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The data is defined by a graph with an affinity, or similarity measure, between graph nodes. The computation–to segment the data–can be performed by linear algebra followed by thresholding. Note that affinities relates to kernels (those that fall off with distance, like radial basis functions) used in machine learning. For some problems it is easier to define affinities between objects directly instead of obtaining them by the more standard method of specifying the objects by features and then calculating the distance between the features.

Spectral clustering is an alternative to probabilistic methods for segmentation. The main difference is that the probabilistic models define data at the nodes of the graph while spectral clustering defines data at the edges between nodes.(There are ways to relate the two approaches which will be discussed later). For image segmentation a typical affinity between pixels i and j is defined by wij= exp {− γ| Ii− Ij|} exp {− τ| xi− xj|} where Ii, Ij are the intensities at pixels i, j and xi, xj are their spatial positions. Hence the affinity is high between neighboring pixels which have similar intensity values (small xi− xj and small| Ii− Ij|) and the affinity is small between pixels which are far apart (large xi− xj|) or which have very different intensity values (large| Ii− Ij|). If this affinity is used, the spectral clustering will segment the data into subregions within which the intensity values changes slowly with position.