Dataset Information

A tractable latent variable model for nonlinear dimensionality reduction.

ABSTRACT: We propose a latent variable model to discover faithful low-dimensional representations of high-dimensional data. The model computes a low-dimensional embedding that aims to preserve neighborhood relationships encoded by a sparse graph. The model both leverages and extends current leading approaches to this problem. Like t-distributed Stochastic Neighborhood Embedding, the model can produce two- and three-dimensional embeddings for visualization, but it can also learn higher-dimensional embeddings for other uses. Like LargeVis and Uniform Manifold Approximation and Projection, the model produces embeddings by balancing two goals-pulling nearby examples closer together and pushing distant examples further apart. Unlike these approaches, however, the latent variables in our model provide additional structure that can be exploited for learning. We derive an Expectation-Maximization procedure with closed-form updates that monotonically improve the model's likelihood: In this procedure, embeddings are iteratively adapted by solving sparse, diagonally dominant systems of linear equations that arise from a discrete graph Laplacian. For large problems, we also develop an approximate coarse-graining procedure that avoids the need for negative sampling of nonadjacent nodes in the graph. We demonstrate the model's effectiveness on datasets of images and text.

SUBMITTER: Saul LK

PROVIDER: S-EPMC7354940 | biostudies-literature | 2020 Jul

REPOSITORIES: biostudies-literature

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Publications

A tractable latent variable model for nonlinear dimensionality reduction.

Saul Lawrence K LK

Proceedings of the National Academy of Sciences of the United States of America 20200622 27

We propose a latent variable model to discover faithful low-dimensional representations of high-dimensional data. The model computes a low-dimensional embedding that aims to preserve neighborhood relationships encoded by a sparse graph. The model both leverages and extends current leading approaches to this problem. Like t-distributed Stochastic Neighborhood Embedding, the model can produce two- and three-dimensional embeddings for visualization, but it can also learn higher-dimensional embeddin ...[more]

PMID: 32571935

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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.

Project description:Sensory neurons often have variable responses to repeated presentations of the same stimulus, which can significantly degrade the stimulus information contained in those responses. This information can in principle be preserved if variability is shared across many neurons, but depends on the structure of the shared variability and its relationship to sensory encoding at the population level. The structure of this shared variability in neural activity can be characterized by latent variable models, although they have thus far typically been used under restrictive mathematical assumptions, such as assuming linear transformations between the latent variables and neural activity. Here we introduce two nonlinear latent variable models for analyzing large-scale neural recordings. We first present a general nonlinear latent variable model that is agnostic to the stimulus tuning properties of the individual neurons, and is hence well suited for exploring neural populations whose tuning properties are not well characterized. This motivates a second class of model, the Generalized Affine Model, which simultaneously determines each neuron's stimulus selectivity and a set of latent variables that modulate these stimulus-driven responses both additively and multiplicatively. While these approaches can detect very general nonlinear relationships in shared neural variability, we find that neural activity recorded in anesthetized primary visual cortex (V1) is best described by a single additive and single multiplicative latent variable, i.e., an "affine model". In contrast, application of the same models to recordings in awake macaque prefrontal cortex discover more general nonlinearities to compactly describe the population response variability. These results thus demonstrate how nonlinear latent variable models can be used to describe population variability, and suggest that a range of methods is necessary to study different brain regions under different experimental conditions.

Dataset Information

A tractable latent variable model for nonlinear dimensionality reduction.

Publications

A tractable latent variable model for nonlinear dimensionality reduction.

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