Computational Intelligence and Neuroscience / 2008 / Article / Fig 1

Research Article

Theorems on Positive Data: On the Uniqueness of NMF

Figure 1

A three-dimensional space is scaled such that the vectors are in the hyper plane: . By the mapping to the hyper plane, a plane in is mapped to a line and a simplicial cone is mapped to an area. In the figure, it can be observed that the dashed triangle (desired solution) is the only triangle (third-order simplicial cone) that contains the shaded area (positive span of ) while being within the solid border (the dual of ). The NMF can be concluded to be unique by Theorem 1.

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