 |
|
Event(s) on March 2007
- 6/3/2007
| 題目: |
A New Algorithm for Minimization without Derivatives |
| 講員: |
Prof. M. J. D. Powell, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK |
| 時間/地點: |
11:30 - 12:30
RRS 905
|
| | |
| 摘要: |
The development of this subject during the last 50 years was surveyed
by
the author in the William Benter Lecture at City University
on February 7th.
His recent research on unconstrained minimization that provided
the NEWUOA
algorithm was mentioned briefly. The main ideas of this algorithm
with an
extension that allows bounds on the variables will be described.
Quadratic
models are employed that are derived from a small number of
interpolation
conditions. Some numerical results will show the efficiency
that is achieved.
|
- 6/3/2007
| 題目: |
CMIV Lecture Series: Optimization for Image Processing (Lecture 3) |
| 講員: |
Prof. Mila Nikolova, CMLA ENS de Cachan, France |
| 時間/地點: |
14:30 - 16:30
FSC 1217
|
| | |
- 13/3/2007
| 題目: |
Optimal Superconvergent Quadratic and Cubic Spline Collocation Methods |
| 講員: |
Prof. Graeme Fairweather, Department of Mathematical and Computer Sciences, Colorado School of Mines, USA |
| 時間/地點: |
11:30 - 12:30
FSC 1217
|
| | |
| 摘要: |
Quadratic and cubic spline collocation methods are popular techniques
for solving boundary value
problems for ordinary and partial differential equations and
for the spatial discretization of time dependent problems.
When used in their basic form, they provide approximations which
are no more than second order accurate. In this
talk, we provide an overview of recent developments in the derivation
of optimal methods. In particular, we describe new
methods for elliptic problems in the unit square which are not
only of optimal accuracy but possess certain superconvergence
properties.
Moreover,
these methods are constructed so that the collocation equations
can be solved
using matrix decomposition algorithms (MDAs). MDAs are
fast direct methods which employ fast Fourier transforms and
require O(N^2 log N) operations on an N x N uniform partition
of the unit square. We present the results of numerical
experiments which exhibit the expected optimal global convergence
rates as well as
superconvergence phenomena.
|
- 13/3/2007
| 題目: |
CMIV Lecture Series: Optimization for Image Processing (Lecture 4) |
| 講員: |
Prof. Mila Nikolova, CMLA ENS de Cachan, France |
| 時間/地點: |
14:30 - 16:30
FSC 1217
|
| | |
- 14/3/2007
| 題目: |
Agglomerative Fuzzy K-means Clustering Algorithm with Selection of Number of Clusters |
| 講員: |
Mr. Junjie Li, Department of Mathematics, Hong Kong Baptist University, HKSAR, China |
| 時間/地點: |
14:30 - 15:30
FSC 1217
|
| | |
| 摘要: |
The k-means algorithm is well known for its efficiency in clustering
large data sets. Fuzzy versions of the k-means algorithm, where
each pattern is allowed to have memberships in all clusters rather
than having a distinct membership to one single cluster. Numerous
problems in real world applications, such as pattern recognition
and computer vision, can be tackled effectively by the fuzzy
k-means algorithms. There are two major issues in application
of the k-means-type (non-fuzzy or fuzzy) algorithms in cluster
analysis. The first issue is that the number of clusters k needs
to be determined in advance as an input to these algorithms.
The second issue is that the k-means-type algorithms are very
sensitive to the initial cluster centers. We propose an agglomerative
fuzzy k-means clustering algorithm to tackle the above two issues
in application of the k-means-type clustering algorithms. The
new algorithm is an extension to the standard fuzzy k-means algorithm
by introducing a penalty term to the objective function to make
the clustering process not sensitive to the initial cluster centers.
The new algorithm can produce more consistent clustering results
from different sets of initial clusters centers. Combined with
cluster validation techniques, the new algorithm can determine
the number of clusters in a data set. Experimental results have
demonstrated the effectiveness of the new algorithm in producing
consistent clustering results and determining the correct number
of clusters in different data sets, some with overlapping inherent
clusters. Some further and promising work is also discussed.
|
- 20/3/2007
| 題目: |
CMIV Lecture Series: Optimization for Image Processing (Lecture 5) |
| 講員: |
Prof. Mila Nikolova, CMLA ENS de Cachan, France |
| 時間/地點: |
14:30 - 16:30
FSC 1217
|
| | |
- 27/3/2007
| 題目: |
A Smoothed Bootstrap Test for Independence Based on Mutual Information |
| 講員: |
Mr. Edmond Wu, Department of Statistics and Actuarial Science, The University of Hong Kong, HKSAR, China |
| 時間/地點: |
11:30 - 12:30
FSC 1217
|
| | |
| 摘要: |
In this talk, we study a computational test for independence of
multivariate time series data based on mutual information. We
first construct a test between a pair of i.i.d. (over time) data
and then extend to the cases of high dimensional and serial dependent
time series data. The smoothed bootstrap method is used to estimate
the null distribution of mutual information. The experimental
results reveal that the proposed bootstrap test performs satisfactory
and can achieve a high power even for moderate sample size. Furthermore,
we adopt the proposed test in independent component analysis
(ICA) applications as a crucial verification step to validate
whether the 'independent' sources estimated by various ICA algorithms
are really independent.
|
- 27/3/2007
| 題目: |
CMIV Lecture Series: Optimization for Image Processing (Lecture 6) |
| 講員: |
Prof. Mila Nikolova, CMLA ENS de Cachan, France |
| 時間/地點: |
14:30 - 16:30
FSC 1217
|
| | |
|
|
|
|
