Principal components analysis (PCA) is a technique applied to multispectral and hyperspectral remotely sensed data. PCA transforms an original correlated dataset into a substantially smaller set of uncorrelated variables that represents most of the information present in the original dataset. It reduces data dimensionality (e.g., number of bands). Instead of throwing away the redundant data, principal components analysis condenses the information in intercorrelated variables into a few variables, called principal components (Figure 1).
The first principal component (PC) accounts for maximum proportion of variance from the original dataset. All subsequent orthogonal components account for the maximum proportion of the remaining variance. Usually, PC 1, PC 2, and PC 3 account for the vast majority of the variance found within the dataset. If, for example, components 1, 2, and 3 account for the majority of the variance found within the dataset, it can be possible to set the original bands aside, and the remainder of the image enhancement or classification process can be performed using just these three PC images. This approach reduces data size and removes redundancy from the analysis. Additionally, researchers can utilize PCs along with original bands to produce the desired combination for analysis (Figure 2).
The purpose of PCA is to translate and/or rotate original axes so that original BVs on axes X1 and X2 are redistributed (reprojected) onto new axes (Figure 1).
Figure 1. PCA transformation process.
Transformation of original data on X1 and X2 axes onto PC1 and PC2 axes requires transformation coefficients that can be applied in linear fashion to original pixel values. These new axes are called first PC. The second PC is perpendicular (orthogonal) to PC1. The third, fourth, fifth, and so on, components contains decreasing amounts of the variance found in the dataset.
By computing the correlation between each band and each PC, it is possible to determine how each band “loads” or is associated with each PC.
A linear combination of original BV and factor scores (eigenvectors) produces the new BV for each pixel of every principal component.
To produce PC images; first, the original brightness values (BVs) for each pixel are identified. Second, a transformation is applied to reproject data onto the first PC’s axis. Lastly, this procedure is applied to all PCs (Figure 1).
In addition to PC images, the PCA also produces the following outputs: eigenvalues, and eigenvectors (factor loading). Eigenvalues contain information about percent of total variance explained by each PC (Table 1). Factor loadings: indicate degree of correlation, Rkp, between each band k and each principal component p (Table 2).
Table 1. Example of eigenvalues for Landsat TM imagery. Source: Jensen 2005. Buenemann 2011.
Table 2. Example of factor loading for Landsat TM imagery. Source: Jensen 2005. Buenemann 2011.
Figure 2 shows how most of the variance of the dataset is found on the first components. The top three images provide most of the information contained within the dataset.
Figure 2. Seven PCA images in combination with original bands derived from Landsat TM imagery. From top left: PC 1 and bands 4, 5, 7. PC 2 and bands 1, 2, 3. PC 3 and band 4. PC 4 and bands 6. PC 5, 6, 7, without additional bands. Source: Jensen 2005. Buenemann 2011.
PCA analysis can be calculated in various remote sensing software packages such as Erdas Imagine and ENVI.
Ammanollahi et al. 2011. Studied the effects of diverse soil properties on range evening.
Lhermitte et al. 2011. Used PCA among other techniques to provide an overview and quantitative comparison of the similarity measures in function of varying time series and ecosystem characteristics, such as amplitude, timing and noise effects.
Muñoz-Robles et al. 2012. Investigated the use of PCA to increase the spatial detail of multispectral Quickbird data.
Amanollahi J, Abdullah AM, and Tilaki GAD. 2011. Relationship between plants evening and soil properties in the rangeland, Lar National Park, Iran. In African Journal of Agricultural Research. 6(24): 5551-5557.
Lhermitte S, Verbesselt J, Verstraaten WW, and Coppin P. 2011. A comparison of time series similarity measures for classification and change detection of ecosystems dynamics. In Remote Sensing of the Environment. 115(12): 3129-3152.
Muñoz-Robles C, Frazier P, Tighe M, Reid N, Briggs SV, and Wilson B. 2012. Assessing Ground Cover at Patch and Hillslope Scale in Semi-arid Woody Vegetation and Pasture Using Fused Quickbird Data. In International Journal of Applied Earth Observation and Geoinformation. 14(1): 94-102.
Buenemann, M. 2011. Image Derivatives III (lecture slides). Advanced Remote Sensing. Geography Department - New Mexico State University.
Jensen, J. R. 2005. Introductory digital image processing: a remote sensing perspective. Upper Saddle River, N.J: Prentice Hall.
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