## 4 Discussion  
For remotely sensed data with a high density of mixed pixels, choosing partial minutia wavelet features in high-level scales could reduce the clustering difficulty caused by a significant amount of minutia, and this also somewhat applies blur to achieve ideal clustering results. Multi-scale classification from fine to coarse could be realized by this method. Furthermore, as the matching speed of abrupt point positions is very high, clustering time increases a little with the increment of referenced minutia. For example, multi-spectral data typically set \(S_{calc}=S_{calc2}\); hyper-spectral data could set \(S_{calc2}=S_{calc}-2\). WFCRMCA applies 1D wavelet transformation on satellite spectral data. Wavelet transform can represent a signal in both time and frequency domains simultaneously. It decomposes a signal into a set of wavelets that are localized in both time and frequency, allowing me to analyze the signal's time-localized features. Wavelet transform excels at capturing localized features and adaptability to non-stationary signals. However, the Fourier transform represents a signal in the frequency domain. It decomposes a signal into a sum of sinusoidal components of different frequencies, providing information about the signal's frequency content. It does not capture information about when these frequencies occur. Fourier transform is excellent for spectral analysis. Ridgelet and curvelet transformation are well-known methods for high-dimensional image analysis, but wavelet transformation is better for 1D spectral feature extraction. In the ridgelet transform, ridgelets are adapted to higher-dimensional singularities, or singularities on curves in dimension two, singularities on surfaces in dimension three, \begin{table}
\begin{tabular}{c c c c} \hline \(\mathbf{T_{\text{end}}}\) & \(\mathbf{S_{\text{cale2}}}\) & **Class Number** & **Time/s** \\ \hline
0.4 & 2 & 8 & 13 \\
0.4 & 3 & 17 & 21 \\
0.4 & 4 & 38 & 51 \\
0.6 & 4 & 85 & 52 \\ \hline \end{tabular}
\end{table} 
Table 4: Sook lake AVIRIS hyper-spectral image WFCRMCA clustering parameters \(T_{\text{end}}\) and \(S_{\text{calc2}}\) comparison (5\(\times\)5 sampling, band number is 190, \(S_{\text{cale}}\) = 5, \(T_{\text{peak}}\) = 5, \(T_{\text{start}}\) = 0.9, \(T_{\text{step}}\) = 0.05). Figure 7: Sook Lake AVIRIS image WFCRMCA clustering result. (**a-f**) are the seven significant signals. and singularities on (n \(-\) 1) dimensional hypersurfaces in dimension n [28]. The curvelet transform uses ridgelet transform as a component step, and it is good at 2D image reconstruction [29]. The proposed WFCRMCA uses wavelet transform to analyze the 1D spectral data instead of 2D images. WFCRMCA accelerates clustering speed during the clustering process. The calculation of CR only needs simply matching corresponding characteristic points without the time-consuming floating-point measure of Euclidean distance [1,2]. A great many sampled pixels with high similarity are clustered together during the clustering process, depressing the number of class centers attending clustering comparison; moreover, clustering centers of newly created classes are re-determined according to common features. So, along with the process of this algorithm, the clustering speed continues to increase. This WFCRMCA only makes statistics of the number of each wavelet feature on every info-position as the class feature and chooses the best pixel as the clustering center but does not directly use the CR matrix to investigate the dependency degree between sampled pixels, resolving spatial complexity problems. Gradually depressing clustering size could let both small and large signals embody efficiently, and too many noise signals are merged so that the WFCRMCA could detect the spatial position of noise signals. The WFCRMCA approach can be applied to any spectral data to differentiate targets. It has demonstrated favorable performance for satellite multi-spectral images and super-spectral images.