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To form the geometric distance, each element of the matrix is calculated as the Euclidean distance ∥ X ( i) − X ( j)∥ 2. A distance function is defined by matrices with a size of N × N, where N is the number of input points (nodes of the graph). They selected 10 × 10 × 10 pixel cubes as graph nodes of the first diffusion map and very thin horizontal cubic boxes (15 × 1 pixels) were used as graph nodes of the second diffusion map. They aggregated a group of pixels/voxels together to form a node. diffusion maps were used to construct input data points. The sixth step is recovering the input data points (nodes) corresponding to each of the clustered diffusion coordinates and replacing the graph partitioning with an image segmentation task. The fifth step is applying the K-means’ clustering on diffusion coordinates and iterating the algorithm many times to select the clustering result for distortion minimization with coarse graining. The right eigenvectors are rescaled with eigenvalues to calculate the diffusion coordinates. The normalization can be simply achieved with dividing the eigenvectors to their first value. The fourth step is calculating the eigenfunctions of the symmetric matrix and obtain the normalized right and left eigenvectors of the Markov matrix. The third step is construction of the kernel (weights of the graph). To form the geometric distance, each element of the matrix is calculated as the Euclidean distance. The second step is construction of distance functions (geometric and feature distances). For instance, in the case of clustering a point distribution, x and y coordinates of points represent the 2-dimensional input data however, in gray-level images, the intensity of points should be separately considered as the third dimension. The first step in diffusion maps is the construction of input data points (nodes of the graph) with the desired dimension. Mohamed Yacin Sikkandar, in Soft Computing Based Medical Image Analysis, 2018 9 Segmentation Based on Diffusion Mapsĭiffusion map process is a dimensionality reduction or feature extraction algorithm.