user login 

BITS2007 Meeting
BITS2007 Meeting

26-28 April 2007 Napoli, Italy

email support
Home > Contribution details
get PDF of this contribution get XML of this contribution get ICal of this contribution
Generating multidimensional embeddings based on fuzzy memberships
Exploratory analysis of  genomic data sets using unsupervised clustering techniques
is often affected by problems due to the small cardinality and high dimensionality of
the data set. These problems may be eased by performing clustering in an embedding
space. This brings about the problem of selecting an appropriate transformation to
perform the required multidimensional embedding, which should be able to keep the
necessary information while reducing data dimensionality.
If the cardinality of the data set is small compared to the input space
dimensionality, then the matrix of mutual distances or other pairwise pattern
evaluation methods such as kernels may be used to represent data sets in a more
compact way. Following this approach, the data matrix is replaced by a pairwise
dissimilarity matrix D.

We have proposed an embedding technique based on the concept of fuzzy membership,
which is related but different from dissimilarity-based representations. A set of
vectors are selected from the data set. These are termed probes and are used as
reference points for the rest of the data set. Probes are interpreted as fuzzy
points; for each of the remaining points in the data set, the fuzzy membership to a
probe can be evaluated. Therefore, for each point an ordered set of membership values
is defined, one for each probe, and this ordered set can be used as a new feature
vector to represent the point itself, embededd in a space induced by the probes. We
will call this representation space the Membership Embedding Space (MES).
We may observe that a point in the embedding space will be represented by a vector
containing only few non-null components (depending on the support of the membership
function), in correspondence of the closest probes in the original feature space. In
our experiments, the memberships of fuzzy sets centered on the probes were modeled as
Gaussians normalized over all probes. 
Here we propose a generative technique based on Simulated Annealing to select sets of
probes of small cardinality. 
An appropriate generalized energy is defined to represent clustering quality and
clustering complexity for the probes.

When applied to clustering, the approach has been demonstrated to lead to 
significant improvements with respect to the application of clustering algorithms in
the original space and in the distance embedding space. We present results based on
standard data commonly available on line, to make them readily comparable with other
These results indicate that the method supports high quality clustering solutions
using compact sets of probes.
Id: 101
Place: Napoli, Italy
Centro Congressi "Federico II"
Via Partenope 36
Starting date:
26-Apr-2007   17:20
Duration: 20'
Contribution type: Oral
Primary Authors: ROVETTA, Stefano (Department of Computer and Information Sciences, University of Genova)
Co-Authors: FRANCESCO, Masulli (Department of Computer and Information Sciences, University of Genova)
MAURIZIO, Filippone (Department of Computer and Information Sciences, University of Genova)
Presenters: ROVETTA, Stefano
Material: slide Slides
Included in session: Session 2: Novel methodologies, algorithms and tools
Included in track: Novel methodologies, algorithms and tools | Last modified 08 July 2009 10:35 |

Powered by Indico 0.90.3