Abstract
BackgroundDimensionality reduction (DR) enables the construction of a lower dimensional space (embedding) from a higher dimensional feature space while preserving object-class discriminability. However several popular DR approaches suffer from sensitivity to choice of parameters and/or presence of noise in the data. In this paper, we present a novel DR technique known as consensus embedding that aims to overcome these problems by generating and combining multiple low-dimensional embeddings, hence exploiting the variance among them in a manner similar to ensemble classifier schemes such as Bagging. We demonstrate theoretical properties of consensus embedding which show that it will result in a single stable embedding solution that preserves information more accurately as compared to any individual embedding (generated via DR schemes such as Principal Component Analysis, Graph Embedding, or Locally Linear Embedding). Intelligent sub-sampling (via mean-shift) and code parallelization are utilized to provide for an efficient implementation of the scheme.ResultsApplications of consensus embedding are shown in the context of classification and clustering as applied to: (1) image partitioning of white matter and gray matter on 10 different synthetic brain MRI images corrupted with 18 different combinations of noise and bias field inhomogeneity, (2) classification of 4 high-dimensional gene-expression datasets, (3) cancer detection (at a pixel-level) on 16 image slices obtained from 2 different high-resolution prostate MRI datasets. In over 200 different experiments concerning classification and segmentation of biomedical data, consensus embedding was found to consistently outperform both linear and non-linear DR methods within all applications considered.ConclusionsWe have presented a novel framework termed consensus embedding which leverages ensemble classification theory within dimensionality reduction, allowing for application to a wide range of high-dimensional biomedical data classification and segmentation problems. Our generalizable framework allows for improved representation and classification in the context of both imaging and non-imaging data. The algorithm offers a promising solution to problems that currently plague DR methods, and may allow for extension to other areas of biomedical data analysis.
Highlights
Dimensionality reduction (DR) enables the construction of a lower dimensional space from a higher dimensional feature space while preserving object-class discriminability
Experiment 1: Synthetic MNI Brain data Figure 2 shows qualitative pixel-level white matter (WM) detection results on MNI brain data for comparisons to be made across 3 different noise and inhomogeneity combinations
The original proton density (PD) MRI image for selected combinations of noise and inhomogeneity with the ground truth for WM superposed as a red contour is shown in Figures 2(a), (f), (k)
Summary
Dimensionality reduction (DR) enables the construction of a lower dimensional space (embedding) from a higher dimensional feature space while preserving object-class discriminability. Non-linear DR involves a non-linear mapping of the data into a reduced dimensional space These methods attempt to project data so that relative local adjacencies between high dimensional data objects, rather than some global measure such as variance, are best preserved during data reduction from N- to n-D space [4]. This tends to better retain class-discriminatory information and may account for any non-linear structures that exist in the data (such as manifolds), as illustrated in [5]. Recent work has shown that in several scenarios, classification accuracy may be improved via the use of non-linear DR schemes (rather than linear DR) for gene-expression data [4,8] as well as medical imagery [9,10]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
