Consensus embedding: theory, algorithms and application to segmentation and classification of biomedical data

Applications 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.We 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.The analysis and classification of high-dimensional biomedical data has been significantly facilitated via the use of dimensionality reduction techniques, which allow classifier schemes to overcome issues such as the curse of dimensionality. This is an issue where the number of variables (features) is disproportionately large compared to the number of training instances (objects) [1]. Dimensionality reduction (DR) involves the projection of data originally represented in a N-dimensional (N-D) space into a lower n-dimensional (n-D) space (known as an embedding) such that n << N. DR techniques are broadly categorized as linear or non-linear, based on the type of projection method used.Linear DR techniques make use of simple linear