Analysis Of High-dimensional Datasets Research Articles

Multiple multi-sample testing under arbitrary covariance dependency.

Modern high-throughput biomedical devices routinely produce data on a large scale, and the analysis of high-dimensional datasets has become commonplace in biomedical studies. However, given thousands or tens of thousands of measured variables in these datasets, extracting meaningful features poses a challenge. In this article, we propose a procedure to evaluate the strength of the associations between a nominal (categorical) response variable and multiple features simultaneously. Specifically, we propose a framework of large-scale multiple testing under arbitrary correlation dependency among test statistics. First, marginal multinomial regressions are performed for each feature individually. Second, we use an approach of multiple marginal models for each baseline-category pair to establish asymptotic joint normality of the stacked vector of the marginal multinomial regression coefficients. Third, we estimate the (limiting) covariance matrix between the estimated coefficients from all marginal models. Finally, our approach approximates the realized false discovery proportion of a thresholding procedure for the marginal p-values for each baseline-category logit pair. The proposed approach offers a sensible trade-off between the expected numbers of true and false findings. Furthermore, we demonstrate a practical application of the method on hyperspectral imaging data. This dataset is obtained by a matrix-assisted laser desorption/ionization (MALDI) instrument. MALDI demonstrates tremendous potential for clinical diagnosis, particularly for cancer research. In our application, the nominal response categories represent cancer (sub-)types.

Opening the black-box of Neighbor Embeddings with Hotelling’s [formula omitted] statistic and [formula omitted]-residuals

In contrast to classical techniques for exploratory analysis of high-dimensional data sets, such as principal component analysis (PCA), neighbor embedding (NE) techniques tend to better preserve the local structure/topology of high-dimensional data. However, the ability to preserve local structure comes at the expense of interpretability: techniques such as t-Distributed Stochastic Neighbor Embedding (t-SNE) or Uniform Manifold Approximation and Projection (UMAP) do not provide insights into which input or to what extent the variables underlie the topological (cluster) structure seen in the corresponding embedding. We here introduce X-MAP, a workflow that employs different “tricks” from the chemometrics field based on PCA, Q-residuals and Hotelling’s T2 contributions in combination with novel visualization approaches to derive local and global explanations of neighbor embeddings. We show how our approach is capable of identifying discriminatory features between groups of data points that remain unnoticed when exploring NEs using standard univariate or multivariate approaches.

Eigenvectors from Eigenvalues Sparse Principal Component Analysis (EESPCA)

We present a novel technique for sparse principal component analysis. This method, named Eigenvectors from Eigenvalues Sparse Principal Component Analysis (EESPCA), is based on the formula for computing squared eigenvector loadings of a Hermitian matrix from the eigenvalues of the full matrix and associated sub-matrices. We explore two versions of the EESPCA method: a version that uses a fixed threshold for inducing sparsity and a version that selects the threshold via cross-validation. Relative to the state-of-the-art sparse PCA methods of Witten et al., Yuan & Zhang and Tan et al., the fixed threshold EESPCA technique offers an order-of-magnitude improvement in computational speed, does not require estimation of tuning parameters via cross-validation, and can more accurately identify true zero principal component loadings across a range of data matrix sizes and covariance structures. Importantly, the EESPCA method achieves these benefits while maintaining out-of-sample reconstruction error and PC estimation error close to the lowest error generated by all evaluated approaches. EESPCA is a practical and effective technique for sparse PCA with particular relevance to computationally demanding statistical problems such as the analysis of high-dimensional data sets or application of statistical techniques like resampling that involve the repeated calculation of sparse PCs.

Evaluating Usability Aspects of a Mixed Reality Solution for Immersive Analytics in Industry 4.0 Scenarios.

In medicine or industry, the analysis of high-dimensional data sets is increasingly required. However, available technical solutions are often complex to use. Therefore, new approaches like immersive analytics are welcome. Immersive analytics promise to experience high-dimensional data sets in a convenient manner for various user groups and data sets. Technically, virtual-reality devices are used to enable immersive analytics. In Industry 4.0, for example, scenarios like the identification of outliers or anomalies in high-dimensional data sets are pursued goals of immersive analytics. In this context, two important questions should be addressed for any developed technical solution on immersive analytics: First, is the technical solutions being helpful or not? Second, is the bodily experience of the technical solution positive or negative? The first question aims at the general feasibility of a technical solution, while the second one aims at the wearing comfort. Extant studies and protocols, which systematically address these questions are still rare. In this work, a study protocol is presented, which mainly investigates the usability for immersive analytics in Industry 4.0 scenarios. Specifically, the protocol is based on four pillars. First, it categorizes users based on previous experiences. Second, tasks are presented, which can be used to evaluate the feasibility of the technical solution. Third, measures are presented, which quantify the learning effect of a user. Fourth, a questionnaireevaluates the stress level when performing tasks. Based on these pillars, a technical setting was implemented that uses mixed reality smartglasses to apply the study protocol. The results of the conducted study show the applicability of the protocol on the one hand and the feasibility of immersive analytics in Industry 4.0 scenarios on the other. The presented protocol includes a discussion of discovered limitations.

Two-group Poisson-Dirichlet mixtures for multiple testing.

The simultaneous testing of multiple hypotheses is common to the analysis of high-dimensional data sets. The two-group model, first proposed by Efron, identifies significant comparisons by allocating observations to a mixture of an empirical null and an alternative distribution. In the Bayesian nonparametrics literature, many approaches have suggested using mixtures of Dirichlet Processes in the two-group model framework. Here, we investigate employing mixtures of two-parameter Poisson-Dirichlet Processes instead, and show how they provide a more flexible and effective tool for large-scale hypothesis testing. Our model further employs nonlocal prior densities to allow separation between the two mixture components. We obtain a closed-form expression for the exchangeable partition probability function of the two-group model, which leads to a straightforward Markov Chain Monte Carlo implementation. We compare the performance of our method for large-scale inference in a simulation study and illustrate its use on both a prostate cancer data set and a case-control microbiome study of the gastrointestinal tracts in children from underdeveloped countries who have been recently diagnosed with moderate-to-severediarrhea.

Systematically Exploring Associations among Multivariate Data

Detecting relationships among multivariate data is often of great importance in the analysis of high-dimensional data sets, and has received growing attention for decades from both academic and industrial fields. In this study, we propose a statistical tool named the neighbor correlation coefficient (nCor), which is based on a new idea that measures the local continuity of the reordered data points to quantify the strength of the global association between variables. With sufficient sample size, the new method is able to capture a wide range of functional relationship, whether it is linear or nonlinear, bivariate or multivariate, main effect or interaction. The score of nCor roughly approximates the coefficient of determination (R2) of the data which implies the proportion of variance in one variable that is predictable from one or more other variables. On this basis, three nCor based statistics are also proposed here to further characterize the intra and inter structures of the associations from the aspects of nonlinearity, interaction effect, and variable redundancy. The mechanisms of these measures are proved in theory and demonstrated with numerical analyses.

Unsupervised feature selection for large data sets

The last decade saw a considerable increase in the availability of data. Unfortunately, this increase was overshadowed by various technical difficulties that arise when analysing large data sets. These include long processing times, large requirements for data storage, and other technical issues related to the analysis of high-dimensional data sets. By consequence, reducing the cardinality of data sets (with minimum information loss) has become of interest to virtually any data scientist. Many feature selection algorithms have been introduced in the literature, however, there are two main issues with these. First, the vast majority of such algorithms require labelled samples to learn from. One should note it is often too expensive to label a meaningful amount of data, particularly when dealing with large data sets. Second, these algorithms were not designed to deal with the volume of data we have nowadays. This paper introduces a novel unsupervised feature selection algorithm designed specifically to deal with large data sets. Our experiments demonstrate the superiority of our method.

On Feature Selection and Rule Extraction for High Dimensional Data: A Case of Diffuse Large B-Cell Lymphomas Microarrays Classification

Neurofuzzy methods capable of selecting a handful of useful features are very useful in analysis of high dimensional datasets. A neurofuzzy classification scheme that can create proper linguistic features and simultaneously select informative features for a high dimensional dataset is presented and applied to the diffuse large B-cell lymphomas (DLBCL) microarray classification problem. The classification scheme is the combination of embedded linguistic feature creation and tuning algorithm, feature selection, and rule-based classification in one neural network framework. The adjustable linguistic features are embedded in the network structure via fuzzy membership functions. The network performs the classification task on the high dimensional DLBCL microarray dataset either by the direct calculation or by the rule-based approach. The 10-fold cross validation is applied to ensure the validity of the results. Very good results from both direct calculation and logical rules are achieved. The results show that the network can select a small set of informative features in this high dimensional dataset. By a comparison to other previously proposed methods, our method yields better classification performance.

Classes of Multiple Decision Functions Strongly Controlling FWER and FDR.

Two general classes of multiple decision functions, where each member of the first class strongly controls the family-wise error rate (FWER), while each member of the second class strongly controls the false discovery rate (FDR), are described. These classes offer the possibility that optimal multiple decision functions with respect to a pre-specified Type II error criterion, such as the missed discovery rate (MDR), could be found which control the FWER or FDR Type I error rates. The gain in MDR of the associated FDR-controlling procedure relative to the well-known Benjamini-Hochberg (BH) procedure is demonstrated via a modest simulation study with gamma-distributed component data. Such multiple decision functions may have the potential of being utilized in multiple testing, specifically in the analysis of high-dimensional data sets.

Approximately-isometric diffusion maps

Diffusion Maps (DM), and other kernel methods, are utilized for the analysis of high dimensional datasets. The DM method uses a Markovian diffusion process to model and analyze data. A spectral analysis of the DM kernel yields a map of the data into a low dimensional space, where Euclidean distances between the mapped data points represent the diffusion distances between the corresponding high dimensional data points. Many machine learning methods, which are based on the Euclidean metric, can be applied to the mapped data points in order to take advantage of the diffusion relations between them. However, a significant drawback of the DM is the need to apply spectral decomposition to a kernel matrix, which becomes infeasible for large datasets.In this paper, we present an efficient approximation of the DM embedding. The presented approximation algorithm produces a dictionary of data points by identifying a small set of informative representatives. Then, based on this dictionary, the entire dataset is efficiently embedded into a low dimensional space. The Euclidean distances in the resulting embedded space approximate the diffusion distances. The properties of the presented embedding and its relation to DM method are analyzed and demonstrated.

A multi-filter enhanced genetic ensemble system for gene selection and sample classification of microarray data

BackgroundFeature selection techniques are critical to the analysis of high dimensional datasets. This is especially true in gene selection from microarray data which are commonly with extremely high feature-to-sample ratio. In addition to the essential objectives such as to reduce data noise, to reduce data redundancy, to improve sample classification accuracy, and to improve model generalization property, feature selection also helps biologists to focus on the selected genes to further validate their biological hypotheses.ResultsIn this paper we describe an improved hybrid system for gene selection. It is based on a recently proposed genetic ensemble (GE) system. To enhance the generalization property of the selected genes or gene subsets and to overcome the overfitting problem of the GE system, we devised a mapping strategy to fuse the goodness information of each gene provided by multiple filtering algorithms. This information is then used for initialization and mutation operation of the genetic ensemble system.ConclusionWe used four benchmark microarray datasets (including both binary-class and multi-class classification problems) for concept proving and model evaluation. The experimental results indicate that the proposed multi-filter enhanced genetic ensemble (MF-GE) system is able to improve sample classification accuracy, generate more compact gene subset, and converge to the selection results more quickly. The MF-GE system is very flexible as various combinations of multiple filters and classifiers can be incorporated based on the data characteristics and the user preferences.

A class comparison method with filtering-enhanced variable selection for high-dimensional data sets.

High-throughput molecular analysis technologies can produce thousands of measurements for each of the assayed samples. A common scientific question is to identify the variables whose distributions differ between some pre-specified classes (i.e. are differentially expressed). The statistical cost of examining thousands of variables is related to the risk of identifying many variables that truly are not differentially expressed, and many different multiple testing strategies have been used for the analysis of high-dimensional data sets to control the number of these false positives. An approach that is often used in practice to reduce the multiple comparisons problem is to lessen the number of comparisons being performed by filtering out variables that are considered non-informative 'before' the analysis. However, deciding which and how many variables should be filtered out can be highly arbitrary, and different filtering strategies can result in different variables being identified as differentially expressed. We propose the filtering-enhanced variable selection (FEVS) method, a new multiple testing strategy for identifying differentially expressed variables. This method identifies differentially expressed variables by combining the results obtained using a variety of filtering methods, instead of using a pre-specified filtering method or trying to identify an optimal filtering of the variables prior to class comparison analysis. We prove that the FEVS method probabilistically controls the number of false discoveries, and we show with a set of simulations and an example from the literature that FEVS can be useful for gaining sensitivity for the detection of truly differentially expressed variables.

Challenges in translating plasma proteomics from bench to bedside: update from the NHLBI Clinical Proteomics Programs

The emerging scientific field of proteomics encompasses the identification, characterization, and quantification of the protein content or proteome of whole cells, tissues, or body fluids. The potential for proteomic technologies to identify and quantify novel proteins in the plasma that can function as biomarkers of the presence or severity of clinical disease states holds great promise for clinical use. However, there are many challenges in translating plasma proteomics from bench to bedside, and relatively few plasma biomarkers have successfully transitioned from proteomic discovery to routine clinical use. Key barriers to this translation include the need for "orthogonal" biomarkers (i.e., uncorrelated with existing markers), the complexity of the proteome in biological samples, the presence of high abundance proteins such as albumin in biological samples that hinder detection of low abundance proteins, false positive associations that occur with analysis of high dimensional datasets, and the limited understanding of the effects of growth, development, and age on the normal plasma proteome. Strategies to overcome these challenges are discussed.

Approximately Sufficient Statistics and Bayesian Computation

The analysis of high-dimensional data sets is often forced to rely upon well-chosen summary statistics. A systematic approach to choosing such statistics, which is based upon a sound theoretical framework, is currently lacking. In this paper we develop a sequential scheme for scoring statistics according to whether their inclusion in the analysis will substantially improve the quality of inference. Our method can be applied to high-dimensional data sets for which exact likelihood equations are not possible. We illustrate the potential of our approach with a series of examples drawn from genetics. In summary, in a context in which well-chosen summary statistics are of high importance, we attempt to put the 'well' into 'chosen.'

Editorial introduction

The papers of this special issue were all presented at the 1 day Symposium on Large Data Sets Organized by the Statistical Software section of Dutch Society for Statistics and Operations Research on 6 November 2003 in Amsterdam. The Statistical Software Section does not exist anymore and this symposium marks the last of a long series of bi-annual symposia on different aspects on statistical computing, e.g. mixed models and missing values. However, the emphasis of this last symposium was more on applications of analysis of high-dimensional data sets as on computational problems. High-dimensional data are nowadays quite common in different fields, like finance, marketing, epidemiology, particle physics, astronomy, life sciences and social sciences. Formerly, data sets used to be large in the sense of containing many observations on a small number of variables. But, in the life sciences or in imaging, data sets with a small number of observations and a huge number of variables are much more common. The three papers which are finally chosen to be in this special issue are from a variety of backgrounds. The paper of Yekutieli et al. gives an overview of some general approaches to address multiplicity in hypothesis testing encountered in the field of life sciences especially in complex research questions, where many variables are observed on a few subjects and hypotheses may be nested. At the other spectrum – long series of continuous correlated data with only a few variables – is the paper of Franses uses examples from the field of macro-economics in which an overview of analysis of panels of time-series data using random coefficients is given. The paper of Brijs et al. challenges the estimation of ranking of large number of multivariate parameters (more than 23,000) in an example of accident locations using a Bayesian approach using a multivariate Poisson distribution. Although the examples are from various fields of application, one needs not much imagination to apply the ideas to other fields as well. The problem of multiplicity is general enough and is encountered in almost any large research project. Panel time series is an issue in, e.g. the modelling of air-pollution data, signalling of infectious diseases or death rates in intensive care units. Finally, the ranking of many parameters can be applied to, e.g. the ranking of hospitals, careproviders and small areas with respect to the prevalence of diseases. We hope that this small sample of papers from the last symposium of the Statistical Software section of the VVS-OR will encourage the use of these models in many other fields of application.

Morphometric Distinction of Sclerosing Adenosis from Tubular Carcinoma of the Breast

Objective features have been identified that assist in distinguishing sclerosing adenosis from tubular carcinoma of the breast. Hematoxylin and eosin stained paraffin sections of 18 sclerosing adenoses and 18 tubular carcinomas were studied using a TAS Plus image analysis system. Histological measurements from lumens and glands included stereologic features of architecture and morphometry of size and shape (the latter by Fourier coefficients). Cytological measurements included nuclear area, perimeter, diameter and formfactor. Initial analysis suggested utility for several individual features. However, after a modified Bonferroni procedure only two of the features were statistically significant, i.e. the coefficient of variation of luminal form factor and the surface density of glands. Multivariate discriminant analysis using these two variables correctly classified 86% of the cases, with three adenoses and two carcinomas misclassified. Validity of the discriminant rules was supported by classification using measurements from a separate, independent set of cases (ten sclerosing adenoses and nine tubular carcinomas). The classification function computed from the first set misclassified only one case from the second set, a tubular carcinoma, leaving 95% of the cases successfully categorized. Chi square test for 2 x 2 contingency tables gave a p-value < 0.001 for both sets of cases. The results suggest that morphometric features are helpful in distinguishing tubular carcinoma from sclerosing adenosis and point out the need for conservative analysis of high-dimensional data sets.