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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This article is concerned with simultaneous tests on linear regression coefficients in high-dimensional settings. When the dimensionality is larger than the sample size, the classic @math -test is not applicable since the sample covariance matrix is not invertible. In order to overcome this issue, both Goeman, Finos and van Houwelingen (2011) and Zhong and Chen (2011) proposed their test procedures after excluding the @math term in @math -statistics. However, both these two test are not invariant under the group of scalar transformations. In order to treat those variables in a fair' way, we proposed a new test statistic and establish its asymptotically normal under certain mild conditions. Simulation studies showed that our test procedure performs very well in many cases. 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. We introduce the notion of a canonical tester for a class of properties on distributions, that is, a tester strong and general enough that a distribution property in the class is testable if and only if the canonical tester tests it. We construct a canonical tester for the class of properties of one or two distributions that are symmetric and satisfy a certain weak continuity condition. Analyzing the performance of the canonical tester on specific properties resolves two open problems, establishing lower bounds that match known upper bounds: we show that distinguishing between entropy @math on distributions over @math requires @math samples, and distinguishing whether a pair of distributions has statistical distance @math requires @math samples. Our techniques also resolve a conjecture about a property that our canonical tester does not apply to: distinguishing identical distributions from those with statistical distance @math requires @math samples.