A unified framework for multi-lead ECG characterization using Laplacian Eigenmaps

BACKGROUND

The analysis of multi-lead electrocardiographic (ECG) signals requires integrating the information derived from each lead to reach clinically relevant conclusions. This analysis could benefit from methods compacting the information in those leads into lower-dimensional representations (i.e., 2 or 3 dimensions instead of 12).

OBJECTIVE

We propose Laplacian Eigenmaps (LE) to create a unified framework where ECGs from different subjects can be compared and their abnormalities are enhanced.

APPROACH

We conceive a normal reference ECG space based on LE, calculated using signals of healthy subjects in sinus rhythm. Signals from new subjects can be mapped onto this reference space creating a loop per heartbeat that captures ECG abnormalities. A set of parameters, based on distance metrics and on the shape of loops, are proposed to quantify the differences between subjects.

MAIN RESULTS

This methodology was applied to find structural and arrhythmogenic changes in the ECG. The LE framework consistently captured the characteristics of healthy ECGs, confirming that normal signals behaved similarly in the LE space. Significant differences between normal signals and those from patients with ischemic heart disease or dilated cardiomyopathy were detected. In contrast, LE biomarkers did not identify differences between patients with cardiomyopathy and a history of ventricular arrhythmia and their matched controls.

SIGNIFICANCE

This LE unified framework offers a new representation of multi-lead signals, reducing dimensionality while enhancing imperceptible abnormalities and enabling the comparison of signals of different subjects.

Application of the combination method based on RF and LE in near infrared spectral modeling

The dimensionality of near-infrared (NIR) spectral data is often extremely large. Dimensionality reduction of spectral data can effectively reduce the redundant information and correlation between spectral variables and simplify the model, which is crucial to increasing the model's performance. As a nonlinear feature extraction method, Laplacian Eigenmaps (LE) may preserve the local neighborhood information of the dataset, has high robustness, and is simple to compute. However, when the LE algorithm maps the data from high-dimensional space to low-dimensional space, it is often disturbed by irrelevant information and multicollinearity in the spectral data, which lowers the model's prediction performance. Random Frog (RF) algorithm can eliminate noise and collinearity in the spectrum. Therefore, before using the LE algorithm, we use the RF algorithm to eliminate irrelevant information in the spectrum and reduce the correlation between the spectra variables to increase the efficiency of the LE algorithm. We used the RF + LE algorithm to reduce the dimensionality of two public NIRS datasets (soil datasets and pharmaceutical tablets datasets) and compared it with RF and LE algorithms alone. We utilized Partial Least Squares Regression (PLSR) and Support Vector Regression (SVR) to establish regression models. The experimental findings demonstrate that compared with the RF algorithm and LE algorithm, the RF + LE combination method can reduce the dimension of spectral variables and model complexity, and improve regression models' prediction accuracy and stability. It is an effective dimensionality reduction method for the near-infrared spectrum.

Application of adaptive Laplacian Eigenmaps in near infrared spectral modeling

Laplacian Eigenmaps is a nonlinear dimensionality reduction algorithm based on graph theory. The algorithm adopted the Gaussian function to measure the affinity between a pair of points in the adjacency graph. However, the scaling parameter σ in the Gaussian function is a hyper-parameter tuned empirically. Once the value of σ is determined and fixed, the weight between two points depends wholly on the Euclidian distance between them, which is not suitable for multi-scale sample sets. To optimize the weight between two points in the adjacency graph and make the weight reflect the scale information of different sample sets, an adaptive LE improved algorithm is used in this paper. Considering the influence of adjacent sample points and multi-scale data, the Euclidean distance between the k-th nearest sample point to sample point x_i is used as the local scaling parameter σ_i of x_i, instead of using a single scaling parameter σ. The efficiency of the algorithm is testified by applying on two public near-infrared data sets. LE-SVR and ALE-SVR models are established after LE and ALE dimension reduction of SNV preprocessed data sets. Compared with the LE-SVR model, the R² and RPD of the ALE-SVR model established on the two data sets are improved, while RMSE is decreased, indicating that the prediction effect and stability of the regression model are established by the ALE algorithm are better than that of the traditional LE algorithm. Experiments show that the ALE algorithm can achieve a better dimensionality reduction effect than the LE algorithm.

Computing low-dimensional representations of speech from socio-auditory structures for phonetic analyses

Low-dimensional representations of speech data, such as formant values extracted by linear predictive coding analysis or spectral moments computed from whole spectra viewed as probability distributions, have been instrumental in both phonetic and phonological analyses over the last few decades. In this paper, we present a framework for computing low-dimensional representations of speech data based on two assumptions: that speech data represented in high-dimensional data spaces lie on shapes called manifolds that can be used to map speech data to low-dimensional coordinate spaces, and that manifolds underlying speech data are generated from a combination of language-specific lexical, phonological, and phonetic information as well as culture-specific socio-indexical information that is expressed by talkers of a given speech community. We demonstrate the basic mechanics of the framework by carrying out an analysis of children's productions of sibilant fricatives relative to those of adults in their speech community using the phoneigen package - a publicly available implementation of the framework. We focus the demonstration on enumerating the steps for constructing manifolds from data and then using them to map the data to a low-dimensional space, explicating how manifold structure affects the learned low-dimensional representations, and comparing the use of these representations against standard acoustic features in a phonetic analysis. We conclude with a discussion of the framework's underlying assumptions, its broader modeling potential, and its position relative to recent advances in the field of representation learning.

Histopathological image analysis for centroblasts classification through dimensionality reduction approaches

We present two novel automated image analysis methods to differentiate centroblast (CB) cells from noncentroblast (non-CB) cells in digital images of H&E-stained tissues of follicular lymphoma. CB cells are often confused by similar looking cells within the tissue, therefore a system to help their classification is necessary. Our methods extract the discriminatory features of cells by approximating the intrinsic dimensionality from the subspace spanned by CB and non-CB cells. In the first method, discriminatory features are approximated with the help of singular value decomposition (SVD), whereas in the second method they are extracted using Laplacian Eigenmaps. Five hundred high-power field images were extracted from 17 slides, which are then used to compose a database of 213 CB and 234 non-CB region of interest images. The recall, precision, and overall accuracy rates of the developed methods were measured and compared with existing classification methods. Moreover, the reproducibility of both classification methods was also examined. The average values of the overall accuracy were 99.22% ± 0.75% and 99.07% ± 1.53% for COB and CLEM, respectively. The experimental results demonstrate that both proposed methods provide better classification accuracy of CB/non-CB in comparison with the state of the art methods.