Research Interests: Computational Neuroscience and Unsupervised learning
One of the most thoroughly studied neural systems is the
stomatogastric ganglion (STG) of the lobster. This system is often
modeled as a ring of coupled, nonlinear oscillators, and interesting
phase relationships can occur, depending on biophysical parameters.
These oscillator ring models are fairly powerful and have been used to
model many phenomena in neuroscience.
Unsupervised learning is at the heart of neural information
processing systems. It also constitutes one of the most freequently
used data analysis
methods with applications in a variety of fields ranging from
bioinformatics to computer vision to ecology, geophysics, and astronomy.
One of the most challenging problems in cluster analysis is to
determine the number of clusters we can resolve from a given data set.
It is related to controlling the complexity of a model, a crucial task
in machine learning. We derived a complexity control term within an
framework. This allows us to determine the maximal number of clusters
which can be resolved given the size of the data set.
This approach allows us to re-visited geometric clustering
algorithms, including the widely used k-means
clustering algorithm, which can be understood in terms of this
framework. The approach suggests a quenched annealing method that
allows one to improve the k-means algorithm, dramatically increasing
the likelyhood of finding the global optimum.
Student Projects (499, 699)
thesis projects: Theory:
1. Learning in neural networks
I am looking
for a student with an interest in learning theory and neuroscience.
2. Coupled oscillator networks
of coupled oscillator models to computational neuroscience. Possible
subjects: STG, movement control, navigation. On the Manoa campus, Dr.
Castelfranco and Prof. Dr. Dan Hartline, at PBRC, are both experts in
modeling. Students interested
in this subject can profit from collaboration with Dr. Castelfranco and
interfacing to the mathbio program.
Foundations of unsupervised learning
addresses open problems at the theoretical foundation of unsupervised
1. Astronomy I am looking for a
student who is interested in applying these methods to astronomical
data. 2. Computer vision
Image segmentation is an important step
in computer vision. This project deals with new approaches to
Cluster analysis is frequently used to
analyze gene expression array data. However, existing methods have
crucial shortcomings. In this project, we will address some of them.
4. Movement primitives
Much work has gone into attempts of
trying to decompose human movements such as to be able to better model
them. This has applications for example in animation. We will take a
new approach to the problem in this project.