TY - JOUR
T1 - Applications of a novel clustering approach using non-negative matrix factorization to environmental research in public health
AU - Fogel, Paul
AU - Gaston-Mathé, Yann
AU - Hawkins, Douglas
AU - Fogel, Fajwel
AU - Luta, George
AU - Young, S. Stanley
N1 - Publisher Copyright:
© 2016 by the authors; licensee MDPI, Basel, Switzerland.
PY - 2016/5/18
Y1 - 2016/5/18
N2 - Often data can be represented as a matrix, e.g., observations as rows and variables as columns, or as a doubly classified contingency table. Researchers may be interested in clustering the observations, the variables, or both. If the data is non-negative, then Non-negative Matrix Factorization (NMF) can be used to perform the clustering. By its nature, NMF-based clustering is focused on the large values. If the data is normalized by subtracting the row/column means, it becomes of mixed signs and the original NMF cannot be used. Our idea is to split and then concatenate the positive and negative parts of the matrix, after taking the absolute value of the negative elements. NMF applied to the concatenated data, which we call PosNegNMF, offers the advantages of the original NMF approach, while giving equal weight to large and small values. We use two public health datasets to illustrate the new method and compare it with alternative clustering methods, such as K-means and clustering methods based on the Singular Value Decomposition (SVD) or Principal Component Analysis (PCA).With the exception of situations where a reasonably accurate factorization can be achieved using the first SVD component, we recommend that the epidemiologists and environmental scientists use the new method to obtain clusters with improved quality and interpretability.
AB - Often data can be represented as a matrix, e.g., observations as rows and variables as columns, or as a doubly classified contingency table. Researchers may be interested in clustering the observations, the variables, or both. If the data is non-negative, then Non-negative Matrix Factorization (NMF) can be used to perform the clustering. By its nature, NMF-based clustering is focused on the large values. If the data is normalized by subtracting the row/column means, it becomes of mixed signs and the original NMF cannot be used. Our idea is to split and then concatenate the positive and negative parts of the matrix, after taking the absolute value of the negative elements. NMF applied to the concatenated data, which we call PosNegNMF, offers the advantages of the original NMF approach, while giving equal weight to large and small values. We use two public health datasets to illustrate the new method and compare it with alternative clustering methods, such as K-means and clustering methods based on the Singular Value Decomposition (SVD) or Principal Component Analysis (PCA).With the exception of situations where a reasonably accurate factorization can be achieved using the first SVD component, we recommend that the epidemiologists and environmental scientists use the new method to obtain clusters with improved quality and interpretability.
KW - K-means
KW - NMF
KW - PCA
KW - SVD
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U2 - 10.3390/ijerph13050509
DO - 10.3390/ijerph13050509
M3 - Article
C2 - 27213413
AN - SCOPUS:84969567757
SN - 1661-7827
VL - 13
JO - International journal of environmental research and public health
JF - International journal of environmental research and public health
IS - 5
M1 - 509
ER -