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.
There are several statistical tests to select features @cite_21 , such as rank sum test @cite_22 , t-test @cite_29 and so on. In the paper these methods are called feature selection methods. Here we take t-test as a representative to study the performance of FS methods derived from statistical test. The t-test assesses whether the means of two groups are statistically different from each other. Normalized distance between two classes of samples can be obtained using the sample mean values: @math , @math and the sample variances @math and @math :
@cite_29 @cite_21 @cite_22
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Given samples from distributions p and q, a two-sample test determines whether to reject the null hypothesis that p = q, based on the value of a test statistic measuring the distance between the samples. One choice of test statistic is the maximum mean discrepancy (MMD), which is a distance between embeddings of the probability distributions in a reproducing kernel Hilbert space. The kernel used in obtaining these embeddings is critical in ensuring the test has high power, and correctly distinguishes unlike distributions with high probability. A means of parameter selection for the two-sample test based on the MMD is proposed. For a given test level (an upper bound on the probability of making a Type I error), the kernel is chosen so as to maximize the test power, and minimize the probability of making a Type II error. The test statistic, test threshold, and optimization over the kernel parameters are obtained with cost linear in the sample size. These properties make the kernel selection and test procedures suited to data streams, where the observations cannot all be stored in memory. In experiments, the new kernel selection approach yields a more powerful test than earlier kernel selection heuristics. Feature selection with specific multivariate performance measures is the key to the success of many applications such as image retrieval and text classification. The existing feature selection methods are usually designed for classification error. In this paper, we propose a generalized sparse regularizer. Based on the proposed regularizer, we present a unified feature selection framework for general loss functions. In particular, we study the novel feature selection paradigm by optimizing multivariate performance measures. The resultant formulation is a challenging problem for high-dimensional data. Hence, a two-layer cutting plane algorithm is proposed to solve this problem, and the convergence is presented. In addition, we adapt the proposed method to optimize multivariate measures for multiple-instance learning problems. The analyses by comparing with the state-of-the-art feature selection methods show that the proposed method is superior to others. Extensive experiments on large-scale and high-dimensional real-world datasets show that the proposed method outperforms l1-SVM and SVM-RFE when choosing a small subset of features, and achieves significantly improved performances over SVMperl in terms of F1-score. Two important problems which can affect the performance of classification models are high-dimensionality (an overabundance of independent features in the dataset) and imbalanced data (a skewed class distribution which creates at least one class with many fewer instances than other classes). To resolve these problems concurrently, we propose an iterative feature selection approach, which repeated applies data sampling (in order to address class imbalance) followed by feature selection (in order to address high-dimensionality), and finally we perform an aggregation step which combines the ranked feature lists from the separate iterations of sampling. This approach is designed to find a ranked feature list which is particularly effective on the more balanced dataset resulting from sampling while minimizing the risk of losing data through the sampling step and missing important features. To demonstrate this technique, we employ 18 different feature selection algorithms and Random Undersampling with two post-sampling class distributions. We also investigate the use of sampling and feature selection without the iterative step (e.g., using the ranked list from a single iteration, rather than combining the lists from multiple iterations), and compare these results from the version which uses iteration. Our study is carried out using three groups of datasets with different levels of class balance, all of which were collected from a real-world software system. All of our experiments use four different learners and one feature subset size. We find that our proposed iterative feature selection approach outperforms the non-iterative approach. Comparing two sets of multivariate samples is a central problem in data analysis. From a statistical standpoint, the simplest way to perform such a comparison is to resort to a non-parametric two-sample test (TST), which checks whether the two sets can be seen as i.i.d. samples of an identical unknown distribution (the null hypothesis). If the null is rejected, one wishes to identify regions accounting for this difference. This paper presents a two-stage method providing feedback on this difference, based upon a combination of statistical learning (regression) and computational topology methods. Consider two populations, each given as a point cloud in Rd. In the first step, we assign a label to each set and we compute, for each sample point, a discrepancy measure based on comparing an estimate of the conditional probability distribution of the label given a position versus the global unconditional label distribution. In the second step, we study the height function defined at each point by the aforementioned estimated discrepancy. Topological persistence is used to identify persistent local minima of this height function, their basins defining regions of points with high discrepancy and in spatial proximity. Experiments are reported both on synthetic and real data (satellite images and handwritten digit images), ranging in dimension from d = 2 to d = 784, illustrating the ability of our method to localize discrepancies. On a general perspective, the ability to provide feedback downstream TST may prove of ubiquitous interest in exploratory statistics and data science.