Linear discriminant analysis

Summary

Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification. LDA is closely related to analysis of variance (ANOVA) and regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements. However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant analysis has continuous independent variables and a categorical dependent variable (i.e. the class label). Logistic regression and probit regression are more similar to LDA than ANOVA is, as they also explain a categorical variable by t

Official source

https://en.wikipedia.org/wiki/Linear_discriminant_analysis

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Kernel Density Estimation of Electromyographic Signals and Ensemble Learning for Highly Accurate Classification of a Large Set of Hand/Wrist Motions

Parviz Ghaderi

The performance of myoelectric control highly depends on the features extracted from surface electromyographic (sEMG) signals. We propose three new sEMG features based on the kernel density estimation. The trimmed mean of density (TMD), the entropy of density, and the trimmed mean absolute value of derivative density were computed for each sEMG channel. These features were tested for the classification of single tasks as well as of two tasks concurrently performed. For single tasks, correlation-based feature selection was used, and the features were then classified using linear discriminant analysis (LDA), non-linear support vector machines, and multi-layer perceptron. The eXtreme gradient boosting (XGBoost) classifier was used for the classification of two movements simultaneously performed. The second and third versions of the Ninapro dataset (conventional control) and Ameri's movement dataset (simultaneous control) were used to test the proposed features. For the Ninapro dataset, the overall accuracy of LDA using the TMD feature was 98.99 +/- 1.36% and 92.25 +/- 9.48% for able-bodied and amputee subjects, respectively. Using ensemble learning of the three classifiers, the average macro and micro-F-score, macro recall, and precision on the validation sets were 98.23 +/- 2.02, 98.32 +/- 1.93, 98.32 +/- 1.93, and 98.88 +/- 1.31%, respectively, for the intact subjects. The movement misclassification percentage was 1.75 +/- 1.73 and 3.44 +/- 2.23 for the intact subjects and amputees. The proposed features were significantly correlated with the movement classes [Generalized Linear Model (GLM); P-value < 0.05]. An accurate online implementation of the proposed algorithm was also presented. For the simultaneous control, the overall accuracy was 99.71 +/- 0.08 and 97.85 +/- 0.10 for the XGBoost and LDA classifiers, respectively. The proposed features are thus promising for conventional and simultaneous myoelectric control.

FRONTIERS MEDIA SA2022

Wavelet Density Estimators in Discriminant Analysis

Olivier Renaud

The purpose of discriminant analysis is to predict group membership of an individual on the basis of a set of measurements that have been made on it. In this goal, the availability of a learning sample, for which it is know where each individual came from, is assumed. In this context, the thresholded wavelet density estimator may capture more easily fine structures of group differences than usual linear density estimators (such as kernel-based methods). This does not apply ``as is'' in high dimensional space. However, in the univariate case, the estimator behaves well, and can, therefore, be used in the framework of Projection Pursuit Discriminant Analysis, a method that searches for the one-dimension projection that best separates the groups.

1996

Humans use their hands mainly for grasping and manipulating objects, performing simple and dexterous tasks. The loss of a hand may significantly affect one's working status and independence in daily life. A restoration of the grasping ability is important to improve the quality of the daily life of the patients with motion disorders. Although neuroprosthetic devices restore partially the lost functionality, the user acceptance is low, possibly due to the artificial and unnatural operation of the devices. This thesis addresses this problem in reach-to-grasp motions with the development of shared control approaches that enable a seamless and more natural operation of hand prosthesis. In the first part, we focus on the identification of the grasping intention during the reach-to-grasp motion with able-bodied individuals. We propose an Electromyographic (EMG)-based learning approach that decodes the grasping intention at an early stage of reach-to-grasp motion, i.e. before the final grasp/hand pre-shape takes place. In this approach, the utilization of Echo State Networks encloses efficiently the dynamics of the muscle activation enabling a fast identification of the grasp type in real-time. We also examine the impact of different object distance and speed on the detection time and accuracy of the classifier. Although the distance from the object has no significant effect, fast motions influence significantly the performance. In the second part, we evaluate and extend our approach on four real end-users, i.e. individuals with below the elbow amputation. For addressing the variability of the EMG signals, we separate the reach-to-grasp motion into three phases, with respect to the arm extension. A multivariate analysis of variance on the muscle activity reveals significant differences among the motion phases. Additionally, we examine the classification performance on these phases and compare the performance of different pattern recognition methods. An on-line evaluation with an upper-limb prosthesis shows that the inclusion of the reaching motion in the training of the classifier improves importantly classification accuracy. In the last part of the thesis, we explore further the concept of motion phases on the EMG signals and its potentials on addressing the variability of the signals. We model the dynamic muscle contractions of each class with Gaussian distributions over the different phases of the overall motion. We extend our previous analysis providing insights on the LDA projection and quantifying the similarity of the distributions of the classes (i.e grasp types) with the Hellinger distance. We notice larger values of the Helinger distance and, thus, smaller overlaps among the classes with the segmentation to motion phases. A Linear Discriminant Analysis classifier with phase segmentation affects positively the classification accuracy.

EPFL2019

Kernel Density Estimation of Electromyographic Signals and Ensemble Learning for Highly Accurate Classification of a Large Set of Hand/Wrist Motions

Parviz Ghaderi

FRONTIERS MEDIA SA2022