Multivariate analysis of Brillouin imaging data by supervised and unsupervised learning

Abstract

Brillouin imaging relies on the reliable extraction of subtle spectral information from hyperspectral datasets. To date, the mainstream practice has been to use line fitting of spectral features to retrieve the average peak shift and linewidth parameters. Good results, however, depend heavily on sufficient signal-to-noise ratio and may not be applicable in complex samples that consist of spectral mixtures. In this work, we thus propose the use of various multivariate algorithms that can be used to perform supervised or unsupervised analysis of the hyperspectral data, with which we explore advanced image analysis applications, namely unmixing, classification and segmentation in a phantom and live cells.The resulting images are shown to provide more contrast and detail, and obtained on a timescale $10 2 faster than fitting. The estimated spectral parameters are consistent with those calculated from pure fitting.

Brillouin–Raman micro-spectroscopy and machine learning techniques to classify osteoarthritic lesions in the human articular cartilage

“…Moreover, PCA, among the other techniques of multivariate statistics, provides discriminants in the distribution—i.e., the principal components (PCs)—more easily interpretable, allowing the qualitative evaluation of the spectral differences generating these clusters. It is widely used in Raman spectroscopy 37 , 38 , but up to the present, only rarely applied to the Brillouin spectrum (for further details see Materials and method section) 39 . The scatter plot at the top of Fig.…”

“…LDA analysis is a method for the reduction of the dimensionality of a dataset similar to a PCA. However, it is a supervised method that in addition to finding the component axes that maximize the variance of the data, also found the axes that maximize the separation between the labelled categories, usually allowing better performances of ML in the discrimination of the subgroups (more details are provided in the Materials and Method section) 39 .…”

“…Principal component analysis (PCA) was applied to the Brillouin spectra collected in different regions of interest to reveal trends in the spectral features useful for the classification of the distinct mechanical phenotypes. PCA is an unsupervised method used to reduce the dimensionality of the dataset, by identifying combinations of variables (the Brillouin intensities at each frequency) more involved in the description of the spectral variance 38 , 39 . The information obtained from the PCA analysis was used to build up a machine learning (ML) algorithm based on Linear Discriminant Analysis (LDA).…”

“…The information obtained from the PCA analysis was used to build up a machine learning (ML) algorithm based on Linear Discriminant Analysis (LDA). LDA is a generalization of Fisher's linear discriminant, finding a linear combination of variables that characterizes or separates known classes of objects (supervised method) 39 . PCA and the LDA-based machine learning algorithm were performed in the Rstudio environment ( www.rstudio.com ) using the basic R package for the PCA algorithm and “mass”,“caret”, “e1071”, and “ROCR” R packages for the ML-LDA model, respectively.…”

Principal component analysis in application to Brillouin microscopy data

“…The data collected in a typical Brillouin imaging experiment consists of a few thousand individual spectra, each representing up to a thousand of points across the frequency range of interest. Therefore, high-dimensionality is one of the common challenges in analysis of Brillouin imaging data [7]. Each Brillouin spectrum demonstrates a set of peaks associated with inelastic scattering of light by hypersound waves inside the material.…”