A new method to detect targets in hyperspectral images based on principal component analysis

Hyperspectral Images (HSIs) contain enriched information due to the presence of various bands, which have gained attention for the past few decades. However, explosive growth in HSIs’ scale and dimensions causes “Curse of dimensionality” and “Hughes phenomenon”. Dimensionality reduction has become an important means to overcome the “Curse of dimensionality”. In hyperspectral images, labeled samples are more difficult to collect because they require many labor and material resources. Semi-supervised dimensionality reduction is very important in mining high-dimensional data due to the lack of costly-labeled samples. The promotion of the supervised dimensionality reduction method to the semi-supervised method is mostly done by graph, which is a powerful tool for characterizing data relationships and manifold exploration. To take advantage of the spatial information of data, we put forward a novel graph construction method for semi-supervised learning, called SLIC Superpixel-based l 2 , 1 -norm Robust Principal Component Analysis (SURPCA2,1), which integrates superpixel segmentation method Simple Linear Iterative Clustering (SLIC) into Low-rank Decomposition. First, the SLIC algorithm is adopted to obtain the spatial homogeneous regions of HSI. Then, the l 2 , 1 -norm RPCA is exploited in each superpixel area, which captures the global information of homogeneous regions and preserves spectral subspace segmentation of HSIs very well. Therefore, we have explored the spatial and spectral information of hyperspectral image simultaneously by combining superpixel segmentation with RPCA. Finally, a semi-supervised dimensionality reduction framework based on SURPCA2,1 graph is used for feature extraction task. Extensive experiments on multiple HSIs showed that the proposed spectral-spatial SURPCA2,1 is always comparable to other compared graphs with few labeled samples.

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Time series analysis for multi-dimensional dynamical systems combining wavelet transformation and local principal component analysis

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptz129 ◽

2019 ◽

Vol 2019 (12) ◽

Author(s):

Kana Fuji ◽

Mikito Toda

Keyword(s):

Principal Component Analysis ◽

Time Series ◽

Phase Space ◽

Degrees Of Freedom ◽

Wavelet Transformation ◽

Vibrational Energy ◽

Principal Component ◽

Component Analysis ◽

New Method ◽

Frequency Variation

Abstract To analyze trajectories for systems of many degrees of freedom, we propose a new method called wavelet local principal component analysis (WlPCA) combining the wavelet transformation and local PCA in time. Our method enables us to reduce the dimensionality of time series both in degrees of freedom and frequency so that characteristic features of oscillatory behavior can be captured. To test the new method, we apply WlPCA to a non-autonomous model of multiple degrees of freedom, the Froeschlé maps of $N=2$ and $N=4$, which correspond to autonomous systems of three and five degrees of freedom, respectively. The eigenvalues and eigenvectors obtained by WlPCA reveal those times when frequency variation exhibits switching between relatively stationary features. Moreover, further analyses indicate which degrees of freedom and frequencies are involved in the switching. We confirm that the switching corresponds to the onset of transport in phase space. These findings imply that, even for systems of larger degrees of freedom, barriers can exist in phase space that block transport for a finite time, thereby dividing the phase space into multiple quasi-stationary regions. Thus, our method is promising for understanding dynamics in systems of many degrees of freedom, such as vibrational-energy redistribution in molecules.

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