This paper introduces a novel approach to Non-negative Matrix Factorization (NMF) by incorporating sparseness constraints. NMF is a technique used to find parts-based, linear representations of non-negative data, but it often does not produce the desired parts-based decompositions. The authors propose a method to explicitly control the sparseness of the factors, which improves the quality of the decompositions. They define a sparseness measure based on the relationship between the $L_1$ and $L_2$ norms and present a projected gradient descent algorithm to enforce this measure. The paper includes experimental results demonstrating that their method can produce more interpretable and parts-based representations, especially in cases where standard NMF fails. Additionally, the authors provide a complete MATLAB package for implementing NMF and its extensions, which they hope will facilitate further research and application in data analysis. The paper also discusses the relationship between their method and other recent extensions of NMF, highlighting the advantages of their approach in terms of explicit control over sparseness and the ability to learn oriented features from natural image data.This paper introduces a novel approach to Non-negative Matrix Factorization (NMF) by incorporating sparseness constraints. NMF is a technique used to find parts-based, linear representations of non-negative data, but it often does not produce the desired parts-based decompositions. The authors propose a method to explicitly control the sparseness of the factors, which improves the quality of the decompositions. They define a sparseness measure based on the relationship between the $L_1$ and $L_2$ norms and present a projected gradient descent algorithm to enforce this measure. The paper includes experimental results demonstrating that their method can produce more interpretable and parts-based representations, especially in cases where standard NMF fails. Additionally, the authors provide a complete MATLAB package for implementing NMF and its extensions, which they hope will facilitate further research and application in data analysis. The paper also discusses the relationship between their method and other recent extensions of NMF, highlighting the advantages of their approach in terms of explicit control over sparseness and the ability to learn oriented features from natural image data.