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    Wyświetlanie 1-3 z 3
    Tytuł:
    Projective nonnegative matrix factorization based on α-divergence
    Autorzy:
    Yang, Z.
    Oja, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/91672.pdf
    Data publikacji:
    2011
    Wydawca:
    Społeczna Akademia Nauk w Łodzi. Polskie Towarzystwo Sieci Neuronowych
    Tematy:
    Nonnegative Matrix Factorization
    NMF
    α-divergence
    PNMF
    α-NMF
    α-PNMF
    Opis:
    The well-known Nonnegative Matrix Factorization (NMF) method can be provided with more flexibility by generalizing the non-normalized Kullback-Leibler divergence to α- divergences. However, the resulting α-NMF method can only achieve mediocre sparsity for the factorizing matrices. We have earlier proposed a variant of NMF, called Projective NMF (PNMF) that has been shown to have superior sparsity over standard NMF. Here we propose to incorporate both merits of α-NMF and PNMF. Our α-PNMF method can produce a much sparser factorizing matrix, which is desired in many scenarios. Theoretically, we provide a rigorous convergence proof that the iterative updates of α-PNMF monotonically decrease the α-divergence between the input matrix and its approximate. Empirically, the advantages of α-PNMF are verified in two application scenarios: (1) it is able to learn highly sparse and localized part-based representations of facial images; (2) it outperforms α-NMF and PNMF for clustering in terms of higher purity and smaller entropy.
    Źródło:
    Journal of Artificial Intelligence and Soft Computing Research; 2011, 1, 1; 7-16
    2083-2567
    2449-6499
    Pojawia się w:
    Journal of Artificial Intelligence and Soft Computing Research
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multiplicative Algorithm for Correntropy-Based Nonnegative Matrix Factorization
    Autorzy:
    Hosseini-Asl, E.
    Zurada, J. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/108758.pdf
    Data publikacji:
    2013
    Wydawca:
    Społeczna Akademia Nauk w Łodzi
    Tematy:
    Nonnegative Matrix Factorization (NMF)
    Correntropy
    Multiplicative Algorithm
    Document Clustering
    Opis:
    Nonnegative matrix factorization (NMF) is a popular dimension reduction technique used for clustering by extracting latent features from highdimensional data and is widely used for text mining. Several optimization algorithms have been developed for NMF with different cost functions. In this paper we evaluate the correntropy similarity cost function. Correntropy is a nonlinear localized similarity measure which measures the similarity between two random variables using entropy-based criterion, and is especially robust to outliers. Some algorithms based on gradient descent have been used for correntropy cost function, but their convergence is highly dependent on proper initialization and step size and other parameter selection. The proposed general multiplicative factorization algorithm uses the gradient descent algorithm with adaptive step size to maximize the correntropy similarity between the data matrix and its factorization. After devising the algorithm, its performance has been evaluated for document clustering. Results were compared with constrained gradient descent method using steepest descent and L-BFGS methods. The simulations show that the performance of steepest descent and LBFGS convergence are highly dependent on gradient descent step size which depends on σ parameter of correntropy cost function. However, the multiplicative algorithm is shown to be less sensitive to σ parameterand yields better clustering results than other algorithms. The results demonstrate that clustering performance measured by entropy and purity improve the clustering. The multiplicative correntropy-based algorithm also shows less variation in accuracy of document clusters for variable number of clusters. The convergence of each algorithm is also investigated, and the experiments have shown that the multiplicative algorithm converges faster than L-BFGS and steepest descent method.
    Źródło:
    Journal of Applied Computer Science Methods; 2013, 5 No. 2; 89-104
    1689-9636
    Pojawia się w:
    Journal of Applied Computer Science Methods
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Regularized nonnegative matrix factorization: Geometrical interpretation and application to spectral unmixing
    Autorzy:
    Zdunek, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/329732.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    blind source separation
    nonnegative matrix factorization
    active set algorithm
    regularized NMF
    polytope approximation
    ślepa separacja sygnału
    nieujemna faktoryzacja macierzy
    Opis:
    Nonnegative Matrix Factorization (NMF) is an important tool in data spectral analysis. However, when a mixing matrix or sources are not sufficiently sparse, NMF of an observation matrix is not unique. Many numerical optimization algorithms, which assure fast convergence for specific problems, may easily get stuck into unfavorable local minima of an objective function, resulting in very low performance. In this paper, we discuss the Tikhonov regularized version of the Fast Combinatorial NonNegative Least Squares (FC-NNLS) algorithm (proposed by Benthem and Keenan in 2004), where the regularization parameter starts from a large value and decreases gradually with iterations. A geometrical analysis and justification of this approach are presented. The numerical experiments, carried out for various benchmarks of spectral signals, demonstrate that this kind of regularization, when applied to the FC-NNLS algorithm, is essential to obtain good performance.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 2; 233-247
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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