## Materials and Methods
### Spectral Feature Selection Algorithms  
#### 2.3.1 Neighborhood Rough Set  
The classical rough set (RS) theory was proposed by Polish mathematician [PERSON] [27]. RS theory understands knowledge as the division of data and classification as the equivalence relation in a specific space, which can describe or reduce uncertain or imprecise knowledge by using feature attributes. In particular, there is no need to provide any other prior information during the process of data analysis. However, when RS theory is used for continuous data processing, it needs to be discretized, which causes the loss of original data feature attributes. Therefore, the concept of neighborhood is introduced into RS theory to form a neighborhood rough set (NRS) model to solve the process of discretization of numeric characteristic variables in the data set [28]. The specific description is as follows:  
Assuming the collected near-infrared spectral dataset of rice is S = Xij (i = 1,2,n; j = 1,2,...,m), n is the number of samples and m is the number of spectral bands. Based on NRS theory, the non-empty real number sample is set as \(\mathrm{U}=\{x_{1},x_{2},\cdots,x_{n}\}\), C is the conditional attribute (spectral information feature), and D is the decision attribute (three states of rice storage). Assuming M is the neighborhood relationship for describing C or a decision attribute table, then \(\mathrm{NDT}=(\mathrm{U},\mathrm{M},\mathrm{D})\) is the neighborhood decision system. Among them, the neighborhood of \(x_{i}(x_{j}\in U)\) can be defined as \(\delta(x_{i})=\left\{x_{i}|x_{i}\in U,\Delta(x_{i},x_{j})\leq\delta,\delta \geq 0\right\}\), where the \(\Delta(\mathrm{x_{i}},\mathrm{x_{j}})\) represents the distance measurement function, which usually can be expressed using the P-norm of \(\Delta_{\mathrm{p}}(\mathrm{x_{1}},\mathrm{x_{2}})=\left(\sum_{i=1}^{\mathrm{ N}}\left|\mathrm{f}(\mathrm{x_{1}},\mathrm{a_{i}})-\mathrm{f}(\mathrm{x_{2}}, \mathrm{a_{i}})\right|^{P}\right)^{\frac{1}{P}}\). In addition, for \(\mathrm{NDT}=<\mathrm{U},\mathrm{M},\mathrm{D}>\), a neighborhood decision system, the set U is divided into N equivalence classes \((X_{1},X_{2},\ldots,X_{N})\) via the decision attribute D and \(\forall\mathbb{Q}\subseteq\mathrm{M}\), the lower approximation \(N_{Q}D\) and upper approximation \((N_{Q}D)\) of D about the Q field are, respectively, expressed as:  
\[\frac{N_{Q}D}{\mathrm{d}N}=\bigcup_{i=1}^{N}N_{Q}X_{i} \tag{1}\]  
Figure 1: Flow chart of spectral data collection of paddy samples. \[N_{Q}D=\bigcup_{i=1}^{N}N_{Q}X_{i} \tag{2}\]  
where \(N_{Q}X_{i}=\{x_{i}|\delta_{Q}(x_{i})\subseteq X,x_{i}\in U\}\), \(\overline{N_{Q}X_{i}}=\{x_{i}|\delta_{Q}(x_{i})\cap X\
eq\Phi,x_{i}\in U\}\). Variable precision is one of the important parameters in neighborhood rough set models, which is usually represented by variable factor \(\beta\). With the introduction of variable factors, the model can be allowed to have a certain degree of classification error rate. That is to say, as many classification samples as possible are classified into the same category under a given relatively small error rate. The data analysis ability of the rough set model is improved by allowing for certain classification errors in upper and lower approximations to analyze classification problems with uncertain relationships in probability. The value range of \(\beta\) is \(0.5<\beta\leq 1\), when \(\beta=1\), equivalent to the classical rough set [29]. Two parameters of \(\beta\) and neighborhood range \(\delta\) directly affect the performance of the neighborhood rough set model and the analysis results of the data. Therefore, \(\beta\) and \(\delta\) parameter matching and selection are important steps in model establishment [30]. In this study, the performance of the model is compared and analyzed under different parameter changes.