| Type of Document |
Master's Thesis |
| Author |
Caņas, Daniel Alberto, |
| Author's Email Address |
dacanas@unity.ncsu.edu |
| URN |
etd-11052004-022839 |
| Title |
Generalizations and unification of centroid-based clustering methods |
| Degree |
Master of Science |
| Graduate Program |
Computer Science |
| Advisory Committee |
| Advisor Name |
Title |
| Dr. Robert Funderlic |
Committee Chair |
| Dr, Jon Doyle |
Committee Member |
| Dr. Steffen Heber |
Committee Member |
|
| Keywords |
- k-means
- data mining
- cluster analysis
|
| Date of Defense |
2004-11-02 |
| Availability |
unrestricted |
Abstract
There are many clustering methods that are referred to as k-means-like. We give the minimal necessary and sufficient components for the mechanism of the k-means (iterative and partitional) clustering method of a finite set of objects, X. Thus k-means is generalized and the methods that mimic k-means are unified. We name these k-center clustering methods. The fundamental mechanism of k-center methods exposes the usual misconceptions of k-means such as (a) ``distance" satisfies some of properties of a mathematical metric, (b) there is a need to measure ``distance" between objects in X, and (c) the centers of clusters have the same nature as the objects of X. Moreover, k-center methods have a common formula to choose or calculate centers of clusters. We characterize the convergent common objective function by expressing it in terms of (a) a distance measure for closeness between center objects and the objects in X and (b) the coherence of clusters. We give a three object example to demonstrate the components of the formal mechanism of a k-center method. We then give examples of various known methods that belong to the class of k-center methods. We exhibit an extensive and thorough comparison of the qualitative k-modes and the numerical spherical k-means. Included are paradigm applications, a matrix environment, an understanding of the duality of a dissimilarity and similarity measure, and an understanding of normalized X and the normalized centers of subsets of X.
|
| Files |
| Filename |
Size |
Approximate Download Time
(Hours:Minutes:Seconds)
|
| 28.8 Modem |
56K Modem |
ISDN (64 Kb) |
ISDN (128 Kb) |
Higher-speed Access |
| |
etd.pdf |
255.24 Kb |
00:01:10 |
00:00:36 |
00:00:31 |
00:00:15 |
00:00:01 |
|
