Local and Global Structures Preserving Projection

Cheng, Hao; Hua, Kien A.; Vu, Khanh

doi:10.1109/ictai.2007.195

Cited by 7 publications

(9 citation statements)

References 8 publications

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“…Simultaneously samples with small distance can be kept close enough in the embedded space. Thus, the local structure can be preserved under the objective functions of (13) and (14), respectively.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…In this subsection, we evaluate our proposed method with PCA [22], LapLDA [24], MFA [23], LPP [10], RP [9], LGSPP [13], and JGLDA [14] on a hyperspectral image, that is, the well-known Indian Pines scenario. In the following experiments, dimension reduction techniques are firstly adopted to reduce the dimensionality of input feature, following a classified procedure with a concrete classifier (e.g., NN classifier or SVM classier).…”

Section: Experiments On Real Hsi Data Setmentioning

confidence: 99%

“…A brief review of discriminant analysis techniques, for example, Locality Preserving Projection (LPP) [10] and discriminant analysis [13,14], are provided in this section. To facilitate the following discussion, we start with a supervised learning problem.…”

Section: Related Workmentioning

confidence: 99%

“…Seven methods, that is, LDA [21], PCA [22], LPP [10], MFA [23], LGSPP [13], JGLDA [14], and proposed LGGSP algorithm, were compared. There are 100 test samples for the toy example, 100 test samples for "tulip, " 1000 test samples for "ripley, " 200 test samples for the multimodal example, and 100 test samples for the "twomoon" data set.…”

Section: Experiments On Synthetic Data Setsmentioning

confidence: 99%

“…Despite this, some articles, such as Local and Global Structures Preserving Projection (LGSPP) [13] and Joint Global and Local Structure Discriminant Analysis (JGLDA) [14], reported that besides locality, the global structure is also important. The locality can be generally captured by a Laplacian matrix that comes from neighborhood relationship, that is, adjacent graph.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Local and Global Geometric Structure Preserving and Application to Hyperspectral Image Classification

Luo

Tang

et al. 2015

Mathematical Problems in Engineering

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Locality Preserving Projection (LPP) has shown great efficiency in feature extraction. LPP captures the locality by the K-nearest neighborhoods. However, recent progress has demonstrated the importance of global geometric structure in discriminant analysis. Thus, both the locality and global geometric structure are critical for dimension reduction. In this paper, a novel linear supervised dimensionality reduction algorithm, called Locality and Global Geometric Structure Preserving (LGGSP) projection, is proposed for dimension reduction.LGGSP encodes not only the local structure information into the optimal objective functions, but also the global structure information. To be specific, two adjacent matrices, that is, similarity matrix and variance matrix, are constructed to detect the local intrinsic structure. Besides, a margin matrix is defined to capture the global structure of different classes. Finally, the three matrices are integrated into the framework of graph embedding for optimal solution. The proposed scheme is illustrated using both simulated data points and the well-known Indian Pines hyperspectral data set, and the experimental results are promising.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%