Examining the effectiveness of weighted spectral mixture analysis (WSMA) in urban environments

Spectral mixture analysis (SMA) has been widely applied for estimating fractional land-cover types from remote sensing pixels. SMA typically assumes each spectral band has equal contribution to the unmixing results, which has attracted debates on whether a different weight should be given to each band. Subsequently, a number of weighted SMA (WSMA) approaches have been developed and applied to different research fields. The necessity and applicability of WSMA, however, have not been adequately addressed, especially when applied to urban environments. This paper, therefore, aims to answer two research questions, including 1) whether significantly different results would be generated through applying a WSMA, and 2) which WSMA approach performs better in an urban environment. Specifically, five existing schemes: Shannon Entropy-weighted method (Entropy), reflected energy fixed-weighted vector (REFWV), InStability Index-based weighting method (ISIb), combined weighting vector (WV), and within-class variance (VW), and five potential schemes: between-class variance (VB), total-class variance (VT), inversed Optimum Index Factor (IOIF), mean (Mean), and standard deviation (SD), were employed to construct WSMAs. We tested each weighting scheme 100 times with different endmember classes’ spectra. Performance of each WSMA was evaluated using the mean absolute error (MAE). Paired-samples t-test was applied to indicate if there is a significant difference between the mean of MAEs. Results illustrated that only REFWV, ISIb, and WV in All samples (samples included vegetation, high albedo impervious surface area, and low albedo impervious surface area) outperformed the unweighted scheme significantly. Other weighting schemes, such as IOIF, VB, VT, and SD illustrated unstable performance in different study areas. The rest of weighting schemes weakened the performance compared to the unweighted scheme. We concluded that REFWV, ISIb, and WV in All samples can be applied in analysing urban environments with three-endmember (vegetation – high albedo impervious surface area – low albedo impervious surface area) model to improve the performance of SMA. The construction of future weighting schemes would be better to consider the class variance.