High-dimensional Small Sample Research Articles

Promoting Similarity of Sparsity Structures in Integrative Analysis With Penalization

ABSTRACTFor data with high-dimensional covariates but small sample sizes, the analysis of single datasets often generates unsatisfactory results. The integrative analysis of multiple independent datasets provides an effective way of pooling information and outperforms single-dataset and several alternative multi-datasets methods. Under many scenarios, multiple datasets are expected to share common important covariates, that is, the corresponding models have similarity in their sparsity structures. However, the existing methods do not have a mechanism to promote the similarity in sparsity structures in integrative analysis. In this study, we consider penalized variable selection and estimation in integrative analysis. We develop an L0-penalty-based method, which explicitly promotes the similarity in sparsity structures. Computationally it is realized using a coordinate descent algorithm. Theoretically it has the selection and estimation consistency properties. Under a wide spectrum of simulation scenarios, it has identification and estimation performance comparable to or better than the alternatives. In the analysis of three lung cancer datasets with gene expression measurements, it identifies genes with sound biological implications and satisfactory prediction performance. Supplementary materials for this article are available online.

Shrinkage-based diagonal Hotelling’s tests for high-dimensional small sample size data

High-throughput expression profiling techniques bring novel tools and also statistical challenges to genetic research. In addition to detecting differentially expressed genes, testing the significance of gene sets or pathway analysis has been recognized as an equally important problem. Owing to the “large p small n” paradigm, the traditional Hotelling’s T2 test suffers from the singularity problem and therefore is not valid in this setting. In this paper, we propose a shrinkage-based diagonal Hotelling’s test for both one-sample and two-sample cases. We also suggest several different ways to derive the approximate null distribution under different scenarios of p and n for our proposed shrinkage-based test. Simulation studies show that the proposed method performs comparably to existing competitors when n is moderate or large, but it is better when n is small. In addition, we analyze four gene expression data sets and they demonstrate the advantage of our proposed shrinkage-based diagonal Hotelling’s test.

Risk Analysis of Ecological Environment Healthy

The risk analysis of ecological environment healthy is limited by multi-factors, high dimensional data, small samples and incomplete information. This paper develops a method of risk analysis model of ecological environment, which is combined with the combination with projection pursuit method and the information diffusion theory. This model spreads the risk information of the actual observation data to the properties of the risk threshold in order to explore the nonlinear relationship between them and calculates the risk probability of the whole ecological environment. This paper takes 35 cities as study objects, evaluates the risk grade of ecological environment of each city and estimates the comprehensive risk probability of ecological environment healthy in China. The research result shows: most of those cities are in the "less safety" risk grade and "unsafety" risk grade. And the whole ecological environment healthy is in high-risk and shows the unstable condition.

A Projection Pursuit framework for supervised dimension reduction of high dimensional small sample datasets

The analysis and interpretation of datasets with large number of features and few examples has remained as a challenging problem in the scientific community, owing to the difficulties associated with the curse-of-the-dimensionality phenomenon. Projection Pursuit (PP) has shown promise in circumventing this phenomenon by searching low-dimensional projections of the data where meaningful structures are exposed. However, PP faces computational difficulties in dealing with datasets containing thousands of features (typical in genomics and proteomics) due to the vast quantity of parameters to optimize. In this paper we describe and evaluate a PP framework aimed at relieving such difficulties and thus ease the construction of classifier systems. The framework is a two-stage approach, where the first stage performs a rapid compaction of the data and the second stage implements the PP search using an improved version of the SPP method (Guo et al., 2000, 32). In an experimental evaluation with eight public microarray datasets we showed that some configurations of the proposed framework can clearly overtake the performance of eight well-established dimension reduction methods in their ability to pack more discriminatory information into fewer dimensions.

Stability SCAD: a powerful approach to detect interactions in large-scale genomic study

BackgroundEvidence suggests that common complex diseases may be partially due to SNP-SNP interactions, but such detection is yet to be fully established in a high-dimensional small-sample (small-n-large-p) study. A number of penalized regression techniques are gaining popularity within the statistical community, and are now being applied to detect interactions. These techniques tend to be over-fitting, and are prone to false positives. The recently developed stability least absolute shrinkage and selection operator (SLASSO) has been used to control family-wise error rate, but often at the expense of power (and thus false negative results).ResultsHere, we propose an alternative stability selection procedure known as stability smoothly clipped absolute deviation (SSCAD). Briefly, this method applies a smoothly clipped absolute deviation (SCAD) algorithm to multiple sub-samples, and then identifies cluster ensemble of interactions across the sub-samples. The proposed method was compared with SLASSO and two kinds of traditional penalized methods by intensive simulation. The simulation revealed higher power and lower false discovery rate (FDR) with SSCAD. An analysis using the new method on the previously published GWAS of lung cancer confirmed all significant interactions identified with SLASSO, and identified two additional interactions not reported with SLASSO analysis.ConclusionsBased on the results obtained in this study, SSCAD presents to be a powerful procedure for the detection of SNP-SNP interactions in large-scale genomic data.

An Efficient Dimensionality Reduction Approach for Small-sample Size and High-dimensional Data Modeling

As for massive multidimensional data are being generated in a wide range of emerging applications, this paper introduces two new methods of dimension reduction to conduct small-sample size and high-dimensional data processing and modeling. Through combining the support vector machine (SVM) and recursive feature elimination (RFE), SVM-RFE algorithm is proposed to select features, and further, adding the higher order singular value decomposition (HOSVD) to the feature extraction which involves successfully organizing the data into high order tensor pattern. The validation of simulation experiment data shows that the proposed novel feature selection and feature extraction methods can be effectively applied to the research work for analyzing and modeling the data of atmospheric corrosion. The feature selection method pledges that the remaining feature subset is optimal; feature extraction method reserves the original structure, discriminate information, and the integrity of data, etc. Finally, this paper proposes a complete data dimensionality reduction solution that can effectively solve the high-dimensional small sample data problem, and code programming for this solution has been implemented.

PLS-based recursive feature elimination for high-dimensional small sample

This paper focused on feature selection for high-dimensional small samples (HDSS). We first presented a general analytical framework for feature selection on a HDSS including selection strategy (single-feature ranking and multi-feature ranking) and evaluation criteria (feature subset consistency and compactness). Then we proposed partial least squares (PLS) based feature selection methods for HDSS and two theorems. The proposed methodologies include a PLS model for classification, parameter selection, PLSRanking, and PLS-based recursive feature elimination. Furthermore, we compared our proposed methods with several existing feature selection methods such as Support Vector Machine (SVM) based feature selection, SVM-based recursive feature elimination (SVMRFE), Random Forest (RF) based feature selection, RF-based recursive feature elimination (RFRFE), ReliefF algorithm and ReliefF-based recursive feature elimination (ReliefFRFE). Using twelve high-dimensional datasets from different areas of research, we evaluated the results in terms of accuracy (sensitivity and specificity), running time, and the feature subset consistency and compactness. The analysis demonstrated that the proposed approach from our research performed very well when handling both two-category and multi-category problems.

Iterative Reconstruction of High-Dimensional Gaussian Graphical Models Based on a New Method to Estimate Partial Correlations under Constraints

In the context of Gaussian Graphical Models (GGMs) with high-dimensional small sample data, we present a simple procedure, called PACOSE – standing for PArtial COrrelation SElection – to estimate partial correlations under the constraint that some of them are strictly zero. This method can also be extended to covariance selection. If the goal is to estimate a GGM, our new procedure can be applied to re-estimate the partial correlations after a first graph has been estimated in the hope to improve the estimation of non-zero coefficients. This iterated version of PACOSE is called iPACOSE. In a simulation study, we compare PACOSE to existing methods and show that the re-estimated partial correlation coefficients may be closer to the real values in important cases. Plus, we show on simulated and real data that iPACOSE shows very interesting properties with regards to sensitivity, positive predictive value and stability.

PLS-Based Gene Selection and Identification of Tumor-Specific Genes

In view of the characteristics of high-dimensional small sample, strong relevance, and high noise of the identification of tumor-specific genes on microarray, a novel partial least squares (PLS) based gene-selection method, which synthesizes genetic relatedness and is suitable for multicategory classification, is presented. Using the explanation difference of independent variables on dependent variable (class), we define three indicators for global gene selection, which takes into accounts the combined effects of all the genes and the correlation among the genes. Integrated with the linear kernel support vector classifier (SVC), the proposed method is tested by MIT acute myeloid leukemia/acute lymphoblastic leukemia (AML/ALL) and small round blue cell tumors (SRBCT) data sets. A subset of specific genes with small numbers and high identification are obtained. The results indicate that our proposed PLS-based method for tumor-specific genes selection is highly efficient. Compared to the literature, the selected specific genes from both two-category dataset AML/ALL and multicategory dataset SRBCT are credible. Further investigation shows that the proposed gene-selection method is robust. Overall, the proposed method can effectively solve feature-selection problem on high-dimensional small sample. At the same time, it has good performance for multicategory classification as well.