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Hiroshi Yamada - One of the best experts on this subject based on the ideXlab platform.
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non negative matrix factorization of a set of economic time series with graph based smoothing of Basis Vectors and sparseness of the coefficients
Systems Man and Cybernetics, 2020Co-Authors: Ueda Ueda, Yuichiro Nomura, Junichi Miyao, Takio Kurita, Hiroshi YamadaAbstract:In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful Basis Vector for the set of data, and indicate which data use which Basis Vector. Usually each of the time series is analyzed independently in economics but here we will analyze the set of time series simultaneously. Since some of the economic data are measured as positive values and we want to decompose them as a mixture of the parts, we will apply non-negative matrix factorization to the economic data. Non-negative matrix factorization can compress dimensions by approximating a non-negative matrix with the product of two non-negative matrices. The two non-negative matrices are called the coefficient matrix and the Basis matrix, and the Basis matrix can be considered as a dimensionally compressed matrix. If the standard non-negative matrix factorization is used for economic data, the Basis matrix may not be smooth. We think that the Basis Vectors should be smooth except a few special economical incidents. In the proposed method, a Graph-based non-negative matrix factorization is introduced to regularize the Basis matrix of the time series. A path graph for representing the time series of economic data is incorporated into the non-negative matrix factorization as regularization. As a result, Basis Vectors that maintains the time series of economic data are decomposed. Furthermore, we propose to introduce a sparsity in the non-negative matrix factorization. Traditionally, the sparsity incorporated into non-negative matrix factorization has been used for Basis Vectors. However, the proposed method introduces the sparsity for coefficient Vectors. Thus the proposed method, which simultaneously incorporates the sparsity for the coefficient Vectors and the smoothness for the Basis Vectors, can extract the smooth Basis Vectors and the original economical data are approximated as the weighted sum of the few bases Vectors. This allows us to discover economic trends and the best-fit trends for each data at the same time.
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SMC - Non-negative Matrix Factorization of a set of Economic Time Series with Graph Based Smoothing of Basis Vectors and Sparseness of the Coefficients
2020 IEEE International Conference on Systems Man and Cybernetics (SMC), 2020Co-Authors: Ueda Ueda, Yuichiro Nomura, Junichi Miyao, Takio Kurita, Hiroshi YamadaAbstract:In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful Basis Vector for the set of data, and indicate which data use which Basis Vector. Usually each of the time series is analyzed independently in economics but here we will analyze the set of time series simultaneously. Since some of the economic data are measured as positive values and we want to decompose them as a mixture of the parts, we will apply non-negative matrix factorization to the economic data. Non-negative matrix factorization can compress dimensions by approximating a non-negative matrix with the product of two non-negative matrices. The two non-negative matrices are called the coefficient matrix and the Basis matrix, and the Basis matrix can be considered as a dimensionally compressed matrix. If the standard non-negative matrix factorization is used for economic data, the Basis matrix may not be smooth. We think that the Basis Vectors should be smooth except a few special economical incidents. In the proposed method, a Graph-based non-negative matrix factorization is introduced to regularize the Basis matrix of the time series. A path graph for representing the time series of economic data is incorporated into the non-negative matrix factorization as regularization. As a result, Basis Vectors that maintains the time series of economic data are decomposed. Furthermore, we propose to introduce a sparsity in the non-negative matrix factorization. Traditionally, the sparsity incorporated into non-negative matrix factorization has been used for Basis Vectors. However, the proposed method introduces the sparsity for coefficient Vectors. Thus the proposed method, which simultaneously incorporates the sparsity for the coefficient Vectors and the smoothness for the Basis Vectors, can extract the smooth Basis Vectors and the original economical data are approximated as the weighted sum of the few bases Vectors. This allows us to discover economic trends and the best-fit trends for each data at the same time.
Ueda Ueda - One of the best experts on this subject based on the ideXlab platform.
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non negative matrix factorization of a set of economic time series with graph based smoothing of Basis Vectors and sparseness of the coefficients
Systems Man and Cybernetics, 2020Co-Authors: Ueda Ueda, Yuichiro Nomura, Junichi Miyao, Takio Kurita, Hiroshi YamadaAbstract:In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful Basis Vector for the set of data, and indicate which data use which Basis Vector. Usually each of the time series is analyzed independently in economics but here we will analyze the set of time series simultaneously. Since some of the economic data are measured as positive values and we want to decompose them as a mixture of the parts, we will apply non-negative matrix factorization to the economic data. Non-negative matrix factorization can compress dimensions by approximating a non-negative matrix with the product of two non-negative matrices. The two non-negative matrices are called the coefficient matrix and the Basis matrix, and the Basis matrix can be considered as a dimensionally compressed matrix. If the standard non-negative matrix factorization is used for economic data, the Basis matrix may not be smooth. We think that the Basis Vectors should be smooth except a few special economical incidents. In the proposed method, a Graph-based non-negative matrix factorization is introduced to regularize the Basis matrix of the time series. A path graph for representing the time series of economic data is incorporated into the non-negative matrix factorization as regularization. As a result, Basis Vectors that maintains the time series of economic data are decomposed. Furthermore, we propose to introduce a sparsity in the non-negative matrix factorization. Traditionally, the sparsity incorporated into non-negative matrix factorization has been used for Basis Vectors. However, the proposed method introduces the sparsity for coefficient Vectors. Thus the proposed method, which simultaneously incorporates the sparsity for the coefficient Vectors and the smoothness for the Basis Vectors, can extract the smooth Basis Vectors and the original economical data are approximated as the weighted sum of the few bases Vectors. This allows us to discover economic trends and the best-fit trends for each data at the same time.
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SMC - Non-negative Matrix Factorization of a set of Economic Time Series with Graph Based Smoothing of Basis Vectors and Sparseness of the Coefficients
2020 IEEE International Conference on Systems Man and Cybernetics (SMC), 2020Co-Authors: Ueda Ueda, Yuichiro Nomura, Junichi Miyao, Takio Kurita, Hiroshi YamadaAbstract:In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful Basis Vector for the set of data, and indicate which data use which Basis Vector. Usually each of the time series is analyzed independently in economics but here we will analyze the set of time series simultaneously. Since some of the economic data are measured as positive values and we want to decompose them as a mixture of the parts, we will apply non-negative matrix factorization to the economic data. Non-negative matrix factorization can compress dimensions by approximating a non-negative matrix with the product of two non-negative matrices. The two non-negative matrices are called the coefficient matrix and the Basis matrix, and the Basis matrix can be considered as a dimensionally compressed matrix. If the standard non-negative matrix factorization is used for economic data, the Basis matrix may not be smooth. We think that the Basis Vectors should be smooth except a few special economical incidents. In the proposed method, a Graph-based non-negative matrix factorization is introduced to regularize the Basis matrix of the time series. A path graph for representing the time series of economic data is incorporated into the non-negative matrix factorization as regularization. As a result, Basis Vectors that maintains the time series of economic data are decomposed. Furthermore, we propose to introduce a sparsity in the non-negative matrix factorization. Traditionally, the sparsity incorporated into non-negative matrix factorization has been used for Basis Vectors. However, the proposed method introduces the sparsity for coefficient Vectors. Thus the proposed method, which simultaneously incorporates the sparsity for the coefficient Vectors and the smoothness for the Basis Vectors, can extract the smooth Basis Vectors and the original economical data are approximated as the weighted sum of the few bases Vectors. This allows us to discover economic trends and the best-fit trends for each data at the same time.
Mark D. Plumbley - One of the best experts on this subject based on the ideXlab platform.
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Gradient Polytope Faces Pursuit for large scale sparse recovery problems
2010Co-Authors: Aris Gretsistas, Ivan Damnjanovic, Mark D. PlumbleyAbstract:Polytope Faces Pursuit is a greedy algorithm that performs Basis Pursuit with similar order complexity to Orthogonal Matching Pursuit. The algorithm adds one Basis Vector at a time and adopts a path-following approach based on the geometry of the polar polytope associated with the dual Linear Program. Its initial implementation uses the method of Cholesky factorization to update the solution Vector at each step, which can be computationally expensive for solving large scale problems as it requires the succesive storage of large matrices. In this paper, we present a different approach using directional updates to estimate the solution Vector at each time. The proposed method uses the gradient descent method, reducing the memory requirements and computational complexity. We demonstrate the application of this Gradient Polytope Faces Pursuit algorithm to a source separation problem.
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ICASSP - Gradient Polytope Faces Pursuit for large scale sparse recovery problems
2010 IEEE International Conference on Acoustics Speech and Signal Processing, 2010Co-Authors: Aris Gretsistas, Ivan Damnjanovic, Mark D. PlumbleyAbstract:Polytope Faces Pursuit is a greedy algorithm that performs Basis Pursuit with similar order complexity to Orthogonal Matching Pursuit. The algorithm adds one Basis Vector at a time and adopts a path-following approach based on the geometry of the polar polytope associated with the dual Linear Program. Its initial implementation uses the method of Cholesky factorization to update the solution Vector at each step, which can be computationally expensive for solving large scale problems as it requires the succesive storage of large matrices. In this paper, we present a different approach using directional updates to estimate the solution Vector at each time. The proposed method uses the gradient descent method, reducing the memory requirements and computational complexity. We demonstrate the application of this Gradient Polytope Faces Pursuit algorithm to a source separation problem.
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an adaptive stereo Basis method for convolutive blind audio source separation
Neurocomputing, 2008Co-Authors: Maria G. Jafari, Mark D. Plumbley, Emmanuel Vincent, Samer A. Abdallah, Michael DaviesAbstract:We consider the problem of convolutive blind source separation of stereo mixtures, where a pair of microphones records mixtures of sound sources that are convolved with the impulse response between each source and sensor. We propose an adaptive stereo Basis (ASB) source separation method for such convolutive mixtures, using an adaptive transform Basis which is learned from the stereo mixture pair. The stereo Basis Vector pairs of the transform are grouped according to the estimated relative delay between the left and right channels for each Basis, and the sources are then extracted by projecting the transformed signal onto the subspace corresponding to each group of Basis Vector pairs. The performance of the proposed algorithm is compared with FD-ICA and DUET under different reverberation and noise conditions, using both objective distortion measures and formal listening tests. The results indicate that the proposed stereo coding method is competitive with both these algorithms at short and intermediate reverberation times, and offers significantly improved performance at low noise and short reverberation times.
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Blind source separation of convolutive audio using an adaptive stereo Basis
2006Co-Authors: Maria G. Jafari, Mark D. Plumbley, Emmanuel Vincent, Samer A. Abdallah, Michael DaviesAbstract:We consider the problem of convolutive blind source separation of audio mixtures. We propose an Adaptive Stereo Basis (ASB) method based on learning a set of Basis Vectors pairs fromthe time-domain stereomixtures. The Basis Vector pairs are clustered using estimated directions of arrival (DOAs) such that each Basis Vector pair is associated with one source. The ASB method is compared with the DUET algorithm on convolutive speech mixtures at different reverberation times and noise levels.
Piotr Fryzlewicz - One of the best experts on this subject based on the ideXlab platform.
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unbalanced haar technique for nonparametric function estimation
Journal of the American Statistical Association, 2007Co-Authors: Piotr FryzlewiczAbstract:The discrete unbalanced Haar (UH) transform is a decomposition of one-dimensional data with respect to an orthonormal Haar-like Basis where jumps in the Basis Vectors do not necessarily occur in the middle of their support. We introduce a multiscale procedure for estimation in Gaussian noise that consists of three steps: a UH transform, thresholding of the decomposition coefficients, and the inverse UH transform. We show that our estimator is mean squared consistent with near-optimal rates for a wide range of functions, uniformly over UH bases that are not “too unbalanced.” A vital ingredient of our approach is Basis selection. We choose each Basis Vector so that it best matches the data at a specific scale and location, where the latter parameters are determined by the "parent" Basis Vector. Our estimator is computable in O(n log n) operations. A simulation study demonstrates the good performance of our estimator compared with state-of-the-art competitors. We apply our method to the estimation of the mea...
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unbalanced haar technique for nonparametric function estimation
LSE Research Online Documents on Economics, 2007Co-Authors: Piotr FryzlewiczAbstract:The discrete unbalanced Haar (UH) transform is a decomposition of one-dimensional data with respect to an orthonormal Haar-like Basis where jumps in the Basis Vectors do not necessarily occur in the middle of their support. We introduce a multiscale procedure for estimation in Gaussian noise that consists of three steps: a UH transform, thresholding of the decomposition coefficients, and the inverse UH transform. We show that our estimator is mean squared consistent with near-optimal rates for a wide range of functions, uniformly over UH bases that are not “too unbalanced.” A vital ingredient of our approach is Basis selection. We choose each Basis Vector so that it best matches the data at a specific scale and location, where the latter parameters are determined by the "parent" Basis Vector. Our estimator is computable in O(n log n) operations. A simulation study demonstrates the good performance of our estimator compared with state-of-the-art competitors. We apply our method to the estimation of the mean intensity of the time series of earthquake counts occurring in northern California. We discuss extensions to image data and to smoother wavelets.
Michael Davies - One of the best experts on this subject based on the ideXlab platform.
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an adaptive stereo Basis method for convolutive blind audio source separation
Neurocomputing, 2008Co-Authors: Maria G. Jafari, Mark D. Plumbley, Emmanuel Vincent, Samer A. Abdallah, Michael DaviesAbstract:We consider the problem of convolutive blind source separation of stereo mixtures, where a pair of microphones records mixtures of sound sources that are convolved with the impulse response between each source and sensor. We propose an adaptive stereo Basis (ASB) source separation method for such convolutive mixtures, using an adaptive transform Basis which is learned from the stereo mixture pair. The stereo Basis Vector pairs of the transform are grouped according to the estimated relative delay between the left and right channels for each Basis, and the sources are then extracted by projecting the transformed signal onto the subspace corresponding to each group of Basis Vector pairs. The performance of the proposed algorithm is compared with FD-ICA and DUET under different reverberation and noise conditions, using both objective distortion measures and formal listening tests. The results indicate that the proposed stereo coding method is competitive with both these algorithms at short and intermediate reverberation times, and offers significantly improved performance at low noise and short reverberation times.
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Blind source separation of convolutive audio using an adaptive stereo Basis
2006Co-Authors: Maria G. Jafari, Mark D. Plumbley, Emmanuel Vincent, Samer A. Abdallah, Michael DaviesAbstract:We consider the problem of convolutive blind source separation of audio mixtures. We propose an Adaptive Stereo Basis (ASB) method based on learning a set of Basis Vectors pairs fromthe time-domain stereomixtures. The Basis Vector pairs are clustered using estimated directions of arrival (DOAs) such that each Basis Vector pair is associated with one source. The ASB method is compared with the DUET algorithm on convolutive speech mixtures at different reverberation times and noise levels.