SSNSC-for-HSIC

This demo implements the method proposed in the paper given below [1];

[1] Kemal Gürkan Toker & Seniha Esen Yuksel (2022) Spectral-spatial nearest subspace classifier for hyperspectral image classification, International Journal of Remote Sensing, 43:6, 2106-2133, DOI: 10.1080/01431161.2022.2055986

Spectral-Spatial Nearest Subspace Classifier (SSNSC) method is a kind of representation-based method. The SSNSC method is proposed, inspired by the geometric interpretation of the Nearest Subspace Classifier (NSC) method. NSC is a simple classifier that works on the assumption that samples from the same class approximately lie on the same subspace. Based on this assumption, the NSC method analyzes the closeness between the test sample and the space spanned by the within-class training samples. Then, the label of the test sample is assigned to the closest class. However, NSC only considers spectral information and neglects spatial information. In addition to the assumption in the NSC method, we add another assumption that spatially adjacent pixels quite likely belong to the same class. By combining these two assumptions, we conclude that spatially adjacent pixels must approximately lie on the same subspace as well. Based on these assumptions, we propose the spectral-spatial nearest subspace classification (SSNSC) approach as a generic classification framework that performs classification by analyzing the closeness between the subspace spanned by the samples used for spatial information and the subspace spanned by the within-class training samples. Canonical Correlation Analysis (CCA) is used to measure the closeness between these two subspaces.
This approach performs well with LIMITED training data and BALANCED training samples.

Let

${\rm{ }}{C}$ : number of classes

${x_{ij}}$ : $j^{th}$ training sample from class $i$

$X_i$ : Training samples belonging to the $i^{th}$ class

$y$ : Test Sample

$Y$ : Neighbouring pixels around the test pixel $y$

Col($X_i$): Column space of $X_i$

Col($Y$): Column space of $Y$

The Figure given below shows the geometric interpretation of the Proposed SSNSC method.

In SSNSC, the maximum correlation ($\rho_i$) between the space spanned by the neighborhood of the test sample Col($Y$) and space spanned by the within-class training samples $Col(\mathbf{X_i})$ ${\forall _i} \in {\rm{ }}{ 1,2, ... ,C}$ is computed separately. Then, the test sample is labelled as the class with the maximum correlation. (The red dot indicates the origin. The two origins are one point and the only one shared by the two planes. This approach performs well with LIMITED training data and BALANCED training samples.

Some issues may affect the method's performance. One of these is that the method is linear and uses spectral similarity between training and test samples during classification, which can negatively affect the performance in datasets with spectrally similar classes. Another area for improvement is that an imbalanced distribution of training data size for different classes can result in bias when classifying instances. The classes with a larger number of training samples, meaning subspaces with larger dimensions, are more likely to be selected even if it is not the correct classification. Furthermore, although our method shows strong performance with limited training data, it may not outperform deep learning approaches when extensive training data is available.

More details in the paper:

https://www.tandfonline.com/doi/full/10.1080/01431161.2022.2055986?scroll=top&needAccess=true&role=tab

and in the thesis,

https://www.researchgate.net/publication/372344956_SPECTRAL-SPATIAL_NEAREST_SUBSPACE_CLASSIFIERS_FOR_HYPERSPECTRAL_IMAGES

You can find the article [1] in English at the end of this thesis. If you find these works interesting in your research, please kindly cite:

@article{doi:10.1080/01431161.2022.2055986, author = {Kemal Gürkan Toker and Seniha Esen Yuksel}, title = {Spectral-spatial nearest subspace classifier for hyperspectral image classification}, journal = {International Journal of Remote Sensing}, volume = {43}, number = {6}, pages = {2106-2133}, year = {2022}, publisher = {Taylor & Francis}, doi = {10.1080/01431161.2022.2055986}}

@phdthesis{phdthesisKGT, author = {Toker, Kemal}, year = {2023}, month = {02}, pages = {}, url = {}, title = {Spectral-Spatial Nearest Subspace Classifiers for Hyperspectral Images}, school={Hacettepe University}, }

If you would like to use other datasets, you can download them from http://www.ehu.eus/ccwintco/index.php/Hyperspectral_Remote_Sensing_Scenes