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implementation of the alternating least squares algorithm for nmf  (MathWorks Inc)


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    MathWorks Inc implementation of the alternating least squares algorithm for nmf
    Non-negative Matrix Factorization of a typical record from a P1 animal. A Grayscale reference image followed by the 13 features required to capture 90% of the variance of the original data, displayed in descending order of relative prominence in sleep vs wake. Note the smaller total number of features required capture the same fraction of variance of the data compared to P6-P8 and the more even weighting of those features between sleep (8) and wake (5), reflecting the more evenly distributed complexity of activity between the two states at P1. Scale bar represents 1mm. B: Time vectors and records as in Fig. 5. C: Relationship between number of features <t>(NMF</t> Rank) and fraction of variance captures for P6-P8 vs P1 animals. On average, fewer features are required to capture equal variances at P1. D-F: Bivariate distributions of Feature Area vs. Sleep Score at P6-P8 (D) and P1 (E), and the Sleep-Wake difference plot (F). Development during the first postnatal week is characterized by added features with wider spread (20–40% area coverage) in sleep (Sleep Score 0.5–1.2). P-values determined using permutation test.
    Implementation Of The Alternating Least Squares Algorithm For Nmf, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/nmf+algorithm/pmc10166374-541-25-16
    Average 90 stars, based on 1 article reviews
    implementation of the alternating least squares algorithm for nmf - by Bioz Stars, 2026-11
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    1) Product Images from "Large-scale waves of activity in the neonatal mouse brain in vivo occur almost exclusively during sleep cycles"

    Article Title: Large-scale waves of activity in the neonatal mouse brain in vivo occur almost exclusively during sleep cycles

    Journal: Developmental neurobiology

    doi: 10.1002/dneu.22901

    Non-negative Matrix Factorization of a typical record from a P1 animal. A Grayscale reference image followed by the 13 features required to capture 90% of the variance of the original data, displayed in descending order of relative prominence in sleep vs wake. Note the smaller total number of features required capture the same fraction of variance of the data compared to P6-P8 and the more even weighting of those features between sleep (8) and wake (5), reflecting the more evenly distributed complexity of activity between the two states at P1. Scale bar represents 1mm. B: Time vectors and records as in Fig. 5. C: Relationship between number of features (NMF Rank) and fraction of variance captures for P6-P8 vs P1 animals. On average, fewer features are required to capture equal variances at P1. D-F: Bivariate distributions of Feature Area vs. Sleep Score at P6-P8 (D) and P1 (E), and the Sleep-Wake difference plot (F). Development during the first postnatal week is characterized by added features with wider spread (20–40% area coverage) in sleep (Sleep Score 0.5–1.2). P-values determined using permutation test.
    Figure Legend Snippet: Non-negative Matrix Factorization of a typical record from a P1 animal. A Grayscale reference image followed by the 13 features required to capture 90% of the variance of the original data, displayed in descending order of relative prominence in sleep vs wake. Note the smaller total number of features required capture the same fraction of variance of the data compared to P6-P8 and the more even weighting of those features between sleep (8) and wake (5), reflecting the more evenly distributed complexity of activity between the two states at P1. Scale bar represents 1mm. B: Time vectors and records as in Fig. 5. C: Relationship between number of features (NMF Rank) and fraction of variance captures for P6-P8 vs P1 animals. On average, fewer features are required to capture equal variances at P1. D-F: Bivariate distributions of Feature Area vs. Sleep Score at P6-P8 (D) and P1 (E), and the Sleep-Wake difference plot (F). Development during the first postnatal week is characterized by added features with wider spread (20–40% area coverage) in sleep (Sleep Score 0.5–1.2). P-values determined using permutation test.

    Techniques Used: Activity Assay

    Related Articles

    Activity Assay:

    Article Title: De novo compartment deconvolution and weight estimation of tumor samples using DECODER
    Article Snippet: The built-in NMF in MATLAB has a few parameters to choose from.

    Article Title: Space-independent community and hub structure of functional brain networks
    Article Snippet: The MATLAB implementation of NMF uses the non-deterministic alternating least squares algorithm to determine W and H . Consequently, we repeated the algorithm 100 times with different initial conditions as we varied the rank from k = 2 to k = 20.

    Article Title: A single-cell landscape of high-grade serous ovarian cancer.
    Article Snippet: For this purpose, we used NMF (as implemented by the MATLAB nnmf function, with the number of factors set to ten) to identify variable expression programs.

    Article Title: Single-cell RNA-seq reveals that glioblastoma recapitulates a normal neurodevelopmental hierarchy
    Article Snippet: In brief, non-negative matrix factorization was run ( nmf , Matlab, multiplicity algorithm, replicates = 20, maximum iterations = 1e6) 100 times for k from 2 to 15 signatures.

    Article Title: Assessing Methods for Evaluating the Number of Components in Non-Negative Matrix Factorization
    Article Snippet: The Kullback-Liebler criterion [ ], [ ] is: (5) K L ( X | W H = ∑ i j [ X i j l o g X i j W H i j − X i j + W H i j ] Brunet’s MATLAB implementation of NMF minimizes this criterion [ ]).



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    Non-negative Matrix Factorization of a typical record from a P1 animal. A Grayscale reference image followed by the 13 features required to capture 90% of the variance of the original data, displayed in descending order of relative prominence in sleep vs wake. Note the smaller total number of features required capture the same fraction of variance of the data compared to P6-P8 and the more even weighting of those features between sleep (8) and wake (5), reflecting the more evenly distributed complexity of activity between the two states at P1. Scale bar represents 1mm. B: Time vectors and records as in Fig. 5. C: Relationship between number of features <t>(NMF</t> Rank) and fraction of variance captures for P6-P8 vs P1 animals. On average, fewer features are required to capture equal variances at P1. D-F: Bivariate distributions of Feature Area vs. Sleep Score at P6-P8 (D) and P1 (E), and the Sleep-Wake difference plot (F). Development during the first postnatal week is characterized by added features with wider spread (20–40% area coverage) in sleep (Sleep Score 0.5–1.2). P-values determined using permutation test.
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    Image Search Results


    Non-negative Matrix Factorization of a typical record from a P1 animal. A Grayscale reference image followed by the 13 features required to capture 90% of the variance of the original data, displayed in descending order of relative prominence in sleep vs wake. Note the smaller total number of features required capture the same fraction of variance of the data compared to P6-P8 and the more even weighting of those features between sleep (8) and wake (5), reflecting the more evenly distributed complexity of activity between the two states at P1. Scale bar represents 1mm. B: Time vectors and records as in Fig. 5. C: Relationship between number of features (NMF Rank) and fraction of variance captures for P6-P8 vs P1 animals. On average, fewer features are required to capture equal variances at P1. D-F: Bivariate distributions of Feature Area vs. Sleep Score at P6-P8 (D) and P1 (E), and the Sleep-Wake difference plot (F). Development during the first postnatal week is characterized by added features with wider spread (20–40% area coverage) in sleep (Sleep Score 0.5–1.2). P-values determined using permutation test.

    Journal: Developmental neurobiology

    Article Title: Large-scale waves of activity in the neonatal mouse brain in vivo occur almost exclusively during sleep cycles

    doi: 10.1002/dneu.22901

    Figure Lengend Snippet: Non-negative Matrix Factorization of a typical record from a P1 animal. A Grayscale reference image followed by the 13 features required to capture 90% of the variance of the original data, displayed in descending order of relative prominence in sleep vs wake. Note the smaller total number of features required capture the same fraction of variance of the data compared to P6-P8 and the more even weighting of those features between sleep (8) and wake (5), reflecting the more evenly distributed complexity of activity between the two states at P1. Scale bar represents 1mm. B: Time vectors and records as in Fig. 5. C: Relationship between number of features (NMF Rank) and fraction of variance captures for P6-P8 vs P1 animals. On average, fewer features are required to capture equal variances at P1. D-F: Bivariate distributions of Feature Area vs. Sleep Score at P6-P8 (D) and P1 (E), and the Sleep-Wake difference plot (F). Development during the first postnatal week is characterized by added features with wider spread (20–40% area coverage) in sleep (Sleep Score 0.5–1.2). P-values determined using permutation test.

    Article Snippet: The resulting matrix was factored into a series of paired spatial and temporal components, using the MatLab implementation of the alternating least squares algorithm for NMF.

    Techniques: Activity Assay