being diagnosed
2. The expected 5-year survival rate for all patients with a diagnosis of lung cancer is merely 15%
3. In the United States, lung cancer is the leading cause of cancer death for both men and women, causes more deaths than the next three most common cancers combined, and costs $9.6 Billion to treat annually.
4. However, lung cancer prognosis varies greatly depending on how early the disease is diagnosed; as with all cancers, early detection provides the best prognosis.
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1. Every pulmonary nodule, independent of size and location may be malign and needs to be looked at (20 - 50% of resected nodules are malignant)
2. The smaller the nodule the better the prognosis after nodule resection with respect to 5 year survival rate
3. There is need for a screening method, as it is already available for mammography.
The need for lung CAD
Page 16 Siemens Medical Solutions, Inc.
CAD in plain words :
Find nodules in a large volume data set- solitary or attached to anatomical structures
Segment nodules correctly- remove structures like vessel, bronchus and pleura consistently and anatomically correct
Quantify nodules- volume, calcification, morphology, localization
Classify nodules as benign or malignant
Lung CAD:Introduction
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Detecting Lung Cancer is hard:Part of a Single CT study of Lung
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Where is the nodule?
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Where is the lung cancer?
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Where is the lung cancer?
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Where is the lung cancer?
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Computer aided detection
automatic detection scheme acts as a second reader
Computer Aided Detection
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Fly aroundinteractive visualization of the nodule, andeven fly around movies are possible ...
CAD Viewing Modes
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Colon CAD
Page 25 Siemens Medical Solutions, Inc.
Motivation
Colorectal cancer is the 3rd most common diagnosed cancer in USA:
- 135,000 new cases forecast for 2001
- 48,000 deaths forecast in 2001
- 95% 5-year mortality rate for patients whose colorectal cancer has spread to other body parts
- 10% 5-year mortality rate if treated at early stage
Source: American Cancer Society
Page 26 Siemens Medical Solutions, Inc.
CT Colonography:Exciting opportunity
Invasive colonoscopy remains the Gold Standard
CT Colonography: a promising non-invasive method
- 0.8 mm slices of abdomen possible in 9 sec breath-hold with a 16-slice CT
- CT has been shown capable of down to 6 mm polyp visualization
- CT exam is more acceptable and comfortable for patients
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Colon CAD Summary
GOALHigh sensitivity(Low specificity is acceptable)
Colon Segmentation (pre-processing)
Polyp Candidate Generation
Pruning/Filtering
CT Volume
Pre-processed Volume
Candidate List
Final List
Feature Extractions
Features for Candidate List
GOALHigh sensitivityHigh specificity
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
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Shown in endo-view (bottom right) example of located polyp. This polyp was missed by the physician prospectively
Detection missed by physician
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
General paradigm for CAD systems
Candidate generation
Image
Candidates
Feature Extraction
Numerical attributes for each candidate
Classification
Final Marks on Image
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Properties of the data used for designing classifiers for CAD systems The training data is highly unbalanced There is a form of stochastic dependence among the labeling
errors of a group of candidates that are closer to a radiologist mark.
The features used to describe spatially close samples are highly correlated
The CG algorithm tends to have varying levels of sensitivity to different types of structures. Some training images tend to contain far more false positive
candidates as compared to the rest of the training dataset.
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Shortcomings in standard classification algorithms Tend to underestimate minority class when problems are very
unbalanced Assume that the training examples or instances are drawn
identically and independently from an underlying unknown distribution
Assume that the appropriate measure for evaluating the classifiers is based only on the accuracy of the system on a per-lesion basis
Correct classification of every candidate instance is the main goal, instead of the ability to detect at least one candidate to points to each malignant lesion.
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
CAD: Correlations among candidate ROI
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Correlations among patients from the same hospital scanner type, patient preparation, geographical location etc Correlations among samples from the same patient: samples pointing to the same structure, samples from different orientations, image characteristics – e.g., contrast/artifacts/noise
Hierarchical Correlation Among Samples
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Initial Idea: Additive Random Effect Models
The classification is treated as iid, but only if given both Fixed effects (unique to sample) Random effects (shared among samples)
Simple additive model to explain the correlations P(yi|xi,w,ri,v)=1/(1+exp(-wT xi –vT ri)) P(yi|xi,w,ri)=s P(yi|xi,w,ri,v) p(v|D) dv
Sharing vT ri among many samples correlated prediction
…But only small improvements in real-life applications
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Candidate Specific Random Effects Model: Polyps
1-Specificity
Sen
sitiv
ity
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
CAD algorithms: Other examples of correlations between samples
Multiple (correlated) views: one detection is sufficient
Systemic treatment of diseases: e.g. detecting one PE sufficient
Modeling the data acquisition mechanism Errors in labeling for training set.
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
The Multiple Instance Learning Problem (NIPS 2006): Motivation
4 Candidates pointing to the same polyp
Only ONE candidate needs to be correctly classified!!!
Bag of candidates
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
The Multiple Instance Learning Problem (NIPS 2006)
A bag is a collection of many instances (samples)
The class label is provided for bags, not instances
Positive bag has at least one positive instance in it
Examples of “bag” definition for CAD applications: Bag=samples from multiple views, for the same region Bag=all candidates referring to same underlying structure Bag=all candidates from a patient
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
CH-MIL Algorithm: 2-D illustration
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
CH-MIL Algorithm for Fisher’s Discriminant
Easy implementation via Alternating Optimization Scales well to very large datasets Convex problem with unique optima
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Lung CAD
Lung Nodules
Computed Tomography
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
CH-MIL: Pulmonary Embolisms
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
CH-MIL: Polyps in Colon
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Classifying a Correlated Batch of Samples (ECML 2006) : Motivation
The candidates that belong to the same patient’s medical images are highly correlated
There is not any correlation between candidates from different patients
The level of correlation is a function of the pair wise distance between candidates
The samples (candidates) are collected naturally in batches
All the samples that belong to the same image constitute a batch
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Classifying a Correlated Batch of Samples (ECML 2006) Let classification of individual samples xi be based on ui
Eg. Linear ui = wT xi ; or kernel-predictor ui= j=1N j k(xi,xj)
Instead of basing the classification on ui, we will base it on an unobserved (latent) random variable zi
Prior: Even before observing any features xi (thus before ui), zi are known to be correlated a-priori, p(z)=N(z|0,)
Eg. due to spatial adjacency = exp(-D), Matrix D=pair-wise dist. between samples
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Classifying a Correlated Batch of Samples Prior: Even before observing any features xi (thus before ui),
zi are known to be correlated a-priori, p(z)=N(z|0,)
Likelihood: Let us claim that ui is really a noisy observation of a random variable zi : p(ui|zi)=N(ui|zi, 2)
Posterior: remains correlated, even after observing the features xi
P(z|u)=N(z|(-12+I)-1u, (-1+2I)-1) Intuition: E[zi]=j=1
N Aij uj ; A=(-12+I)-1
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Related Work
Conditional Random Fields and Maximum Margin Markov Networks used for Natural Language Processing
Computationally expensive
Multiple Instance Learning (MIL)
MIL Batch
Same label is assigned to the entire batch (bag) of related samples
Individuals in the same batch may have different labels
Samples in the same bag are assumed to be equally related
More fine grained differences in the level of correlation
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Support Vector MachinesMaximizing the Margin between Bounding Planes
x0w= í +1
x0w= í à 1
A+
A-
jjwjj22
w
Support vectors
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Algebra of the Classification Problem 2-Category Linearly Separable Case
Given m points in n dimensional space Represented by an m-by-n matrix A
More succinctly:D(Awà eí ) õ e;
where e is a vector of ones.
x0w= í æ1: Separate by two bounding planes,
A iwõ í +1; for D i i =+1;A iwô í à 1; for D i i =à 1:
An m-by-m diagonal matrix D with +1 & -1 entries
Membership of each A i in class +1 or –1 specified by:
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Support Vector MachinesLinear Programming Formulation
Use the 1-norm instead of the 2-norm:
÷e0y+kwk1y> 0;w; íD(Awà eí ) +yõ e
min
s.t. This is equivalent to the following linear program:
min ÷e0y+e0vyõ 0;w;í ;vD(Awà eí ) +yõ es.t.
võ wõ à v
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Mathematical Programming formulation (cont.)
eeBwD )(
To be learned during training
eewBID jjjj
)(1
21
Standard SVM constraint replaced by the proposed equation
eewBID jjjj )(
Probabilistic-inspired approach replaced by a simpler
approximation
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Testing in Batch Classification
)'()( xwsignxfDecision function for standard SVM:
Samples are tested one at a time
wBxwsignxf jji
ji')(
^
Decision function for batch classification:
Samples are tested in batchesContribution of
other samples in the same batch
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
SVM-like Approximate Algorithm Intuition: classify using E[zi]=j=1
N Aij uj ; A=(-12+I)-1
What if we used A=( + I) instead? Reduces computation by avoiding inversion. Not principled, but a heuristic for speed.
Yields an SVM-like mathematical programming algorithm:
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Mathematical Programming Formulation: Nonlinear versionA “kernelized” version can be also easily derived using the usual duality relation:
''' ee j
j
v0
min
s.t. eevABKID jjjj ',
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Toy Example: Geometrical Intuition
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Toy Example II
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Toy Example III
Point
Batch Label SVM Pre-classifier
Final classifier
12345
11111
++-+-
0.28260.2621-0.2398-0.3188
-0.4787
0.17230.13150.0153
-0.0259
-0.0857
0.19180.2122-0.07810.2909-0.0276
678910
22222
+-+--
0.23970.2329
0.1490-0.2525-0.2399
0.06590.0432
0.0042-0.0752-0.1135
0.0372-0.08880.0680-0.1079-0.1671
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Detecting Polyps in Colon
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Detecting Pulmonary Embolisms
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Detecting Nodules in the Lung
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
Conclusions IID assumption is universal in ML Often violated in real life, but ignored Explicit modeling can substantially improve accuracy Described 3 models in this talk, utilizing varying levels of
information Additive Random Effects Models: weak correlation information Multiple Instance Learning: stronger correlations enforced Batch-wise classification models: explicit information
Statistically significant improvement in accuracy Only starting to scratch the surface, lots to improve!
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
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©2007 Siemens Medical Solutions. All rights reserved. Computer-aided Diagnosis & Therapy
We are hiring!Research Scientists (Machine Learning / Probabilistic Inference)Entry Level to Senior Level OpportunitiesComputer-Aided Diagnosis & Therapy Solutions GroupSiemens Medical Solutions USA, Inc.Multiple open positions for candidates with a Ph.D. (or graduating with a PhD in ‘07)
to perform leading-edge R&D in activities involving all areas of probabilistic inference (Bayesian methods, temporal reasoning, graphical models) and/or machine learning (classification, statistical learning theory, optimization). We seek outstanding scientists who can solve challenging medical problems and continue to publish in leading journals and conferences.
Qualifications:Ph.D. in CS/EE/Statistics/Applied Math or an engineering discipline with an
interdisciplinary background.Strong publication record in leading conferences and journals in machine learning /
probabilistic inference.The ability to learn new technologies and apply them to challenging problems
involving reasoning from incomplete and unstructured medical patient data, classification of patients/diseases, as well as machine learning for automatically extracting patterns from massive amounts of free text, numeric, imaging, and symbolic data; combine imaging and clinical information; and other related areas. NLP is a plus.
We are located in Malvern, PA, less than an hour from Center City Philadelphia in the suburban Main Line area. Siemens offers a competitive salary and benefits package that reflects our leadership status.