Joint low‐rank project embedding and optimal mean principal component analysis

Self Cite

The sparse matrix regression (SMR) model for the feature selection method has attracted much attention. However, most existing models do not consider the globality and adaptively preserve the local structure of the image data in projection space. To settle such issues, an adaptive non‐negative low‐rank preserving SMR model for supervised image feature selection is proposed. It first uses the low‐rank representation with non‐negative constraint to capture the globality and more discriminative information of image data and makes the error matrix in self‐representation of training data sparse. Next, the non‐negative low‐rank representation coefficients are used to establish a graph matrix learning model to reveal the local manifold structure of the image data. Thus, the proposed model enhances the discriminative ability as well as performs feature selection by the obtained transformation matrix. Finally, an alternating iterative algorithm for solving this model is developed and its convergence and complexity are also analyzed. Experimental results on some image data sets show that the proposed algorithm is effective for images and its recognition ability is obviously superior to other existing methods. In addition, the proposed method is also applied to two scene image classifications to further verify its effectiveness.

Section: 21mentioning

confidence: 99%

“…Similar to the method in [46], suppose that

{{\bf{E}}^{(t)}}

{{\bf{S}}^{(t)}}

{{\bf{F}}^{(t)}}

{{\bm{\Lambda }}^{(t)}}

and

{{\bm{\Delta }}^{(t)}}

are the values of S , E , F , Λ and Δ at the t th iteration, respectively, then the update of the variable S at the ( t + 1)th iteration is:

$$\begin{eqnarray} &&{\mathbf{S}}^{(t+1)} = {\mathbf{U}}^{(t)}\mathrm{diag}\left(\max \left({\sigma}_{1}^{(t)}-\beta (\mu {\eta}_{Z})^{-1},0\right),\right.\nonumber\\ &&\quad\left. \max \left({\sigma}_{2}^{(t)}-\beta (\mu {\eta}_{Z})^{-1},0\right),\ldots,\max \left({\sigma}_{r}^{(t)}-\beta (\mu {\eta}_{Z})^{-1},0)\right)({\mathbf{V}}^{(t)}\right)^{T}\nonumber\\ \end{eq...

…”

Section: Non‐negative Low‐rank and Adaptive Preserving Smrmentioning

confidence: 99%

Non‐negative low‐rank adaptive preserving sparse matrix regression model for supervised image feature selection and classification

Chen

Zhu

et al. 2023

Self Cite

“…By linearizing the quadratic term in () at S (t) and adding a proximal term [39], this problem becomes

\begin{equation}\mathop {\min }\limits_{\bf{S}} \beta {\left\| {\bf{S}} \right\|_*} + \frac{{\mu {\eta _{\tilde X}}}}{2}\left\| {{\bf{S}} - {{\bf{S}}^{(t)}} + \frac{1}{{{\eta _{\tilde X}}}}{{{{\tilde {\bf X}}}}^T}({{\tilde {\bf X}}}{{\bf{S}}^{(t)}} - {{\bf{A}}^{(t)}})} \right\|_F^2{\rm{ ,}}\end{equation}

where

{\eta _{\tilde X}} &gt; \sigma _{\max }^2({{\tilde {\bf X}}})

. Suppose that

{{\bf{B}}^{(t)}} = {{\bf{U}}_{{r_t}}}{{\bm{\Sigma }}_{{r_t}}}{\bf{V}}_{{r_t}}^T

is the truncated singular value decomposition of the matrix

{{\bf{B}}^{(t)}} = {{\bf{S}}^{(t)}} - \frac{1}{{{\eta _{\tilde X}}}}{{{\tilde {\bf X}}}^T}({{\tilde {\bf X}}}{{\bf{S}}^{(t)}} - {{\bf{A}}^{(t)}})

, where

Σ_{r_{}}

…”

Section: Model and Algorithmmentioning

confidence: 99%

“…By linearizing the quadratic term in (14) at S (t) and adding a proximal term [39], this problem becomes…”

Section: Algorithmmentioning

confidence: 99%

Latent low‐rank representation sparse regression model with symmetric constraint for unsupervised feature selection

Guo

Chen

2023

Self Cite

Unsupervised feature selection is a dimensionality reduction method and has been widely used as an important and indispensable preprocessing step in many tasks. However, realworld data are not only high-dimensional, but also have intrinsic correlations between data points, which are not fully utilized in feature selection. Furthermore, real-world data usually inevitably contain noise or outliers. In order to select features from data more effectively, a sparse regression model based on latent low-rank representation with the symmetric constraint for unsupervised feature selection is proposed. With the coefficient matrix of non-negative symmetric low-rank representation, an affinity matrix characterized by the correlation relationship between data points is adaptively obtained, which reveals the intrinsic geometric relationship, global structure, and discrimination of data points. A latent representation of all data points obtained from this affinity matrix is employed as a pseudolabel, and feature selection is carried out by sparse linear regression. This method performs feature selection in the learned latent space instead of the original data space. An alternating iteration algorithm is designed to solve the proposed model, and its effectiveness and efficiency are verified on several benchmark data sets.

“…Feature extraction methods are divided into two main groups: unsupervised and supervised [9]. Unsupervised feature extraction methods such as principal component analysis (PCA) [10] do not use the information of class labels. So, they often ignore discrimination among different classes.…”

Section: Introductionmentioning

confidence: 99%

Polarimetric SAR image classification using binary coding‐based polarimetric‐morphological features

Imani

2022

Polarimetric synthetic aperture radar (POLSAR) systems provide high resolution images containing polarimetric information. So, they have high capability in land cover classification. In this work, a binary coding-based polarimetric-morphological (BCPM) feature extraction is proposed for POLSAR image classification. At first, a set of polarimetric features is proposed. Then, a new morphological framework is introduced for contextual feature extraction from the POLSAR cube. The coherence matrix is composed from diagonal and non-diagonal elements with different information. These elements are analysed separately in the proposed method. Moreover, the amplitude and phase components of the non-diagonal elements are individually analysed using morphological filters by reconstruction. Finally, a binary coding-based polarimetric-spatial feature reduction, which uses the first order statistics, is proposed for feature transformation. The experiments on three real POLSAR images and a synthetic dataset show the superior performance of BCPM compared to several classification methods.