P. Paatero and U. Tapper, Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values, Environmetrics, vol. 5, pp. 111126, 1994. Home/Search Document Not in Database Summary Related Articles Check |
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Probabilistic Models of Early Vision - Hoyer (Correct)
....s j given the input x and the generative weight matrix A, under these non negativity constraints. We also showed how to learn the generative weights from the observed data. We are certainly not the first to consider non negativity constraints in linear models. As early as 1994, Paatero and Tapper [112] described positive matrix factorization, which attempts to reconstruct the non negative input matrix as a product of two non negative matrices with lower dimensionality. This was subsequently put into a neurobiological context by Lee and Seung [81] calling it non negative matrix factorization) ....
P. Paatero and U. Tapper, "Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values," Environmetrics, vol. 5, pp. 111--126, 1994.
Probabilistic Models of Early Vision - Hoyer (2002) (Correct)
....s j given the input x and the generative weight matrix A, under these non negativity constraints. We also showed how to learn the generative weights from the observed data. We are certainly not the first to consider non negativity constraints in linear models. As early as 1994, Paatero and Tapper [112] described positive matrix factorization, which attempts to reconstruct the non negative input matrix as a product of two non negative matrices with lower dimensionality. This was subsequently put into a neurobiological context by Lee and Seung [81] calling it non negative matrix factorization) ....
P. Paatero and U. Tapper, "Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values," Environmetrics, vol. 5, pp. 111--126, 1994.
Algorithms for Non-Negative Independent Component Analysis - Plumbley (2002) (2 citations) (Correct)
....and texts are widely available (see e.g. 3] 4] Source separation using constraints of non negativity (or alternatively, positivity) of the sources and or mixing matrices have be proposed by a number of authors in various fields in recent years. In environmental modelling, Paatero and Tapper [5] introduced Positive Matrix Factor ization (PMF) as a method of solving (1) with positivity constraints. Building on PMF, Lee and Seung [2] introduced a set of ecient algorithms for performing non negative matrix factorization (NMF) which has been applied to, for example, the discovery of ....
P. Paatero and U. Tapper, "Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values," Environmetrics, vol. 5, pp. 111 126, 1994.
Positive Tensor Factorization - Welling, Weber (2001) (1 citation) (Correct)
....the number of color channels of the image in Figure 1a from 3 to 2, using both PTF (1b) and SVD (1c) While the factors produced by PTF can easily be interpreted as reflections and peel, the second SVD factor is meaningless since the colorscheme is undefined for negative values. Following [4] and [3] we propose to drop the orthogonality constraint in the linear factorization, and simply minimize the recontruction error directly under a posi (a) b) c) Figure 1. Decomposition of a color image in terms of two color components . The image was represented as X I;c = A I;1 B c;1 A ....
....However, linear transformations are often not sufficient to capture more complicated structure in the data. It would therefore be advantageous to have a simple, nonlinear method to produce meaningful distributed codes. Non negative matrix factorization [3] NMF) positive matrix factorization [4] (PMF) and, as we will see, PTF partly achieve this goal. They tend to generate sparse codings (a few but not all basis vectors help explain the datum) while being slightly nonlinear due to the positivity constraint. In this paper we present a novel algorithm that computes positive factors for ....
P. Paatero and U. Tapper, "Positive Matrix Factorization - a Nonnegative Factor Model with Optimal Utilization of Error-Estimates of Data Values" Environmetrics, 1994, pp. 111-126.
Nonnegative Matrix Factorization And Applications - Moody Chu And (Correct)
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P. Paatero and U. Tapper, Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values, Environmetrics, vol. 5, pp. 111126, 1994.
Journal of Machine Learning Research 7 (2006).. - Non-Negative Matrix .. (Correct)
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P. Paatero and U. Tapper. Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics, 5:111--126, 1994.
On the Use of Sparse Signal Decomposition in the Analysis of.. - Theis, Garcia (Correct)
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P. Paatero, U. Tapper, Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values, Environmetrics 5 (1994) 111--126. 28
Bubbles: A Unifying Framework for Low-Level Statistical .. - Hyvärinen, Hurri.. (2003) (1 citation) (Correct)
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P. Paatero and U. Tapper, "Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values," Environmetrics 5, 111 --126 (1994).
Optimization using Fourier Expansion over a Geodesic For.. - Plumbley (2004) (Correct)
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Paatero, P., Tapper, U.: Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5 (1994) 111--126
A Bayesian Method For Positive Source Separation - Sa Moussaoui David (2004) (1 citation) (Correct)
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P. Paatero and U. Tapper, "Positive matrix factorization: A non--negative factor model with optimal utilization of error estimates of data values," Environmetrics, vol. 5, pp. 111--126, 1994.
Blind Separation Of Positive Sources Using Non-Negative PCA - Oja, Plumbley (2003) (1 citation) (Correct)
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P. Paatero and U. Tapper, "Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values," Environmetrics, vol. 5, pp. 111-- 126, 1994.
Patrik O. Hoyer - Neural Networks Research (Correct)
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P. Paatero and U. Tapper, "Positive Matrix Factorization: A Non-negative Factor Model with Optimal Utilization of Error Estimates of Data Values," Environmetrics, vol. 5, pp. 111--126, 1994.
Modeling Receptive Fields With - Non-Negative Sparse Coding (Correct)
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P. Paatero and U. Tapper. Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics, 5:111--126, 1994.
Patrik O. Hoyer - Neural Networks Research (Correct)
No context found.
P. Paatero and U. Tapper, "Positive Matrix Factorization: A Non-negative Factor Model with Optimal Utilization of Error Estimates of Data Values," Environmetrics, vol. 5, pp. 111--126, 1994.
Modeling Receptive Fields With - Non-Negative Sparse Coding (Correct)
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P. Paatero and U. Tapper. Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values. Environmetrics, 5:111--126, 1994.
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