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Forward Stepwise Deep Autoencoder-based Monotone Nonlinear Dimensionality Reduction Methods.

ABSTRACT: Dimensionality reduction is an unsupervised learning task aimed at creating a low-dimensional summary and/or extracting the most salient features of a dataset. Principal components analysis (PCA) is a linear dimensionality reduction method in the sense that each principal component is a linear combination of the input variables. To allow features that are nonlinear functions of the input variables, many nonlinear dimensionality reduction methods have been proposed. In this paper we propose novel nonlinear dimensionality reduction methods based on bottleneck deep autoencoders (Kramer, 1991). Our contributions are two-fold: (1) We introduce a monotonicity constraint into bottleneck deep autoencoders for estimating a single nonlinear component and propose two methods for fitting the model. (2) We propose a new, forward stepwise (FS) deep learning architecture for estimating multiple nonlinear components. The former helps extract interpretable, monotone components when the assumption of monotonicity holds, and the latter helps evaluate reconstruction errors in the original data space for a range of components. We conduct numerical studies to compare different model fitting methods and use two real data examples from the studies of human immune responses to HIV to illustrate the proposed methods.

SUBMITTER: Fong Y

PROVIDER: S-EPMC8673912 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Visualization of anatomical structures using radiological imaging methods is an important tool in medicine to differentiate normal from pathological tissue and can generate large amounts of data for a radiologist to read. Integrating these large data sets is difficult and time-consuming. A new approach uses both supervised and unsupervised advanced machine learning techniques to visualize and segment radiological data. This study describes the application of a novel hybrid scheme, based on combining wavelet transform and nonlinear dimensionality reduction (NLDR) methods, to breast magnetic resonance imaging (MRI) data using three well-established NLDR techniques, namely, ISOMAP, local linear embedding (LLE), and diffusion maps (DfM), to perform a comparative performance analysis.Twenty-five breast lesion subjects were scanned using a 3T scanner. MRI sequences used were T1-weighted, T2-weighted, diffusion-weighted imaging (DWI), and dynamic contrast-enhanced (DCE) imaging. The hybrid scheme consisted of two steps: preprocessing and postprocessing of the data. The preprocessing step was applied for B(1) inhomogeneity correction, image registration, and wavelet-based image compression to match and denoise the data. In the postprocessing step, MRI parameters were considered data dimensions and the NLDR-based hybrid approach was applied to integrate the MRI parameters into a single image, termed the embedded image. This was achieved by mapping all pixel intensities from the higher dimension to a lower dimensional (embedded) space. For validation, the authors compared the hybrid NLDR with linear methods of principal component analysis (PCA) and multidimensional scaling (MDS) using synthetic data. For the clinical application, the authors used breast MRI data, comparison was performed using the postcontrast DCE MRI image and evaluating the congruence of the segmented lesions.The NLDR-based hybrid approach was able to define and segment both synthetic and clinical data. In the synthetic data, the authors demonstrated the performance of the NLDR method compared with conventional linear DR methods. The NLDR approach enabled successful segmentation of the structures, whereas, in most cases, PCA and MDS failed. The NLDR approach was able to segment different breast tissue types with a high accuracy and the embedded image of the breast MRI data demonstrated fuzzy boundaries between the different types of breast tissue, i.e., fatty, glandular, and tissue with lesions (>86%).The proposed hybrid NLDR methods were able to segment clinical breast data with a high accuracy and construct an embedded image that visualized the contribution of different radiological parameters.

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Forward Stepwise Deep Autoencoder-based Monotone Nonlinear Dimensionality Reduction Methods.

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