Large Margin Graph Embedding-Based Discriminant Dimensionality Reduction

Abstract

Discriminant graph embedding-based dimensionality reduction methods have attracted more and more attention over the past few decades. These methods construct an intrinsic graph and penalty graph to preserve the intrinsic geometry structures of intraclass samples and separate the interclass samples. However, the marginal samples cannot be accurately characterized only by penalty graphs since they treat every sample equally. In practice, these marginal samples often influence the classification performance, which needs to be specially tackled. In this study, the near neighbors’ hypothesis margin of marginal samples has been further maximized to separate the interclass samples and improve the discriminant ability by integrating intrinsic graph and penalty graph. A novel discriminant dimensionality reduction named LMGE-DDR has been proposed. Several experiments on public datasets have been conducted to verify the effectiveness of the proposed LMGE-DDR such as ORL, Yale, UMIST, FERET, CMIU-PIE09, and AR. LMGE-DDR performs better than other compared methods, and the corresponding standard deviation of LMGE-DDR is smaller than others. This demonstrates that the evaluation method verifies the effectiveness of the introduced method.

Marginal Fisher Analysis With Polynomial Matrix Function

“…For the proposed PMFA method, according to section III C, two polynomial functions are selected to map the matrices p Z and Z to the corresponding matrix functions: =+ . In the further experiment, the PMFA method is also compared with the latest proposed manifold-based learning algorithms, including GDE [18], LMGE-DDR [19], CR-DLPP [20], GEU-MFA-U and GEU-MFA-S [17].…”

“…In this section, we also compare the PMFA method and other latest proposed manifold-based learning algorithms on PIE, AR, Yale, FERET and Yale B [33] datasets in Table 8. These including GDE [18], LMGE-DDR [19], CR-DLPP [20], GEU-MFA-U and GEU-MFA-S [17]. Where GEU-MFA-U and GEU-MFA-S are the latest methods of MFA.…”

“…The graph embedding framework is reformulated in [17], as a special case of the GEU framework formula, the MFA technique is extended as GEU-MFA. Recently, there are many algorithms based on manifold learning, such as GDE [18], LMGE-DDR [19] and CR-DLPP [20].…”