On Faculty:

Breaking the "Curse of Dimensionality"





Phil Sneiderman

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Homewood News and Information



     Lenore Cowen is trying to find a way around a roadblock that

often stops statisticians dead in their tracks.



     Cowen, an assistant professor of mathematical sciences,

knows little about statistics; her expertise is in other areas of

math. But some researchers believe this handicap may help Cowen

succeed where others have failed in their efforts to crack a

complex problem called the "Curse of Dimensionality." The curse

rears its head when a statistician is working with data in a

sufficiently high-dimensional space that it becomes impossible to

make reliable predictions from the data.



     But Cowen, using her expertise in combinatorics--the

mathematics of finite objects and combinations of objects--

believes she can sometimes sneak around the curse and pull useful

information from problems that usually stump the statisticians.



     "My goal is to break the Curse of Dimensionality," Cowen

says. "I think combinatorics is going to help deal with this

curse. We're going to come up with a very powerful set of tools

that, in many practical instances, can get completely around it."



     If Cowen's quest is successful, it may lead to breakthroughs

in areas such as medical image processing and computer network

routing.



     Her novel approach received strong encouragement and a

financial boost recently when the Office of Naval Research picked

Cowen to receive one of its prestigious Young Investigator

Program awards. The Hopkins faculty member was one of only 34

recipients this year, chosen from a nationwide field of 416

applicants. The three-year grant will provide $90,000 annually,

primarily for graduate students to assist Cowen in her research.



     The award was also another feather in the cap for the

Mathematical Sciences Department in the Whiting School of

Engineering. Cowen was the department's second consecutive Young

Investigator award winner. Last year, Carey Priebe, an assistant

professor whose office is right next to Cowen's, won the honor.

It is given to promising faculty members who have received their

graduate degrees within the previous five years.



     "It's extremely unusual to have two of these award winners

in a single department," said John C. Wierman, chairman of the

Department of Mathematical Sciences. "This is great, both for

Lenore and the department. We're very proud of her."



     More than coincidence led Maryland Hall neighbors Cowen and

Priebe to earn the same national award, even though they come

from completely different fields of mathematics.



     Priebe, a statistician, had talked to Cowen about data sets

that are notoriously difficult to analyze, because of problems

such as the Curse of Dimensionality. These obstacles were

presented in a form that was new to Cowen but seemed to have

promising analogies in discrete mathematics, the area in which

she works.



     "The mathematical world is really divided in two," she

explains. "There's continuous math and discrete math. Continuous

math is the study of things that change with time. So, nearly all

math that's involved in physics, calculus and statistics is

continuous math. Anything that involves measuring the physical

universe is usually continuous math.



     "However, the mathematics that deals with a computer is

discrete math. Discrete math is the study of particular objects,

a finite set of objects."



     At many schools, faculty members from these two fields are

based in different departments, even different buildings. But the

Mathematical Sciences Department in Hopkins' engineering school

has professors from both disciplines, allowing for unusual,

fruitful collaborations, like the one between Priebe and Cowen.



     "The people in her field don't usually address the problems

we're talking about," Priebe said. "They're not statisticians.

But with her sitting in the office next to me and hearing the

kind of things I was doing, for some reason it clicked between us

that some things that she knew about might apply.



     "Maybe it's novel because the people who know the stuff that

she knows don't normally sit next to the people who try to solve

the problems that I'm trying to solve. That may be one reason we

can do things that haven't been done."



      The approach that Cowen will use draws from graph theory

and randomized algorithms. The weighted graph of pair-wise

distances between samples is distorted to a simpler structure in

a lower-dimensional space where, nonetheless, the original

distances are approximately preserved. The use of randomness

allows the approximation to be constructed quickly.



     Cowen, 28, joined the Hopkins faculty in 1994, a year after

earning her doctorate in mathematics at Massachusetts Institute

of Technology. She completed her undergraduate studies at Yale,

which she entered at 16.



     Cowen learned the importance of education at an early age.

Her father is a math professor at Queens College in New York,

while her mother teaches high school English. Cowen has played

classical violin since the age of 5 and continues to make music

with a quintet at Hopkins. While attending graduate school, she

dabbled in folk music and performed as an accompanist for an

international dance group.



     Though her research is challenging, Cowen has a less serious

side. Her World Wide Web page directs visitors to a huge

collection of jokes that poke fun at people who play the viola.

She describes herself as a "beginning but determined swing

dancer."



     Despite her academic achievements, Cowen did not learn to

drive until she was 25. With a tinge of embarrassment, she admits

that she failed her driving test in two states before finally

obtaining a license. Though she is a whiz at the geometry of

graphs, Cowen had trouble with parallel parking.



     "That was the hardest thing I've ever had to do in my life,"

she says with a laugh. "Learning to drive."