Multi-view clustering (MVC) aims to integrate complementary information from multiple views to enhance clustering performance. Late Fusion Multi-View Clustering (LFMVC) has shown promise by synthesizing diverse clustering results into a unified consensus. However, current LFMVC methods struggle with noisy and redundant partitions and often fail to capture high-order correlations across views. To address these limitations, we present a novel theoretical framework for analyzing the generalization error bounds of multiple kernel $k$-means, leveraging local Rademacher complexity and principal eigenvalue proportions. Our analysis establishes a convergence rate of $\mathcal{O}(1/n)$, significantly improving upon the existing rate in the order of $\mathcal{O}(\sqrt{k/n})$. Building on this insight, we propose a low-pass graph filtering strategy within a multiple linear $k$-means framework to mitigate noise and redundancy, further refining the principal eigenvalue proportion and enhancing clustering accuracy. Experimental results on benchmark datasets confirm that our approach outperforms state-of-the-art methods in clustering performance and robustness. The related codes is available at https://github.com/csliangdu/GMLKM .

Earth observation data have shown promise in predicting species richness of vascular plants ($\alpha$-diversity), but extending this approach to large spatial scales is challenging because geographically distant regions may exhibit different compositions of plant species ($\beta$-diversity), resulting in a location-dependent relationship between richness and spectral measurements. In order to handle such geolocation dependency, we propose Spatioformer, where a novel geolocation encoder is coupled with the transformer model to encode geolocation context into remote sensing imagery. The Spatioformer model compares favourably to state-of-the-art models in richness predictions on a large-scale ground-truth richness dataset (HAVPlot) that consists of 68,170 in-situ richness samples covering diverse landscapes across Australia. The results demonstrate that geolocational information is advantageous in predicting species richness from satellite observations over large spatial scales. With Spatioformer, plant species richness maps over Australia are compiled from Landsat archive for the years from 2015 to 2023. The richness maps produced in this study reveal the spatiotemporal dynamics of plant species richness in Australia, providing supporting evidence to inform effective planning and policy development for plant diversity conservation. Regions of high richness prediction uncertainties are identified, highlighting the need for future in-situ surveys to be conducted in these areas to enhance the prediction accuracy.

The diversity of terrestrial vascular plants plays a key role in maintaining the stability and productivity of ecosystems. Monitoring species compositional diversity across large spatial scales is challenging and time consuming. The advanced spectral and spatial specification of the recently launched DESIS (the DLR Earth Sensing Imaging Spectrometer) instrument provides a unique opportunity to test the potential for monitoring plant species diversity with spaceborne hyperspectral data. This study provides a quantitative assessment on the ability of DESIS hyperspectral data for predicting plant species richness in two different habitat types in southeast Australia. Spectral features were first extracted from the DESIS spectra, then regressed against on-ground estimates of plant species richness, with a two-fold cross validation scheme to assess the predictive performance. We tested and compared the effectiveness of Principal Component Analysis (PCA), Canonical Correlation Analysis (CCA), and Partial Least Squares analysis (PLS) for feature extraction, and Kernel Ridge Regression (KRR), Gaussian Process Regression (GPR), Random Forest Regression (RFR) for species richness prediction. The best prediction results were r=0.76 and RMSE=5.89 for the Southern Tablelands region, and r=0.68 and RMSE=5.95 for the Snowy Mountains region. Relative importance analysis for the DESIS spectral bands showed that the red-edge, red, and blue spectral regions were more important for predicting plant species richness than the green bands and the near-infrared bands beyond red-edge. We also found that the DESIS hyperspectral data performed better than Sentinel-2 multispectral data in the prediction of plant species richness. Our results provide a quantitative reference for future studies exploring the potential of spaceborne hyperspectral data for plant biodiversity mapping.