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\subsection{The Denominator – A Generalized Approach to Normalize Spatial Statistics}  To cast the correlations as a probability, the cumulative sum of probabilities in the numerator must be normalized. EQUATION $S^{ii'}_{t}$  is the number of samples taken by a vector indexed by t for local states in the numerator h and h' derived from signals i and i', respectively. The simplest set of statistics to normalizenormalization criteria is a dataset where each piece of material information is assumed to be completeoccurs when complete material information is provided, or a weight, w_s^i=1, such that ∀s,i. $\forall s,i $.  Traditionally, this normalization (for complete non-periodic information) is computed using the following relationship EQUATION \begin{equation}  S_{t} = \prod_{j=1}^{d} (S_{j} - t_{j})  \end{equation}  where S_i and t_i are the size of the sample volume and length of the vector in the ijth dimension, respectively. This relationship is only useful for complete cuboidal microstructure functionsmaterial information. This relationship provides a count of vectors of length t that are sampled when computing non-periodic statistics. For incomplete and partial datasets, a more generalized approach is necessary for the normalization.   In this paper, we restrict the normalization to partial datasets; a more complete definition for uncertain datasets will be presented in future work. Partial datasets are defined by a dataset with weights, EQUATION; a complete dataset is a partial dataset. The normalization for each vector is expressed as the convolution  EQUATION