Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAdaptive gPCA: A method for structured dimensionality reduction
173
0
0.0
(
0
)
Added by
Julia Fukuyama
Publication date
2017
fields
Mathematical Statistics
and research's language is
English
Authors
Julia Fukuyama
Ask ChatGPT about the research
No Arabic abstract
When working with large biological data sets, exploratory analysis is an important first step for understanding the latent structure and for generating hypotheses to be tested in subsequent analyses. However, when the number of variables is large compared to the number of samples, standard methods such as principal components analysis give results which are unstable and difficult to interpret. To mitigate these problems, we have developed a method which allows the analyst to incorporate side information about the relationships between the variables in a way that encourages similar variables to have similar loadings on the principal axes. This leads to a low-dimensional representation of the samples which both describes the latent structure and which has axes which are interpretable in terms of groups of closely related variables. The method is derived by putting a prior encoding the relationships between the variables on the data and following through the analysis on the posterior distributions of the samples. We show that our method does well at reconstructing true latent structure in simulated data and we also demonstrate the method on a dataset investigating the effects of antibiotics on the composition of bacteria in the human gut.
rate research
Read More
In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor distributions in high dimensions. Some benchmark datasets are studied. We find that the local rank correlation closely corresponds to our visual interpretation of the quality of the output. In addition, we demonstrate that the local rank correlation is useful in estimating the intrinsic dimensionality of the original data, and in selecting a suitable value of tuning parameters used in some algorithms.
High-dimensional classification has become an increasingly important problem. In this paper we propose a Multivariate Adaptive Stochastic Search (MASS) approach which first reduces the dimension of the data space and then applies a standard classification method to the reduced space. One key advantage of MASS is that it automatically adjusts to mimic variable selection type methods, such as the Lasso, variable combination methods, such as PCA, or methods that combine these two approaches. The adaptivity of MASS allows it to perform well in situations where pure variable selection or variable combination methods fail. Another major advantage of our approach is that MASS can accurately project the data into very low-dimensional non-linear, as well as linear, spaces. MASS uses a stochastic search algorithm to select a handful of optimal projection directions from a large number of random directions in each iteration. We provide some theoretical justification for MASS and demonstrate its strengths on an extensive range of simulation studies and real world data sets by comparing it to many classical and modern classification methods.
VARCLUST algorithm is proposed for clustering variables under the assumption that variables in a given cluster are linear combinations of a small number of hidden latent variables, corrupted by the random noise. The entire clustering task is viewed as the problem of selection of the statistical model, which is defined by the number of clusters, the partition of variables into these clusters and the cluster dimensions, i.e. the vector of dimensions of linear subspaces spanning each of the clusters. The optimal model is selected using the approximate Bayesian criterion based on the Laplace approximations and using a non-informative uniform prior on the number of clusters. To solve the problem of the search over a huge space of possible models we propose an extension of the ClustOfVar algorithm which was dedicated to subspaces of dimension only 1, and which is similar in structure to the $K$-centroid algorithm. We provide a complete methodology with theoretical guarantees, extensive numerical experimentations, complete data analyses and implementation. Our algorithm assigns variables to appropriate clusterse based on the consistent Bayesian Information Criterion (BIC), and estimates the dimensionality of each cluster by the PEnalized SEmi-integrated Likelihood Criterion (PESEL), whose consistency we prove. Additionally, we prove that each iteration of our algorithm leads to an increase of the Laplace approximation to the model posterior probability and provide the criterion for the estimation of the number of clusters. Numerical comparisons with other algorithms show that VARCLUST may outperform some popular machine learning tools for sparse subspace clustering. We also report the results of real data analysis including TCGA breast cancer data and meteorological data. The proposed method is implemented in the publicly available R package varclust.
Spectral dimensionality reduction methods enable linear separations of complex data with high-dimensional features in a reduced space. However, these methods do not always give the desired results due to irregularities or uncertainties of the data. Thus, we consider aggressively modifying the scales of the features to obtain the desired classification. Using prior knowledge on the labels of partial samples to specify the Fiedler vector, we formulate an eigenvalue problem of a linear matrix pencil whose eigenvector has the feature scaling factors. The resulting factors can modify the features of entire samples to form clusters in the reduced space, according to the known labels. In this study, we propose new dimensionality reduction methods supervised using the feature scaling associated with the spectral clustering. Numerical experiments show that the proposed methods outperform well-established supervised methods for toy problems with more samples than features, and are more robust regarding clustering than existing methods. Also, the proposed methods outperform existing methods regarding classification for real-world problems with more features than samples of gene expression profiles of cancer diseases. Furthermore, the feature scaling tends to improve the clustering and classification accuracies of existing unsupervised methods, as the proportion of training data increases.
To analyse a very large data set containing lengthy variables, we adopt a sequential estimation idea and propose a parallel divide-and-conquer method. We conduct several conventional sequential estimation procedures separately, and properly integrate their results while maintaining the desired statistical properties. Additionally, using a criterion from the statistical experiment design, we adopt an adaptive sample selection, together with an adaptive shrinkage estimation method, to simultaneously accelerate the estimation procedure and identify the effective variables. We confirm the cogency of our methods through theoretical justifications and numerical results derived from synthesized data sets. We then apply the proposed method to three real data sets, including those pertaining to appliance energy use and particulate matter concentration.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
