2.2.2. Feature Space Construction and Endmember Selection

The key for the unmixing is the selection of appropriate endmembers. The accuracy of unmixing was directly affected by the quality and quantity of the selected endmembers. A triangle is the simplest simplex when the convex geometry is introduced for the unmixing [47]. Convex cone analysis takes the boundary points of the convex cone constructed from the observed spectra as the endmembers [48].

Two PCA components were employed to implement a projection from image space to feature space and visually examine the distribution of the candidate endmembers in the feature space. The combinations were from any two of the first three components. Candidate endmember land-cover classes were sourced from the major land-cover types of the study area and include natural vegetation, water bodies, double-cropping, singlecropping and built-up areas. Since the purpose of the study was to map cropping intensity, the cropland was subdivided into single-cropping and double-cropping, while other landcover types were used in broad categories.

Through observing these combinations, four candidate endmembers were obtained: double-cropping, single-cropping, natural vegetations and water bodies (Figure 6).

**Figure 6.** The feature space and the distributions of major land-cover types with different PCA component combinations, in which the gray dots are all pixels of the images. (**a**) PCA 1, PCA 2 combination, (**b**) PCA 1, PCA 3 combination, (**c**) PCA 2, PCA 3 combination.

Through visually examining the scatter points based on the N-dimensional visualization tool in ENVI, we found that the PCA 1 and PCA 3 combination and PCA 2 and PCA 3 combination should be excluded, and the PCA 1 and PCA 2 combination would be the best choice (Figure 6). The mixture of single-cropping and natural vegetation could explain the exclusion of the PCA 1 and PCA 3 combination. As for the exclusion of the PCA 2 and PCA 3 combination, the single-cropping could not be used as an endmember because its cropping intensity was about half that of double-cropping theoretically and could only be inside the boundary of the feature space. With the PCA 1 and PCA 2 combination, all pixels clustered closest to a triangle in the feature space, with three vertexes representing doublecropping, natural vegetation and water bodies, which could be the candidate endmembers (Figure 7).

**Figure 7.** The triangular feature space, in which the black dots are all pixels of the images, and the colored dots are candidate endmember land-cover types. The EVI profiles of relevant land-cover types are also presented.

We also found that single-cropping was located in the transition zone from doublecropping to the center of the feature space, and built-up areas were located in the transition zone from water bodies to the center of the feature space. Double-cropping occupied one of the corners and had the highest cropping intensity; natural vegetation and water bodies were located in the other two corners and had zero cropping intensity; single-cropping was on the transition zone from double-cropping to the center of the feature space and had decreased cropping intensity. From these analyses, the unmixing based on this triangle feature space met the requirements of our research. Therefore, three endmembers were selected finally: double-cropping, natural vegetation and water bodies.

To guarantee the purity of endmembers, the Sentinel-2 images and historical images on the Google Earth platform were used to identify large fields to assist the manual endmember collection. High accuracy can be obtained by manually selecting endmember pixels through the visual interpretation method [49]. The pure pixels corresponding to the endmembers were widely distributed across the study area, and the amount reached about 0.5% of the total pixels.
