.png){kind=icon}
.png){kind=icon}
Return
Robust linear clustering
.png){kind=icon}
OA
AI
DOI：10.1111/j.1467-9868.2008.00682.x.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Non-hierarchical clustering methods are frequently based on the idea of forming groups around 'objects'. The main exponent of this class of methods is the k-means method, where these objects are points. However, clusters in a data set may often be due to certain relationships between the measured variables. For instance, we can find linear structures such as straight lines and planes, around which the observations are grouped in a natural way. These structures are not well represented by points. We present a method that searches for linear groups in the presence of outliers. The method is based on the idea of impartial trimming. We search for the 'best' subsample containing a proportion 1-alpha of the data and the best k affine subspaces fitting to those non-discarded observations by measuring discrepancies through orthogonal distances. The population version of the sample problem is also considered. We prove the existence of solutions for the sample and population problems together with their consistency. A feasible algorithm for solving the sample problem is described as well. Finally, some examples showing how the method proposed works in practice are provided.
Keywords:
Affine subspaces
Orthogonal regression
Principal components
Robustness
Trimmed k-means
Trimming
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
J
IF:
3.6
Papers:
1.5K
Citations:
3.2W
View more organizations