distribution has its own mean and variance. For the data which can be negative as well as positive, the null distribution for cosine similarity is the distribution of the dot product of two independent random unit vectors. This distribution has a mean of zero and a variance of 1/n. While Euclidean distance will be invariant to this correction. Clustering Documents The implementation of hierarchical clustering with distance-based metrics to organize and group similar documents together will require the need and utilization of a distance matrix. The distance matrix will represent the degree of association that a document has with another document that will be used to create clusters of closely associated documents that will be utilized in retrieval methods of relevant documents for a user's query. ISOMAP Isomap incorporates distance matrices to utilize geodesic distances to able to compute lower-dimensional embeddings. This helps address a collection of documents that reside within a massive number of dimensions and be able perform document clustering. Neighborhood Retrieval Visualizer (NeRV) An algorithm used for both unsupervised and supervised visualization that uses distance matrices to find similar data based on the similarities shown on a display/screen. The distance matrix needed for Unsupervised NeRV can be computed through fixed input pairwise distances. The distance matrix needed for Supervised NeRV requires formulating a supervised distance metric to be able to compute the distance of the input in a supervised manner. Chemistry The distance matrix is a mathematical object widely used in both graphical-theoretical (topological) and geometric (topographic) versions of chemistry. The distance matrix is used in chemistry in both explicit and implicit forms. Interconversion mechanisms between two permutational isomers Distance matrices were used as the main approach to depict and reveal the shortest path sequence needed to determine the rearrangement between the two permutational isomers. Distance Polynomials and Distance Spectra Explicit use of Distance matrices is required in order to construct the distance polynomials and distance spectra of molecular structures. Structure-property model Implicit use of Distance matrices was applied through the use of the distance based metric Weiner number/Weiner Index which was formulated to represent the distances in all chemical structures. The Weiner number is equal to half-sum of the elements of the distance matrix. Graph-theoretical Distance matrix Distance matrix in chemistry that are used for the 2-D realization of molecular graphs, which are used to illustrate the main foundational features of a molecule in a myriad