nents (leftand one component (rightfor nmf with two componentsas shown on the leftit is clear that all points in the data can be written as positive combination of the two components if there are enough components to perfectly reconstruct the data (as many components as there are features)the algorithm will choose directions that point toward the extremes of the data if we only use single componentnmf creates component that points toward the meanas pointing there best explains the data you can see that in contrast with pcareducing the number of components not only removes some directionsbut creates an entirely different set of componentscomponents in nmf are also not ordered in any specific wayso there is no "first non-negative component"all components play an equal part nmf uses random initializationwhich might lead to different results depending on the random seed in relatively simple cases such as the synthetic data with two componentswhere all the data can be explained perfectlythe randomness has little effect (though it might change the order or scale of the componentsin more complex situationsthere might be more drastic changes applying nmf to face images nowlet' apply nmf to the labeled faces in the wild dataset we used earlier the main parameter of nmf is how many components we want to extract usually this is lower than the number of input features (otherwisethe data could be explained by making each pixel separate componentfirstlet' inspect how the number of components impacts how well the data can be reconstructed using nmf (figure - )dimensionality reductionfeature extractionand manifold learning