Fuzzy logic approaches to structure preserving dimensionality reduction

Dimensionality reduction (DR) plays an important role in hyperspectral image (HSI) classification. Unsupervised DR (uDR) is more practical due to the difficulty of obtaining class labels and their scarcity for HSIs. However, many existing uDR algorithms lack the comprehensive exploration of spectral-locational-spatial (SLS) information, which is of great significance for uDR in view of the complex intrinsic structure in HSIs. To address this issue, two uDR methods called SLS structure preserving projection (SLSSPP) and SLS reconstruction preserving embedding (SLSRPE) are proposed. Firstly, to facilitate the extraction of SLS information, a weighted spectral-locational (wSL) datum is generated to break the locality of spatial information extraction. Then, a new SLS distance (SLSD) excavating the SLS relationships among samples is designed to select effective SLS neighbors. In SLSSPP, a new uDR model that includes a SLS adjacency graph based on SLSD and a cluster centroid adjacency graph based on wSL data is proposed, which compresses intraclass samples and approximately separates interclass samples in an unsupervised manner. Meanwhile, in SLSRPE, for preserving the SLS relationship among target pixels and their nearest neighbors, a new SLS reconstruction weight was defined to obtain the more discriminative projection. Experimental results on the Indian Pines, Pavia University and Salinas datasets demonstrate that, through KNN and SVM classifiers with different classification conditions, the classification accuracies of SLSSPP and SLSRPE are approximately 4.88%, 4.15%, 2.51%, and 2.30%, 5.31%, 2.41% higher than that of the state-of-the-art DR algorithms.

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Robust Structure Preserving Nonnegative Matrix Factorization for Dimensionality Reduction

Mathematical Problems in Engineering ◽

10.1155/2016/7474839 ◽

2016 ◽

Vol 2016 ◽

pp. 1-14

Author(s):

Bingfeng Li ◽

Yandong Tang ◽

Zhi Han

Keyword(s):

Dimensionality Reduction ◽

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Noisy Data ◽

Nonnegative Matrix ◽

Structure Preserving ◽

Structure Preservation ◽

Significant Performance ◽

Linear Dimensionality Reduction ◽

Low Dimensional

As a linear dimensionality reduction method, nonnegative matrix factorization (NMF) has been widely used in many fields, such as machine learning and data mining. However, there are still two major drawbacks for NMF: (a) NMF can only perform semantic factorization in Euclidean space, and it fails to discover the intrinsic geometrical structure of high-dimensional data distribution. (b) NMF suffers from noisy data, which are commonly encountered in real-world applications. To address these issues, in this paper, we present a new robust structure preserving nonnegative matrix factorization (RSPNMF) framework. In RSPNMF, a local affinity graph and a distant repulsion graph are constructed to encode the geometrical information, and noisy data influence is alleviated by characterizing the data reconstruction term of NMF withl2,1-norm instead ofl2-norm. With incorporation of the local and distant structure preservation regularization term into the robust NMF framework, our algorithm can discover a low-dimensional embedding subspace with the nature of structure preservation. RSPNMF is formulated as an optimization problem and solved by an effective iterative multiplicative update algorithm. Experimental results on some facial image datasets clustering show significant performance improvement of RSPNMF in comparison with the state-of-the-art algorithms.

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