6 results
Search Results
2. An aggressive reduction on the complexity of optimization for non-strongly convex objectives.
- Author
-
Luo, Zhijian, Chen, Siyu, Hou, Yueen, Gao, Yanzeng, and Qian, Yuntao
- Subjects
- *
REGULARIZATION parameter , *LOGISTIC regression analysis , *MACHINE learning , *LOGARITHMS , *ALGORITHMS - Abstract
Tremendous efficient optimization methods have been proposed for strongly convex objectives optimization in modern machine learning. For non-strongly convex objectives, a popular approach is to apply a reduction from non-strongly convex to a strongly convex case via regularization techniques. Reduction on objectives with adaptive decrease on regularization tightens the optimal convergence of algorithms to be independent on logarithm factor. However, the initialization of parameter of regularization has a great impact on the performance of the reduction. In this paper, we propose an aggressive reduction to reduce the complexity of optimization for non-strongly convex objectives, and our reduction eliminates the impact of the initialization of parameter on the convergent performances of algorithms. Aggressive reduction not only adaptively decreases the regularization parameter, but also modifies regularization term as the distance between current point and the approximate minimizer. Our aggressive reduction can also shave off the non-optimal logarithm term theoretically, and make the convergent performance of algorithm more compact practically. Experimental results on logistic regression and image deblurring confirm this success in practice. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. Algorithm of adaptive Fourier decomposition in H2(ℂ+).
- Author
-
Mai, Weixiong and Qian, Tao
- Subjects
- *
HILBERT transform , *ALGORITHMS , *HARDY spaces , *SIGNALS & signaling - Abstract
In this paper, we propose an applicable algorithm of the so-called adaptive Fourier decomposition in H 2 (ℂ +) the Hardy H 2 space on the upper half-plane ℂ + , which provides a new method for decomposing real-valued signals and analytic signals on the real line. As a by-product, a new approach for computing the Hilbert transform on the real line is also given. Numerical experiments are used to demonstrate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
4. Estimation of sub-endmembers using spatial-spectral approach for hyperspectral images.
- Author
-
Chetia, Gouri Shankar and Devi, Bishnulatpam Pushpa
- Subjects
- *
COMPUTATIONAL complexity , *EIGENVALUES , *ALGORITHMS - Abstract
In Blind Hyperspectral Unmixing, the accuracy of the estimated number of endmembers affects the succeeding steps of extraction of endmember signatures and acquiring their fractional abundances. The characteristics of endmember signature depend on the nature of the material on the ground and share similar characteristics for variants of the same material. In this paper, we introduce a new concept of sub-endmembers to identify similar materials that are variants of a global endmember. Identifying the sub-endmembers will provide a meaningful interpretation of the endmember variability along with increased unmixing accuracy. This paper proposes a new algorithm exploiting both the spatial and spectral information present in hyperspectral data. The hyperspectral data are segmented into homogenous regions (superpixels) based on the Simple Linear Iterative Clustering (SLIC) algorithm, and the mean spectral of each region is accounted for in finding the global endmembers. The difference of eigenvalues-based thresholding method is used to find the number of global and sub-endmembers. The method has been tested on synthetic and real hyperspectral data and has successfully estimated the number of global endmembers as well as sub-endmembers. The method is also compared with other state-of-the-art methods, and better performances are obtained at a reasonably lower computational complexity. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
5. An algorithm for constructing the two-direction Armlet multiwavelet.
- Author
-
Wang, Gang and Zhou, Xiaohui
- Subjects
- *
ALGORITHMS , *WAVELET transforms , *SIGNS & symbols , *MATRICES (Mathematics) , *DEFINITIONS - Abstract
In this paper, an algorithm is discussed for constructing the two-direction Armlet multiwavelet. First, the definition of two-direction Armlet multiwavelet is presented in this paper. A two-direction multiwavelet can be changed to a special multi-wavelet. By Two-scale Similar Transform (TST), a transform can be taken on the two-scale matrix symbols of a two-direction multi-wavelets. This transform keeps the orthogonality of the two-direction multi-wavelets. However, the condition is discussed which the two-direction multi-wavelet corresponding to a two-direction multi-scaling function is an Armlet with order n. An approach is given for constructing the transform matrix. Finally, an example is given for discussing the two-direction Armlet multi-wavelet with order 2. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
6. Iterative gradient descent for outlier detection.
- Author
-
Zhuang Qi, Dazhi Jiang, and Xiaming Chen
- Subjects
- *
OUTLIER detection , *MATRIX inversion , *ALGORITHMS , *REGRESSION analysis , *CONVEX functions , *DATA analysis - Abstract
In linear regression, outliers have a serious effect on the estimation of regression model parameters and the prediction of final results, so outlier detection is one of the key steps in data analysis. In this paper, we use a mean shift model and then we apply the penalty function to penalize the mean shift parameters, which is conducive to get a sparse parameter vector. We choose Sorted L1 regularization (SLOPE), which provides a convex loss function, and shows good statistical properties in parameter selection. We apply an iterative process which using gradient descent method and parameter selection at each step. Our algorithm has higher computational efficiency since the calculation of inverse matrix is avoided. Finally, we use Cross-Validation rules (CV) and Bayesian Information Criterion (BIC) criteria to fine tune the parameters, which helps our program identify outliers and obtain more robust regression coefficients. Compared with other methods, the experimental results show that our program has a fantastic performance in all aspects of outlier detection. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.