Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an urgent need of dimensionality reduction with fast increase of big genomics data. However, the performance of RP is usually lower. We attempt to improve classification accuracy of RP through combining other reduction dimension methods such as Principle Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Feature Selection (FS). We compared classification accuracy and running time of different combination methods on three microarray datasets and a simulation dataset. Experimental results show a remarkable improvement of 14.77 in classification accuracy of FS followed by RP compared to RP on BC-TCGA dataset. LDA followed by RP also helps RP to yield a more discriminative subspace with an increase of 13.65 on classification accuracy on the same dataset. FS followed by RP outperforms other combination methods in classification accuracy on most of the datasets.
In @cite_3 and @cite_0 , RP has been proposed to address the burdensome computation time in dimensionality reduction. In RP, transformation matrix @math is randomly generated. Experiment results @cite_3 @cite_6 have reveals that RP is computationally less expensive with a little distortion of original data. On the other hand, RP may not capture intrinsic structure underlying original data because @math is generated without considering the structure of data.
@cite_0 @cite_6 @cite_3
1977580401 2060783161 2214177029 2096730755
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics, machine learning, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint mixed relaxations (i.e., l 1 -norm and trace norm) under certain conditions. However, all current provable algorithms suffer from superlinear per-iteration cost, which severely limits their applicability to large-scale problems. In this paper, we propose a scalable, provable and structured robust bilinear factorization (RBF) method to recover low-rank and sparse matrices from missing and grossly corrupted data, i.e., robust matrix completion (RMC), or incomplete and grossly corrupted measurements, i.e., compressive principal component pursuit (CPCP). Specifically, we first present two small-scale matrix trace norm regularized bilinear factorization models for RMC and CPCP problems, in which repetitively calculating SVD of a large-scale matrix is replaced by updating two much smaller factor matrices. Then, we apply the alternating direction method of multipliers (ADMM) to efficiently solve the RMC problems. Finally, we provide the convergence analysis of our algorithm, and extend it to address general CPCP problems. Experimental results verified both the efficiency and effectiveness of our method compared with the state-of-the-art methods. We propose a new method for linear dimensionality reduction of manifold-modeled data. Given a training set X of Q points belonging to a manifoldM ⊂ R , we construct a linear operator P : R → R that approximately preserves the norms of all Q 2 pairwise difference vectors (or secants) of X . We design the matrix P via a trace-norm minimization that can be efficiently solved as a semi-definite program (SDP). When X comprises a sufficiently dense sampling of M, we prove that the optimal matrix P preserves all pairs of secants over M. We numerically demonstrate the considerable gains using our SDP-based approach over existing linear dimensionality reduction methods, such as principal components analysis (PCA) and random projections. Motivated by the recent developments of nonconvex penalties in sparsity modeling, we propose a nonconvex optimization model for handing the low-rank matrix recovery problem. Different from the famous robust principal component analysis (RPCA), we suggest recovering low-rank and sparse matrices via a nonconvex loss function and a nonconvex penalty. The advantage of the nonconvex approach lies in its stronger robustness. To solve the model, we devise a majorization-minimization augmented Lagrange multiplier (MM-ALM) algorithm which finds the local optimal solutions of the proposed nonconvex model. We also provide an efficient strategy to speedup MM-ALM, which makes the running time comparable with the state-of-the-art algorithm of solving RPCA. Finally, empirical results demonstrate the superiority of our nonconvex approach over RPCA in terms of matrix recovery accuracy. Coupled training of dimensionality reduction and classification is proposed previously to improve the prediction performance for single-label problems. Following this line of research, in this paper, we first introduce a novel Bayesian method that combines linear dimensionality reduction with linear binary classification for supervised multilabel learning and present a deterministic variational approximation algorithm to learn the proposed probabilistic model. We then extend the proposed method to find intrinsic dimensionality of the projected subspace using automatic relevance determination and to handle semi-supervised learning using a low-density assumption. We perform supervised learning experiments on four benchmark multilabel learning data sets by comparing our method with baseline linear dimensionality reduction algorithms. These experiments show that the proposed approach achieves good performance values in terms of hamming loss, average AUC, macro F"1, and micro F"1 on held-out test data. The low-dimensional embeddings obtained by our method are also very useful for exploratory data analysis. We also show the effectiveness of our approach in finding intrinsic subspace dimensionality and semi-supervised learning tasks.