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| 1 | Generalization errors of Laplacian regularized least squares regression显示文摘Semi-supervised learning is an emerging computational paradigm for machine learning,that aims to make better use of large amounts of inexpensive unlabeled data to improve the learning performance.While various methods have been proposed based on different intuitions,the crucial issue of generalization performance is still poorly understood.In this paper,we investigate the convergence property of the Laplacian regularized least squares regression,a semi-supervised learning algorithm based on manifold regularization.Moreover,the improvement of error bounds in terms of the number of labeled and unlabeled data is presented for the first time as far as we know.The convergence rate depends on the approximation property and the capacity of the reproducing kernel Hilbert space measured by covering numbers.Some new techniques are exploited for the analysis since an extra regularizer is introduced. | CAO Ying CHEN DiRong | 2012 | Science China Mathematics2012，55，9： | 2 |
| 2 | On the performance of regularized regression learning in Hilbert space显示文摘 | Chen Dirong Li Han | 2012 | Neurocomputing2012，93，： | 1 |
| 3 | Partially-Linear Least- Squares regularized regression for system identifi- cation显示文摘 | An introduction to other kernel-based cambridge univer- Xu Yongli Chen Dirong | 2009 | IEEE Transactions on Automatic Control2009，54，11： | 1 |
| 4 | The independence of initial vectors in the subdivision schemes显示文摘 | Chen Dirong Li Luoqing | 2002 | Science in China Series A: Mathematics2002，，11： | 1 |
| 5 | Support vector machine soft margin classifiers:Error analysis显示文摘 | CHEN Dirong WU Qiang YING Yiming | 2004 | The Journal of Machine Learning Research2004，12，5： | 1 |
| 6 | Support vector machine soft margin classifiers: error analysis显示文摘 | Chen Dirong Wu Qiang Ying Yiming | 2004 | Journal of Machine Learning Research2004，5，5： | 1 |
| 7 | On the Cardinal Spline Interpolation Corresponding to Infinite Order Differential Operators | Chen Dirong Department of Mathematics Beijing Normal University Beijing,100875 and Center for Mathematical Sciences Zhejiang University Hangzhou,310027 China | 1994 | Acta Mathematica Sinica,English Series1994，10，3： | 0 |
| 8 | BEST ONE-SIDED APPROXIMATION OF CONVOLUTION CLASSES BY CARDINAL SPLINES显示文摘Let G be a Polya frequency density and G its periodization.We get the exact value of upper approxi-mation of S1(G),which is a convolution class with kernel G.by cardinal splines cprrespnding to G.Similarresult has been obtained for periodic convolution class with kernel G as well. | Chen Dirong (Academia Sinica,China) | 1994 | Analysis in Theory and Applications1994，10，4： | 0 |
| 9 | ANALYSIS TO NEYMAN-PEARSON CLASSIFICATION WITH CONVEX LOSS FUNCTION显示文摘Neyman-Pearson classification has been studied in several articles before. But they all proceeded in the classes of indicator functions with indicator function as the loss function, which make the calculation to be difficult. This paper investigates Neyman- Pearson classification with convex loss function in the arbitrary class of real measurable functions. A general condition is given under which Neyman-Pearson classification with convex loss function has the same classifier as that with indicator loss function. We give analysis to NP-ERM with convex loss function and prove it's performance guarantees. An example of complexity penalty pair about convex loss function risk in terms of Rademacher averages is studied, which produces a tight PAC bound of the NP-ERM with convex loss function. | Min Han Dirong Chen Zhaoxu Sun | 2008 | Analysis in Theory and Applications2008，24，1： | 0 |
| 10 | Convergence of cascade algorithm for individual initial function and arbitrary refinement masks显示文摘The cascade algorithm plays an important role in computer graphics and wavelet analysis. For any initial function φ0, a cascade sequence (φn)∞n=1 is constructed by the iteration φn=Caφn-1,n=1,2,…,where Ca is defined by Cag=∑a(α)g(2·-α),g∈Lp(R).a∈Z In this paper, we characterize the convergence of a cascade sequence in terms of a sequence of functions and in terms of joint spectral radius. As a consequence, it is proved that any convergent cascade sequence has a convergence rate of geometry, i.e.,||φn+1 - φn||Lp(R)= O(n) for some ∈ (0, 1). The condition of sum rules for the mask is not required. Finally, an example is presented to illustrate our theory. | CHEN Dirong HAN Min | 2005 | Science China Mathematics2005，48，3： | 0 |
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