1. Jeremy Bolton, Seniha Yuksel, Paul Gader
Multiple Instance Hidden Markov Model: Application to Landmine Detection in GPR Data
Jeremy Bolton, Seniha Yuksel, Paul Gader
CSI Laboratory
University of Florida

2. Highlights
Hidden Markov Models (HMMs) are useful tools for landmine detection in GPR imagery
Explicitly incorporating the Multiple Instance Learning (MIL) paradigm in HMM learning is intuitive and effective
Classification performance is improved when using the MI-HMM over a standard HMM
Results further support the idea that explicitly accounting for the MI scenario may lead to improved learning under class label uncertainty

3. Outline HMMs for Landmine detection in GPR MIL Scenario MI-HMM
Data
Feature Extraction
Training
MIL Scenario
MI-HMM
Classification Results

4. HMMs for landmine detection

5. GPR Data GPR data 3d image cube
Dt, xt, depth
Subsurface objects are observed as hyperbolas

6. GPR Data Feature Extraction
Many features extracted from in GPR data measure the occurrence of an “edge”
For the typical HMM algorithm (Gader et al.),
Preprocessing techniques are used to emphasize edges
Image morphology and structuring elements can be used to extract edges
Image
Preprocessed
Edge Extraction

7. 4-d Edge Features
Edge Extraction

8. Concept behind the HMM for GPR
Using the extracted features (an observation sequence when scanning from left to right in an image) we will attempt to estimate some hidden states

9. Concept behind the HMM for GPR

10. HMM Features Current AIM viewer by Smock Rising Edge Feature
Image
Feature Image
Rising Edge Feature
Falling Edge Feature

11. Sampling HMM Summary Feature Calculation HMM Models
Dimensions (Not always relevant whether positive or negative diagonal is observed …. Just simply a diagonal is observed)
HMMSamp: 2d
Down sampling depth
HMMSamp: 4
HMM Models
Number of States
HMMSamp : 4
Gaussian components per state (Fewer total components for probability calculation)
HMMSamp : 1 (recent observation)

12. Training the HMM
Xuping Zhang proposed a Gibbs Sampling algorithm for HMM learning
But, given an image(s) how do we choose the training sequences?
Which sequence(s) do we choose from each image?
There is an inherent problem in many image analysis settings due to class label uncertainty per sequence
That is, each image has a class label associated with it, but each image has multiple instances of samples or sequences. Which sample(s) is truly indicative of the target?
Using standard training techniques this translates to identifying the optimal training set within a set of sequences
If an image has N sequences this translates to a search of 2N possibilities

13. Training Sample Selection Heuristic
Currently, an MRF approach (Collins et al.) is used to bound the search to a localized area within the image rather than search all sequences within the image.
Reduces search space, but multiple instance problem still exists

14. Multiple Instance Learning

15. Standard Learning vs. Multiple Instance Learning
Standard supervised learning
Optimize some model (or learn a target concept) given training samples and corresponding labels
MIL
Learn a target concept given multiple sets of samples and corresponding labels for the sets.
Interpretation: Learning with uncertain labels / noisy teacher

16. Multiple Instance Learning (MIL)
Given:
Set of I bags
Labeled + or -
The ith bag is a set of Ji
samples in some feature space
Interpretation of labels
Goal: learn concept
What characteristic is common to the positive bags that is not observed in the negative bags

17. Standard learning doesn’t always fit: GPR Example
Each training sample (feature vector) must have a label
But which ones and how many compose the optimal training set?
Arduous task: many feature vectors per image and multiple images
Difficult to label given GPR echoes, ground truthing errors, etc …
Label of each vector may not be known
EHD: Feature Vector
Is it easy here to label every depth bin as mine or non-mine? So WHICH one(s) do we present to the learning algorithm?

18. Learning from Bags In MIL, a label is attached to a set of samples.
A bag is a set of samples
A sample within a bag is called an instance.
A bag is labeled as positive if and only if at least one of its instances is positive.
POSITIVE BAGS
(Each bag is an image)
NEGATIVE BAGS
(Each bag is an image)

19. MI Learning: GPR Example
Multiple Instance Learning
Each training bag must have a label
No need to label all feature vectors, just identify images (bags) where targets are present
Implicitly accounts for class label uncertainty …
EHD: Feature Vector
After producing multiple sets for multiple GPR images, the multiple instance learner will 1) identify the commonalities (common patterns) shared by the positives bags that are not observed in the negative bags – it will learn the target concept. 2) given the classifier/model chosen, it will aid in the optimization of classifier or model parameters.
Some supervised, semi-supervised, or active learning methods may attempt to assign labels to all training samples, such that some expert is aiding, some criterion is satisfied, or some objective is optimized. With multiple instance learning, we say, FORGET ABOUT IT. The multiple instance learner will figure it out.

20. Multiple Instance Learning HMM: MI-HMM

21. MI-HMM In MI-HMM, instances are sequences NEGATIVE BAGS POSITIVE BAGS
Direction of
movement
NEGATIVE BAGS
POSITIVE BAGS
Learning sequences can be applied to GPR as well!

22. MI-HMM
Assuming independence between the bags and assuming the Noisy-OR (Pearl) relationship between the sequences within each bag
where
This is a slide showing equations

23. MI-HMM learning
Due to the cumbersome nature of the noisy-OR, the parameters of the HMM are learned using Metropolis – Hastings sampling.

24. Sampling HMM parameters are sampled from Dirichlet
A new state is accepted or rejected based on the ratio r at iteration t + 1
where P is the noisy-or model.

25. Discrete Observations
Note that since we have chosen a Metropolis Hastings sampling scheme using Dirichlets, our observations must be discretized.

26. MI-HMM Summary Feature Calculation HMM Models Dimensions
HMMSamp: 2d
MI-HMM: 2d features are descretized into 16 symbols
Down sampling depth
HMMSamp: 4
MI-HMM: 4
HMM Models
Number of States
HMMSamp : 4
Components per state (Fewer total components for probability calculation)
HMMSamp : 1 Gaussian
MI-HMM: Discrete mixture over 16 symbols

27. Classification Results

28. MI-HMM vs Sampling HMM
Small Millbrook
HMM Samp (12,000)
MI-HMM (100)

29. What’s the deal with HMM Samp?

30. Concluding Remarks

31. Concluding Remarks
Explicitly incorporating the Multiple Instance Learning (MIL) paradigm in HMM learning is intuitive and effective
Classification performance is improved when using the MI-HMM over a standard HMM
More effective and efficient
Future Work
Construct bags without using MRF heuristic
Apply to EMI data: spatial uncertainty

32. Back up Slides

34. Standard Learning vs. Multiple Instance Learning
Standard supervised learning
Optimize some model (or learn a target concept) given training samples and corresponding labels
MIL
Learn a target concept given multiple sets of samples and corresponding labels for the sets.
Interpretation: Learning with uncertain labels / noisy teacher

35. Multiple Instance Learning (MIL)
Given:
Set of I bags
Labeled + or -
The ith bag is a set of Ji
samples in some feature space
Interpretation of labels
Goal: learn concept
What characteristic is common to the positive bags that is not observed in the negative bags

36. MIL Application: Example GPR
EHD: Feature Vector
Collaboration: Frigui, Collins, Torrione
Construction of bags
Collect 15 EHD feature vectors from the 15 depth bins
Mine images = + bags
FA images = - bags
Explain GPR images and target signatures.
Given a GPR image, typically multiple features vectors are calculated at each depth bin or image subsets. Note that some feature vectors exhibit the target concept and some do not, which ones exhibit it can be considered uncertain, unless an expert is used label each feature vector.
Note that this is exactly the multiple instance scenario – when optimizing a classifier for landmine detection we are learning in conditions of uncertainty: we know that there is a target in this image, but we don’t know which features vectors contain the target and which do not.

37. Standard vs. MI Learning: GPR Example
Standard Learning
Each training sample (feature vector) must have a label
Arduous task
many feature vectors per image and multiple images
difficult to label given GPR echoes, ground truthing errors, etc …
label of each vector may not be known
EHD: Feature Vector

38. Standard vs MI Learning: GPR Example
Multiple Instance Learning
Each training bag must have a label
No need to label all feature vectors, just identify images (bags) where targets are present
Implicitly accounts for class label uncertainty …
EHD: Feature Vector
After producing multiple sets for multiple GPR images, the multiple instance learner will 1) identify the commonalities (common patterns) shared by the positives bags that are not observed in the negative bags – it will learn the target concept. 2) given the classifier/model chosen, it will aid in the optimization of classifier or model parameters.
Some supervised, semi-supervised, or active learning methods may attempt to assign labels to all training samples, such that some expert is aiding, some criterion is satisfied, or some objective is optimized. With multiple instance learning, we say, FORGET ABOUT IT. The multiple instance learner will figure it out.

39. Random Set Framework for Multiple Instance Learning

40. Random Set Brief
Random Set

41. How can we use Random Sets for MIL?
Random set for MIL: Bags are sets
Idea of finding commonality of positive bags inherent in random set formulation
Sets have an empty intersection or non-empty intersection relationship
Find commonality using intersection operator
Random sets governing functional is based on intersection operator
Capacity functional : T
A.K.A. : Noisy-OR gate (Pearl 1988)
It is NOT the case that EACH
element is NOT the
target concept

42. Random Set Functionals
Capacity functionals for intersection calculation
Use germ and grain model to model random set
Multiple (J) Concepts
Calculate probability of intersection given X and germ and grain pairs:
Grains are governed by random radii with assumed cumulative:
Random Set model parameters
Germ
Grain

43. RSF-MIL: Germ and Grain Model
Positive Bags = blue
Negative Bags = orange
Distinct shapes = distinct bags x T

44. Multiple Instance Learning with Multiple Concepts

45. Multiple Concepts: Disjunction or Conjunction?
When you have multiple types of concepts
When each instance can indicate the presence of a target
Conjunction
When you have a target type that is composed of multiple (necessary concepts)
When each instance can indicate a concept, but not necessary the composite target type

46. Conjunctive RSF-MIL
Previously Developed Disjunctive RSF-MIL (RSF-MIL-d)
Conjunctive RSF-MIL (RSF-MIL-c)
Noisy-OR combination across concepts and samples
Standard noisy-OR for one concept j
Noisy-AND combination across concepts

47. Synthetic Data Experiments
Extreme Conjunct data set requires that a target bag exhibits two distinct concepts rather than one or none
AUC (AUC when initialized near solution)

48. Application to Remote Sensing

49. Disjunctive Target Concepts
Type 1
NoisyOR
NoisyOR
Target Concept
Type 2
Type n OR
Target Concept Present? …
Using Large overlapping bins (GROSS Extraction) the target concept can be encapsulated within 1 instance: Therefore a disjunctive relationship exists

50. What if we want features with finer granularity
Constituent Concept 1
(top of hyperbola)
Constituent Concept 2
(wings of hyperbola)
Our features have more granularity, therefore our concepts may be constituents of a target, rather than encapsulating the target concept
NoisyOR …
AND
Target Concept Present?
Fine Extraction
More detail about image and more shape information, but may loose disjunctive nature between (multiple) instances

51. GPR Experiments Extensive GPR Data set Experimental Design Hypothesis
~800 targets
~ 5,000 non-targets
Experimental Design
Run RSF-MIL-d (disjunctive) and RSF-MIL-c (conjunctive)
Compare both feature extraction methods
Gross extraction: large enough to encompass target concept
Fine extraction: Non-overlapping bins
Hypothesis
RSF-MIL will perform well when using gross extraction whereas RSF-MIL-c will perform well using Fine extraction

52. Experimental Results Highlights
RSF-MIL-d using gross extraction performed best
RSF-MIL-c performed better than RSF-MIL-d when using fine extraction
Other influencing factors: optimization methods for RSF-MIL-d and RSF-MIL-c are not the same
Gross Extraction
Fine Extraction

53. Future Work
Implement a general form that can learn disjunction or conjunction relationship from the data
Implement a general form that can learn the number of concepts
Incorporate spatial information
Develop an improved optimization scheme for RSF-MIL-C

55. HMM Model Visualization
Points =
Gaussian Component means
DTXTHMM
Falling
Diagonal
Color =
State Index
State index1
State index 2
State index 3
Rising Diagonal
Transition probabilities from state to state (red = high probability)
Initial probabilities
Pattern Characterized

63. Backup Slides

64. MIL Example (AHI Imagery)
Robust learning tool
MIL tools can learn target signature with limited or incomplete ground truth
Which spectral signature(s) should we use to train a target model or classifier?
Spectral mixing
Background signal
Ground truth not exact

65. MI-RVM
Addition of set observations and inference using noisy-OR to an RVM model
Prior on the weight w

66. SVM review
Classifier structure
Optimization

67. MI-SVM Discussion
RVM was altered to fit MIL problem by changing the form of the target variable’s posterior to model a noisy-OR gate.
SVM can be altered to fit the MIL problem by changing how the margin is calculated
Boost the margin between the bag (rather than samples) and decision surface
Look for the MI separating linear discriminant
There is at least one sample from each bag in the half space

68. mi-SVM Enforce MI scenario using extra constraints
Mixed integer program: Must find optimal hyperplane and optimal labeling set
At least one sample in each positive bag must have a label of 1.
All samples in each negative bag must have a label of -1.

69. Current Applications Multiple Instance Learning
MI Problem
MI Applications
Multiple Instance Learning: Kernel Machines
MI-RVM
MI-SVM
Current Applications
GPR imagery
HSI imagery

70. HSI: Target Spectra Learning
Given labeled areas of interest: learn target signature
Given test areas of interest: classify set of samples

71. Overview of MI-RVM Optimization
Two step optimization
Estimate optimal w, given posterior of w
There is no closed form solution for the parameters of the posterior, so a gradient update method is used
Iterate until convergence. Then proceed to step 2.
Update parameter on prior of w
The distribution on the target variable has no specific parameters.
Until system convergence, continue at step 1.

72. 1) Optimization of w Optimize posterior (Bayes’ Rule) of w
Update weights using Newton-Raphson method

73. 2) Optimization of Prior
Optimization of covariance of prior
Making a large number of assumptions, diagonal elements of A can be estimated

74. Random Sets: Multiple Instance Learning
Random set framework for multiple instance learning
Bags are sets
Idea of finding commonality of positive bags inherent in random set formulation
Find commonality using intersection operator
Random sets governing functional is based on intersection operator

75. MI issues MIL approaches
Some approaches are biased to believe only one sample in each bag caused the target concept
Some approaches can only label bags
It is not clear whether anything is gained over supervised approaches

76. RSF-MIL MIL-like Positive Bags = blue Negative Bags = orange
Distinct shapes = distinct bags x T

77. Side Note: Bayesian Networks
Noisy-OR Assumption
Bayesian Network representation of Noisy-OR
Polytree: singly connected DAG

78. Side Note Full Bayesian network may be intractable
Occurrence of causal factors are rare (sparse co-occurrence)
So assume polytree
So assume result has boolean relationship with causal factors
Absorb I, X and A into one node, governed by randomness of I
These assumptions greatly simplify inference calculation
Calculate Z based on probabilities rather than constructing a distribution using X

79. Diverse Density (DD) Probabilistic Approach Goal:
Standard statistics approaches identify areas in a feature space with high density of target samples and low density of non-target samples
DD: identify areas in a feature space with a high “density” of samples from EACH of the postitive bags (“diverse”), and low density of samples from negative bags.
Identify attributes or characteristics similar to positive bags, dissimilar with negative bags
Assume t is a target characterization
Assuming the bags are conditionally independent

80. It is NOT the case that EACH
Diverse Density
Calculation (Noisy-OR Model):
Optimization
It is NOT the case that EACH
element is NOT the
target concept

81. Random Set Brief
Random Set

82. Random Set Functionals
Capacity and avoidance functionals
Given a germ and grain model
Assumed random radii

83. When disjunction makes senseOR
Target Concept Present
Using Large overlapping bins the target concept can be encapsulated within 1 instance: Therefore a disjunctive relationship exists

84. Theoretical and Developmental Progress
Previous Optimization:
Did not necessarily promote
diverse density
Current optimization
Better for context learning and MIL
Previously no feature relevance or selection (hypersphere)
Improvement: included learned weights on each feature dimension
Previous TO DO list
Improve Existing Code
Develop joint optimization for context learning and MIL
Apply MIL approaches (broad scale)
Learn similarities between feature sets of mines
Aid in training existing algos: find “best” EHD features for training / testing
Construct set-based classifiers?

85. How do we impose the MI scenario?: Diverse Density (Maron et al.)
Calculation (Noisy-OR Model):
Inherent in Random Set formulation
Optimization
Combo of exhaustive search and gradient ascent
It is NOT the case that EACH
element is NOT the
target concept

86. How can we use Random Sets for MIL?
Random set for MIL: Bags are sets
Idea of finding commonality of positive bags inherent in random set formulation
Sets have an empty intersection or non-empty intersection relationship
Find commonality using intersection operator
Random sets governing functional is based on intersection operator
Example:
Bags with target
{l,a,e,i,o,p,u,f}
{f,b,a,e,i,z,o,u}
{a,b,c,i,o,u,e,p,f}
{a,f,t,e,i,u,o,d,v}
Bags without target
{s,r,n,m,p,l}
{z,s,w,t,g,n,c}
{f,p,k,r}
{q,x,z,c,v}
{p,l,f}
{a,e,i,o,u,f}
intersection
union
{f,s,r,n,m,p,l,z,w,g,n,c,v,q,k}
Target concept = \
= {a,e,i,o,u}