## 1 Introduction  
Identifying suspected targets from remotely sensed data is paramount in everyday life and research. Researchers have extensively investigated numerous clustering algorithms, including cutting-edge technologies, for remotely sensed images, such as Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and Thermal Mapping (TM) data. However, several limitations exist in these algorithms. One widely used clustering algorithm is K-means clustering, which, unfortunately, cannot automatically determine the number of classes [1, 2]. Moreover, it exhibits slow convergence due to its reliance on minimal spatial distance [3, 4].  
The approaches ISODATA [5, 6] and ISMC [7, 8] can determine the class number through self-iteration. Nevertheless, the challenge lies in determining their parameters, particularly in adjusting distance parameters with changing dimensions. On the other hand, orthogonal projection classification suffers from projection fluctuation issues under the restriction of the number of bands [9, 10]. [PERSON] introduced a feature extraction method that computes vectorized pixel values from a localized window, enhancing Bag-of-Words (BoW) performance. However, this approach may lead to a reduction in classification accuracy [11, 12]. [PERSON] et al. proposed a graph-based structural deep spectral-spatial clustering network to sufficiently explore the structure information among pixels. They designed a self-expression-embedded multi-graph auto-encoder to explore high-order structure associations among pixels, thereby capturing robust spectral-spatial features and global clustering structure [13].  
Furthermore, [PERSON] et al. developed a hybrid 3D residual spatial-spectral convolution network to extract deep spatio-spectral features using 3D CNN and ResNet architecture [14]. [PERSON] combined wavelet theory and neuro-fuzzy techniques for segmentation purposes [15; 16]. However, their feature extraction approach solely considers the absolute values of wavelet coefficients, neglecting the specific spectral patterns, and the computational requirements take time and effort.  
A wavelet-feature correlation ratio Markov clustering algorithm (WFCRMCA) is proposed to differentiate the pixels according to the spectrum similarity among pixels. Of course, the spectrums of one object under different conditions are different. Still, they have the same features (up, down, protruding, concave, see Figure 1) at the same spectral positions, which are the main parameters used to evaluate the difference among remotely sensed pixels [17; 18]. Therefore, these characteristic positions can denote class features. Fortunately, band-pass wavelet filters can decompose data at different scales to detect these characteristics.  
WFCRMCA can statistically control clustering accuracy by adjusting parameters such as \(T_{\text{start}}\), \(T_{\text{end}}\), and \(T_{\text{step}}\). A new concept, correlation ratio (CR), is proposed to reflect the similarity between two wavelet-transformed samples. With an accurate description of the abrupt spectral features, wavelet correlation ratios can differentiate pixels along spectral dimensions. Expanding spectral bands of multi-spectral images increases the number of characteristic points to enrich the features of classes. WFCRMCA forms the clustering space and initial class centers with evenly sampled pixels. Without the initial parameter problem of the K-means algorithm, WFCRMCA can quickly reach the best class centers at each clustering temperature and obtain optimal class centers on the whole scope at high speed by gradually decreasing the clustering scale and temperature. Several theorems are provided and proved to strengthen the WFCRMCA in the Section 2. In the Section 3, WFCRMCA receives favorable results for clustering Landsat TM images and AVIRIS hyperspectral images.