A note on the solvability for generalized Sylvester equations

Chen, Huaxi; Wang, Long; Li, Tingting

doi:10.1007/s13398-020-00957-6

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Constructing An Adjacency Graph1

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2022

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“…As a well-known Sylvester equation, the computational complexity of ( 13) is O(n 3 ) [34][35][36]. We can use MATLAB command lyap to get the weight matrix…”

Section: Constructing An Adjacency Graphmentioning

confidence: 99%

A Smoothed Matrix Multivariate Elliptical Distribution-Based Projection Method for Feature Extraction

Qiu

Wang

Sun

et al. 2022

Computational Intelligence and Neuroscience

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Big data has the traits such as “the curse of dimensionality,” high storage cost, and heavy computation burden. Self-representation-based feature extraction methods cannot effectively deal with the image-level structural noise in the data, so how to character a better relationship of reconstruction representation is very important. Recently, sparse representation with smoothed matrix multivariate elliptical distribution (SMED) using structural information to handle low-rank error images caused by illumination or occlusion has been proposed. Based on SMED, we present a new method named SMEDP for feature extraction. SMEDP firstly utilizes SMED to automatically construct an adjacency graph and then obtains an optimal projection matrix by maximizing the ratio of the local scatter matrix and the total scatter matrix in the PCA subspace. Experiments on the COIL-20 object database, ORL face database, and CMU PIE face database prove that SMEDP works well and can achieve considerable visual and recognition performance than the relevant methods.

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“…As a well-known Sylvester equation, the computational complexity of ( 13) is O(n 3 ) [34][35][36]. We can use MATLAB command lyap to get the weight matrix…”

Section: Constructing An Adjacency Graphmentioning

confidence: 99%