How to determine the number of factor in positive matrix factorization (PMF) ?
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Positive matrix factorization (PMF) is a method used to determine the number of factors in environmental data. Traditional methods for factorization have become impractical due to increasing computational costs. To address this, a new weighting method has been developed to decrease computational costs for traditional algorithms. The Randomized Hierarchical Alternating Least Squares (RHALS) algorithm, combined with this weighting method, has been shown to reproduce interpretable factors in a large environmental dataset. This algorithm provides a significant computational speedup compared to other algorithms such as Multiplicative Update (MU), deterministic Hierarchical Alternating Least Squares (HALS), and non-negative Alternating Least Squares (ALS) algorithms. Additionally, rotational ambiguity in the solution can be addressed using a "pulling" method to rotate a set of factors, which can lead to alternative solutions and potentially lower the weighted residual error of the algorithm .
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13 Citations | The number of factors in positive matrix factorization (PMF) can be determined by assessing the reliability of the results obtained with different factor solutions. |
1 Citations | The number of factors in positive matrix factorization (PMF) is determined through analysis of the data using statistical methods such as cross-validation or information criteria. |
19 Nov 2022 | The paper does not provide information on how to determine the number of factors in positive matrix factorization (PMF). |
1 Citations | The paper discusses that a completely positive matrix may have many, even infinitely many, factorizations. |
20 Dec 2022 | The paper does not provide information on how to determine the number of factors in positive matrix factorization (PMF). |
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