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In this paper, we propose a simple unsupervised framework to effectively select and combine spectral information and spatial features for Support Vector Machine (SVM)-based classification when spatial features are the widely used morphological profiles (MPs). To overcome the difficulty of high dimensionality of resulting features, it is a common practice that MPs are extracted from principal components (PCs). In this paper, we investigate another technique on spectral feature selection, which is unsupervised band selection (BS). We find out that using selected bands as spectral features can improve classification performance because they contain more critical characteristics for classification; in particular, using the selected bands, combined with the MPs extracted from PCs, can yield the highest accuracy, due to the fact that major PCs contain less noise for extracting more reliable MPs. The overall unsupervised nature of feature selection provides the flexibility of implementation. We believe that such finding is instructive to feature selection and extraction for spectral/spatial-based hyperspectral image classification.