Linear Discriminant Analysis for Functional Data

2019 ◽  
Vol 09 (02) ◽  
pp. 156-164
Author(s):  
馨彤 王
Keyword(s):  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Functional Data ◽  
Linear Discriminant

scholarly journals Multi-class classification of biomechanical data: A functional LDA approach based on multi-class penalized functional PLS

2019 ◽  
pp. 1471082X1787115
Author(s):  
M. Carmen Aguilera-Morillo ◽  
Ana M. Aguilera
Keyword(s):  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Functional Data ◽  
Repeated Measures ◽  
Linear Acceleration ◽  
Human Movement ◽  
Angular Rotation ◽  
Kinematic Data ◽  
Linear Discriminant ◽  
Multi Class Classification

A functional linear discriminant analysis approach to classify a set of kinematic data (human movement curves of individuals performing different physical activities) is performed. Kinematic data, usually collected in linear acceleration or angular rotation format, can be identified with functions in a continuous domain (time, percentage of gait cycle, etc.). Since kinematic curves are measured in the same sample of individuals performing different activities, they are a clear example of functional data with repeated measures. On the other hand, the sample curves are observed with noise. Then, a roughness penalty might be necessary in order to provide a smooth estimation of the discriminant functions, which would make them more interpretable. Moreover, because of the infinite dimension of functional data, a reduction dimension technique should be considered. To solve these problems, we propose a multi-class approach for penalized functional partial least squares (FPLS) regression. Then linear discriminant analysis (LDA) will be performed on the estimated FPLS components. This methodology is motivated by two case studies. The first study considers the linear acceleration recorded every two seconds in 30 subjects, related to three different activities (walking, climbing stairs and down stairs). The second study works with the triaxial angular rotation, for each joint, in 51 children when they completed a cycle walking under three conditions (walking, carrying a backpack and pulling a trolley). A simulation study is also developed for comparing the performance of the proposed functional LDA with respect to the corresponding multivariate and non-penalized approaches.

scholarly journals Multi-class classification of biomechanical data: A functional LDA approach based on multi-class penalized functional PLS

2020 ◽  
Vol 20 (6) ◽  
pp. 592-616
Author(s):  
M. Carmen Aguilera-Morillo ◽  
Ana M. Aguilera
Keyword(s):  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Functional Data ◽  
Repeated Measures ◽  
Linear Acceleration ◽  
Human Movement ◽  
Angular Rotation ◽  
Kinematic Data ◽  
Linear Discriminant ◽  
Multi Class Classification

A functional linear discriminant analysis approach to classify a set of kinematic data (human movement curves of individuals performing different physical activities) is performed. Kinematic data, usually collected in linear acceleration or angular rotation format, can be identified with functions in a continuous domain (time, percentage of gait cycle, etc.). Since kinematic curves are measured in the same sample of individuals performing different activities, they are a clear example of functional data with repeated measures. On the other hand, the sample curves are observed with noise. Then, a roughness penalty might be necessary in order to provide a smooth estimation of the discriminant functions, which would make them more interpretable. Moreover, because of the infinite dimension of functional data, a reduction dimension technique should be considered. To solve these problems, we propose a multi-class approach for penalized functional partial least squares (FPLS) regression. Then linear discriminant analysis (LDA) will be performed on the estimated FPLS components. This methodology is motivated by two case studies. The first study considers the linear acceleration recorded every two seconds in 30 subjects, related to three different activities (walking, climbing stairs and down stairs). The second study works with the triaxial angular rotation, for each joint, in 51 children when they completed a cycle walking under three conditions (walking, carrying a backpack and pulling a trolley). A simulation study is also developed for comparing the performance of the proposed functional LDA with respect to the corresponding multivariate and non-penalized approaches.

Effect of Topography on Maize Grains Elemental Profile: A Chemometric Approach

2020 ◽  
Vol 16 (8) ◽  
pp. 1079-1087
Author(s):  
Jorgelina Z. Heredia ◽  
Carlos A. Moldes ◽  
Raúl A. Gil ◽  
José M. Camiña
Keyword(s):  
Cluster Analysis ◽  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Microwave Plasma ◽  
Emission Spectrometry ◽  
Linear Discriminant ◽  
Maize Seeds ◽  
Elemental Profile ◽  
Mineral Profile ◽  
Topographic Characteristics

Background: The elemental composition of maize grains depends on the soil, land and environment characteristics where the crop grows. These effects are important to evaluate the availability of nutrients with complex dynamics, such as the concentration of macro and micronutrients in soils, which can vary according to different topographies. There is available scarce information about the influence of topographic characteristics (upland and lowland) where culture is developed with the mineral composition of crop products, in the present case, maize seeds. On the other hand, the study of the topographic effect on crops using multivariate analysis tools has not been reported. Objective: This paper assesses the effect of topographic conditions on plants, analyzing the mineral profiles in maize seeds obtained in two land conditions: uplands and lowlands. Materials and Methods: The mineral profile was studied by microwave plasma atomic emission spectrometry. Samples were collected from lowlands and uplands of cultivable lands of the north-east of La Pampa province, Argentina. Results: Differentiation of maize seeds collected from both topographical areas was achieved by principal components analysis (PCA), cluster analysis (CA) and linear discriminant analysis (LDA). PCA model based on mineral profile allowed to differentiate seeds from upland and lowlands by the influence of Cr and Mg variables. A significant accumulation of Cr and Mg in seeds from lowlands was observed. Cluster analysis confirmed such grouping but also, linear discriminant analysis achieved a correct classification of both the crops, showing the effect of topography on elemental profile. Conclusions: Multi-elemental analysis combined with chemometric tools proved useful to assess the effect of topographic characteristics on crops.

Colorectal Cancer Classification and Survival Analysis Based on an Integrated RNA and DNA molecular signature

2020 ◽  
Vol 15 ◽  
Author(s):  
Mohanad Mohammed ◽  
Henry Mwambi ◽  
Bernard Omolo
Keyword(s):  
Colorectal Cancer ◽  
Survival Analysis ◽  
Discriminant Analysis ◽  
Linear Discriminant Analysis ◽  
Negative Binomial ◽  
Sub Saharan Africa ◽  
Support Vector ◽  
Mutation Status ◽  
Linear Discriminant ◽  
Rnaseq Data

Background: Colorectal cancer (CRC) is the third most common cancer among women and men in the USA, and recent studies have shown an increasing incidence in less developed regions, including Sub-Saharan Africa (SSA). We developed a hybrid (DNA mutation and RNA expression) signature and assessed its predictive properties for the mutation status and survival of CRC patients. Methods: Publicly-available microarray and RNASeq data from 54 matched formalin-fixed paraffin-embedded (FFPE) samples from the Affymetrix GeneChip and RNASeq platforms, were used to obtain differentially expressed genes between mutant and wild-type samples. We applied the support-vector machines, artificial neural networks, random forests, k-nearest neighbor, naïve Bayes, negative binomial linear discriminant analysis, and the Poisson linear discriminant analysis algorithms for classification. Cox proportional hazards model was used for survival analysis. Results: Compared to the genelist from each of the individual platforms, the hybrid genelist had the highest accuracy, sensitivity, specificity, and AUC for mutation status, across all the classifiers and is prognostic for survival in patients with CRC. NBLDA method was the best performer on the RNASeq data while the SVM method was the most suitable classifier for CRC across the two data types. Nine genes were found to be predictive of survival. Conclusion: This signature could be useful in clinical practice, especially for colorectal cancer diagnosis and therapy. Future studies should determine the effectiveness of integration in cancer survival analysis and the application on unbalanced data, where the classes are of different sizes, as well as on data with multiple classes.

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