SYLLABUS
MATH
4/5779 – Math Clinic
Medical Image Analysis Using Artificial Neural Nets, Support Vector
Machines, and Fuzzy Sets
Sponsor:
Fall
Semester ‑ 2008
Instructors: Weldon A.
Lodwick and Francis Newman
Research Assistant:
Elizabeth Untiedt
Office:
UCD-
Telephone: 303.556.8462 (office),
303.556.8442 (secretary), 303.556.8550 (fax)
E-Mail: UCD-DDC,
Web Site: Instructors’ website http://www-math.ucdenver.edu/~wlodwick
Clinic website http://www-math.cudenver.edu/~euntiedt/5779/
Office Hours: M/W
W
Other times by appointment
Text: Learning and
Softcomputing: Support Vector Machines, Neural Networks, and Fuzzy Logic Models
by Vojislav Kecman, MIT Press, 2001.
Students with Disabilities: If you have a disability that requires
accommodation in this course, please see me as soon as possible. I am happy to make appropriate
accommodations, provided timely notice is received.
Cell Phones: You are to turn off your
cell phones prior to entering class.
1.
To
develop a software system utilizing artificial neural networks, support vector
machines and/or fuzzy methods for the detection of lesions or pathology from real
medical images such as in lung or liver disease.
2.
To
develop a software system utilizing any of the tools mentioned in 1 above that
will detect the difference between the liver and the spleen in real medical
images
3.
To
develop a software system to differentiate between liver disease caused by
obesity and
pre-cirrhotic liver disease utilizing any of the tools mentioned above in 1
above.
4.
To
compare and contrast the methods developed
5.
To
explore MATLAB parallelization of specified artificial neural networks using
automatic differentiation where needed
6.
To
explore different image representations such as statistical, Fourier, wavelet
transforms, and texture transforms
7.
To
explore the connection between Hilbert’s 13th problem, artificial
neural networks, non-linear programming and linear programming
8.
Other
objectives that emerge during the course of our work.
Therefore, upon completion
the student should have a good foundation in the mathematics of artificial
neural networks, support vector machines, fuzzy methods, and how to apply them
to medical images. The “deliverable” to our sponsor is MATLAB code that (or
makes good progress such that it):
To accomplish these objectives, the clinic will split up into several
teams to work on a semester project. Each individual will be working on
subtasks leading to the completion of the team project and each team will have
a team leader to coordinate the tasks. Software development involves research
to create, to test, to analyze, and to document (the software).
Prerequisites
Linear algebra, advanced
calculus or junior level engineering mathematics or mathematical physics. The
student should have some familiarity with MATLAB or be ready to learn quickly.
Assignments
<to be given during the
semester – there will be three assignment sets>
Topics from the Text
This semester we will cover
Chapters 1-7 of the text in addition to materials that will be handed out
during the semester. Chapters 8 and 9 of
our text should be read on your own.
The proposed outline is the
initial guess of the topics that will be fruitful to investigate. Research is a process of discovery when one
does not know, so the rule is that we will modify our topics during the
semester. Thus the proposed outline will
undoubtedly change as we learn more
during the semester.
The tentative topics we will cover are:
I.
Introduction
A.
Conduct
of the course, expectations, assignments, projects
B.
History
of Artificial Neural Networks (ANNs), Support Vector Machines (SVMs), and Fuzzy
Sets/Logic
C.
Problem
statement for this semester’s Math Clinic
II.
Artificial
Neural Networks
A.
Examples
B.
Theory
C.
Taxonomy,
Functions, Complexity
D.
Applications
III.
Support
Vector Machines
A.
Examples
B.
Theory
C.
Applications
IV.
Image
representation
A.
Feature
representation, image transforms
B.
Texture
transforms
V.
Fuzzy
Sets, Fuzzy Logic, Fuzzy Neural Nets, Fuzzy Clustering
A.
Examples
B.
Theory
C.
Applications
Tentative
Outline of the Schedule
Week of: Topics
Covered
August 11,
13 Discussion
of conduct of course, projects, expectations,
timetables, assignments, motivation
History
of ANNs, SVMs, Fuzzy Sets and Logic, and
basic
definitions
Perceptrons,
learning rules, convergence, multi-level
preceptrons, back propagation, SVMs
August 18 Learning
Vector Quantization (LVQ), Radial basis function ANNs, Cascade correlation,
Probabilistic ANNs
August 20 Fuzzy set
theory, fuzzy logic
September 3 Adaptive
Resonance Theory (ART), Hopfield ANN,
Multi-Valued
Neurons (MVN), feature extraction
September 8 Project proposal due, (initial
annotated bibliography,
methods,
materials, schedule, division of labor)
September
15, 17 Fuzzy ANNs, Fuzzy
SVMs
September 22 Speaker – Karen Kafaddar (?)
September 24 Lyapunov
Stability and LaSalle Invariance
September 29 Hilbert’s 13th
Problem, ANNs, and Optimization
October 1 Progress report 1 due – Written paper and a 15
minute oral
presentation by each team
October 6 Catching up
and review of ANNs and SVMs, feature
extraction
October 8 Catching up
and review of fuzzy methods
October 13 Automatic
Differentiation
October 15 Topics in ANNs –
Thermodynamics and ANNs
October 20 Guest Speaker
TBA or Progress Evaluation
October 22 Guest Speaker
TBA or Progress Evaluation
October 27 Speaker
– Masahiro Inuiguchi, Rough Sets
October 29 Progress report 2 due – Written paper and a 15
minute oral presentation by
each team, annotated bibliography
November 3,
5 – to be specified
November 10,
12 – to be specified
November 17,
19 – to be specified
November 24
– 29 Fall Semester Thanksgiving Break
December 1,
3 – to be specified,
December 5 –
Final written reports (with
software) due by
December 8,
10 – Presentations, 30 minutes/group
Projects
You are to choose projects from the following list. Projects
could evolve, be added, subtracted or modified during the course - not
arbitrarily but as a result of circumstances. Preferably, those interested in, for example,
SVMs should collect in one group and should consider fuzzification of the SVM.
Likewise, this applies to other methods. The difference between applying SVMs
to distinguish liver from spleen will likely be only a feature vector away from
using SVMs to distinguish diseased liver from normal liver:
Project 1: SVMs, ANNs and/or fuzzy methods applied to the image
segmentation problem
Project 2: SVMs,
ANNs and/or fuzzy methods applied to the
lesion/pathology detection problem (also known as computer assisted diagnosis,
CAD, in medical imaging) for example in lung or liver disease
Project 3: SVMs, ANNs and/or fuzzy
methods to distinguish pre-cirrhosis from
diffuse liver disease due to obesity or cirrhotic versus normal liver
Project 4: SVMs, ANNs and/or fuzzy
methods applied to lesion detection in brain MRIs
Project 5: Image representation, image
and texture transforms
Project 6: Parallelization of specified
ANNs using MATLAB’s parallel computing tools
Project 7: Other, for example, Hilbert’s 13th problem
and its relation to ANNs, NLP and LP
OUR APPROACH
We
believe that teaching is a process that involves an active partnership. Our role is that of a guide to your
learning. Therefore, we are responsible
to open the way, to encourage, and to nudge you toward your own learning. In the context of the math clinic, we will
try to model the process of applying mathematics to the medical image analysis.
We will help guide you toward this learning by providing mathematics for you to
experience. It is our aim to communicate
mathematics in a way that is supportive and nurturing of your efforts. Your
role is to find a way to experience and articulate the mathematics that is presented
and that you encounter. We believe that
it is your responsibility to let us know when you find yourself not
understanding mathematical concepts that are presented in class. Once you make this known, it is our
responsibility to work on trying to attain clarity. We will try to be as proactive as
possible. We believe that results on
projects give us the opportunity to clearly see where the areas of mathematical
understanding are and what areas need more attention.
OUTCOMES
By the end of the semester you should be able to
read, understand, and apply appropriate methods associated with aspects of
medical image analysis we’ve studied this semester to model correctly and to solve
associated problems. Secondly, given a medical
image analysis problem, you should be able to: (i) translate the description of
the problem into an algorithm, (ii) choose and apply the appropriate software
method(s), (iii) obtain the an appropriate solution(s), and (iv) (correctly)
interpret and display results. Lastly,
by the end of the semester you should be able to judge, for yourself, the
veracity of statements made in the areas of our study.
EVALUATION
** Graduate students will
have extended content and be held to higher standards.
The grade assignments are
on the 10 percent scale (A = 90%-100%, B = 80%-89%, C = 70%-79%, D = 60-69%).
IMPORTANT DATES:
Group/team/project selection
– on or before
Report 1: Written report and
presentation (15 minutes each team) –
(task
identification, division of labor for each group, methods, materials)
Report 2: Written report, presentation, and annotated
bibliography –
Final Report: Written report
and software –
Final Report: Presentation –
December 8, 10, 2008
General advice: Keep all materials that we turn back in case you think we have not
credited you with the points you earned.
we can only correct your score if you have what we have turned back to
you. It is a good idea to xerox anything that you turn in just in case we lose
what you turn in. Please check to make
sure that the points you earned are the points we have recorded. Note: The statistics that we have read about
correctness of professors in recording grades state that there is a 6% error
rate in our recording of your grades.
Please make sure that we have correctly recorded your points.
POLICIES
Adds, Drops and incomplete grades:
See Schedule of Courses for the
relevant dates with respect to adding dropping this course. Given the budget cuts facing universities,
you must be registered by the dates specified or you will not get credit. The incomplete policy of the Department of
Mathematical and Statistical Sciences and the
Legitimate Excuses: Legitimate excuses
are for reasons that are beyond your control.
You may be required to produce an official, signed excuse. If you are needed in a wedding, for example,
you must talk to us prior to the
(blessed) event. If you are legally
arrested, then this is not a legitimate excuse.
For matters that are within your control, the general rule is that it is
not excused. However, talk to us prior to the event or arrest or
departure.
INSTRUCTIONS FOR PROJECTS
A project consists of:
1. Proposal – Depending on the size of the class, projects may
be coalesced or deleted. Each proposed project will be divided into tasks and
assigned to each group so that the assignment is equitable. These tasks and assignments need to be
written up and submitted to us. Once the tasks have been identified, assigned,
and approved, a division of labor is written by each of the groups.
2. Division of labor – Each group must take their tasks and subdivide
them into subtasks that are assigned to individuals in the group with an
associated due-date. A division of labor
is a formal contract between the members of the group. Once the tasks have been approved and a
written division of labor submitted, the group needs to schedule a meeting with
us so that we can go over the division of labor, its associated
responsibilities and expectations.
3. Methods and Materials
4. Annotated Bibliography
5. Code - the actual computer implementation of the project. Attention must be paid to efficiency,
readability, and portability.
b. Input – the way information is passed to the software must
be transparent and easily usable by the client.
c. Execution - the algorithm as run must correctly perform what it
was designed to do.
d. Output - relevant, clear display of solution(s) such as
tables, graphs, images, reports/lists.
e. Ease – ease of use.
f. Documentation – an in-line and hardcopy of the documentation on how
to use the software needs to be written.
Moreover, help files must be part of the software.
6. Testing and analysis
a. Testing - this part in the context of
our clinic consists of running the software developed on the test problems.
b.
Analysis - the purpose of an
analysis is to get you to critically
evaluate the results obtained from the software as it was run on the test
problems. Part of an analysis is a
critique of the software.
* A caveat: Negative results are not prohibited.
Negative results can be very valuable. However the negative results must be
robust in that it would be novel and instructive to the expert community to
avoid a particular pathway.
7. Report that will be a chapter in the Clinic
Report – Each team will need
to be responsible for parts of the final report. This will be done in MS-Word (needs to be
translatable into PDF-Adobe) or Latex as long as we can merge the files in
Latex or Adobe Acrobat. The final report will (subject to modifications we
uncover) consist of:
a. Introduction – clinic instructors
b. Project 1
i.
Theoretical
foundations – theory, application,
algorithms
ii.
Software – description
iii.
Results – summary, tables, graphs, images, lists,
distinguishing features, performance, and limitations
iv.
Opportunities
for further research
v.
Conclusions
vi.
Bibliography
vii.
Appendices
·
Source
code
·
Test
problems, data, example runs
·
Documentation
·
Proofs
·
Other
c. Project 2 (same as Project 1) …
d. Project N (same as Project 1)
NOTE: The software
from all teams needs to be burned onto one disk where each team will have a
directory into which the software is stored.
At the head of each team’s directory entry, there must be a “read-me”
file and the software system must have a “help” command that assists the
user.
|
Fall 2008 The following policies
pertain to all students and are strictly adhered to by the
Students who drop after the published
drop/add period will not be eligible for a refund of the COF hours or
tuition. |
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Important
Dates
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