Wildfires increasingly threaten ecosystems and infrastructure, making accurate burn severity mapping (BSM) essential for effective disaster response and environmental management. Machine learning (ML) models utilizing satellite-derived vegetation indices are crucial for assessing wildfire damage; however, incorporating many indices can lead to multicollinearity, reducing classification accuracy. While principal component analysis (PCA) is commonly used to address this issue, its effectiveness relative to other feature extraction (FE) methods in BSM remains underexplored. This study aims to enhance ML classifier accuracy in BSM by evaluating various FE techniques that mitigate multicollinearity among vegetation indices. Using composite burn index (CBI) data from the 2014 Carlton Complex fire in the United States as a case study, we extracted 118 vegetation indices from seven Landsat-8 spectral bands. We applied and compared 13 different FE techniques—including linear and nonlinear methods such as PCA, t-distributed stochastic neighbor embedding (t-SNE), linear discriminant analysis (LDA), Isomap, uniform manifold approximation and projection (UMAP), factor analysis (FA), independent component analysis (ICA), multidimensional scaling (MDS), truncated singular value decomposition (TSVD), non-negative matrix factorization (NMF), locally linear embedding (LLE), spectral embedding (SE), and neighborhood components analysis (NCA). The performance of these techniques was benchmarked against six ML classifiers to determine their effectiveness in improving BSM accuracy. Our results show that alternative FE techniques can outperform PCA, improving classification accuracy and computational efficiency. Techniques like LDA and NCA effectively capture nonlinear relationships critical for accurate BSM. The study contributes to the existing literature by providing a comprehensive comparison of FE methods, highlighting the potential benefits of underutilized techniques in BSM.