Global-Local Partial Least Squares Discriminant Analysis And Its Extension In Reproducing Kernel Hilbert Space
| dc.contributor.author | Muhammad, Aminu | |
| dc.date.accessioned | 2022-02-23T07:15:39Z | |
| dc.date.available | 2022-02-23T07:15:39Z | |
| dc.date.issued | 2021-04 | |
| dc.description.abstract | Subspace learning is an essential approach for learning a low dimensional representation of a high dimensional space. When data samples are represented as points in a high dimensional space, learning with the high dimensionality becomes challenging as the effectiveness and efficiency of the learning algorithms drops significantly as the dimensionality increases. Thus, subspace learning techniques are employed to reduce the dimensionality of the data prior to employing other learning algorithms. Recently, there has been a lot of interest in subspace learning techniques that are based on the global and local structure preserving (GLSP) framework. The main idea of the GLSP approach is to find a transformation of the high dimensional data into a lower dimensional subspace, where both the global and local structure information of the data are preserved in the lower dimensional subspace. This thesis consider the case where data is sampled from an underlying manifold embedded in a high dimensional ambient space. Two novel subspace learning algorithms called locality preserving partial least squares discriminant analysis (LPPLS-DA) and neighborhood preserving partial least squares discriminant analysis (NPPLS-DA) which are based on the GLSP framework are proposed for discriminant subspace learning. Unlike the conventional partial least squares discriminant analysis (PLS-DA) which aims at preserving only the global Euclidean structure of the data space, the proposed LPPLS-DA and NPPLS-DA algorithms find an embedding that preserves both the global and local manifold structure. As a result, both LPPLS-DA and NPPLS-DA can extract more discriminant information in the original data than PLS-DA and are well-suited for dimensionality reduction and visualization of complex datasets. Furthermore, kernel extensions of LPPLS-DA and NPPLS-DA in reproducing kernel Hilbert space (RKHS) are proposed to handle situations where a strong nonlinear relation exist between the sets of observed data. Performance improvement of the proposed algorithms over the conventional PLSDA is demonstrated through several experiments. It is shown that LPPPLS-DA and NPPLS-DA are very effective for face analysis (recognition and representation). Their kernel extensions are applied to tumor classification and chemical data analysis respectively and it was shown that the kernel extensions outperform their linear counterparts when a strong nonlinear relationship exist between the set of observed data. | en_US |
| dc.identifier.uri | http://hdl.handle.net/123456789/14752 | |
| dc.language.iso | en | en_US |
| dc.publisher | Universiti Sains Malaysia | en_US |
| dc.subject | Mathematics | en_US |
| dc.title | Global-Local Partial Least Squares Discriminant Analysis And Its Extension In Reproducing Kernel Hilbert Space | en_US |
| dc.type | Thesis | en_US |
Files
License bundle
1 - 1 of 1
Loading...
- Name:
- license.txt
- Size:
- 1.71 KB
- Format:
- Item-specific license agreed upon to submission
- Description: