Multiclass Linear Discriminant Analysis With Ultrahigh-Dimensional Features

Liu, Yanming; Hong, Hyokyoung Grace; Yi, Li

doi:10.1111/biom.13065

Cited by 13 publications

(17 citation statements)

References 39 publications

(71 reference statements)

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“…As stated before, jointly estimating the whole Ω matrix of all 185,000 voxels is computationally prohibitive. Here we employed a “divide-and-conquer” algorithm introduced in Li et al 36 , to detect the local brain networks. The local networks are much smaller in size and thus their corresponding precision matrices are much easier to calculate.…”

Section: Methodsmentioning

confidence: 99%

“…They are, therefore, usually ignored in contemporary neuroimaging association studies. However, when taken into consideration their connections with other signals, marginally weak signals could exude strong predictive effects 35,36 . Such a case is illustrated in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we analyzed the ADNI Fluorine-fluorodeoxyglucose (FDG)-PET imaging and clinical data by detecting local brain networks and marginally weak signals 36 . To the best of our knowledge, this is the first whole-brain voxel-level connectivity study in the literature.…”

Section: Introductionmentioning

confidence: 99%

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A machine-learning approach for detection of local brain networks and marginally weak signals identifies novel AD/MCI differentiating connectomic neuroimaging biomarkers

Liu

Kang

et al. 2021

Preprint

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Introduction: A computationally fast machine learning method is introduced for uncovering the whole-brain voxel-level connectomic spectra that differentiates different status of Alzheimer's disease (AD). The method is applied to the Alzheimer's Disease Neuroimaging Initiative (ADNI) Fluorine-fluorodeoxyglucose Positron Emission Tomography (FDG-PET) imaging and clinical data and identified novel AD/MCI differentiating connectomic neuroimaging biomarkers. Methods: A divide-and-conquer algorithm is introduced for detect informative local brain networks at voxel level and whole-brain scale. The connection information within the local networks is integrated into the node voxels, which makes detection of the marginally weak signals possible. Prediction accuracy is significantly improved by incorporating the local brain networks and marginally weak signals. Results: Brain connectomic structures differentiating AD and mild cognitive impairment (MCI), AD and healthy, and MIC and healthy were discovered. We identified novel AD/MCI-associated neuroimaging biomarkers by integrating local brain networks and marginally weak signals. For example, network-based signals in paracentral lobule (p-value=6.1e-5), olfactory cortex (p-value=4.6e-5), caudate nucleus (1.8e-3) and precentral gyrus (1.8e-3) are informative in differentiating AD and MCI. Connections between calcarine sulcus and lingual gyrus (p-value=0.049), between parahippocampal gyrus and Amygdala (p-value=0.025), between rolandic opercula and insula lobes (p-values=0.0028 and 0.0026). An overall prediction accuracy of 95.3% was achieved by integrating the selected local brain networks and marginally weak signals, compared to 84.0% by not considering the inter-voxel connections and using marginally strong signals only. Conclusion: (i) The connectomic structures differentiating AD and MCI are significantly different to that differentiating MCI and healthy, which may indicate different neuronal etiology for AD and MCI. (ii) Many neuroimaging biomarkers exert their effects on the outcome diseases through their connections to other markers. Integrating such connections can help identify novel neuroimaging biomarkers and improve disease prediction accuracy.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A machine-learning approach for detection of local brain networks and marginally weak signals identifies novel AD/MCI differentiating connectomic neuroimaging biomarkers

Liu

Kang

et al. 2021

Preprint

Self Cite

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“…To deal with the curse of dimensionality, several developments have been made over the last decade or so. For example, among others, new developments include the nearest shrunken centroids [40], shrunken centroids regularized discriminant analysis [18], features annealed independence rule (fair) [12], sparse and penalized LDA [38,42], regularized optimal affine discriminant (road) [13], multi-group sparse discriminant analysis [16], pairwise sure independent screening [29], and the ultra highdimensional multiclass LDA [23]. The general idea of these methods is to incorporate a feature selection strategy in a classifier in order to obtain certain optimality properties in the sense of misclassification rates.…”

Section: Introductionmentioning

confidence: 99%

New hard-thresholding rules based on data splitting in high-dimensional imbalanced classification

Mojiri

Khalili

Hamadani

2022

Electron. J. Statist.

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In binary classification, imbalance refers to situations in which one class is heavily under-represented. This issue is due to either a data collection process or because one class is indeed rare in a population. Imbalanced classification frequently arises in applications such as biology, medicine, engineering, and social sciences. In this paper, for the first time, we theoretically study the impact of imbalance class sizes on the linear discriminant analysis (LDA) in high dimensions. We show that due to data scarcity in one class, referred to as the minority class, and highdimensionality of the feature space, the LDA ignores the minority class yielding a maximum misclassification rate. We then propose a new construction of hard-thresholding rules based on a data splitting technique that reduces the large difference between the misclassification rates. We show that the proposed method is asymptotically optimal. We further study two well-known sparse versions of the LDA in imbalanced cases. We evaluate the finite-sample performance of different methods using simulations and by analyzing two real data sets. The results show that our method either outperforms its competitors or has comparable performance based on a much smaller subset of selected features, while being computationally more efficient. MSC2020 subject classifications: 62H30.

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“…As in our brain‐GWAS, each response image consists of Q ≈ 350,000 voxels, and each genome consists of P ≈ 560,000 SNPs, while we only have n = 373 samples. Furthermore, conditions that guarantee selection consistency for the MSGLasso may fail to hold for ultrahigh‐dimensional cases (Li, Hong & Li 2019).…”

Section: Introductionmentioning

confidence: 99%

A structured brain‐wide and genome‐wide association study using ADNI PET images

et al. 2021

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A multistage variable selection method is introduced for detecting association signals in structured brain-wide and genome-wide association studies (brain-GWAS). Compared to conventional methods that link one voxel to one single nucleotide polymorphism (SNP), our approach is more efficient and powerful in selecting the important signals by integrating anatomic and gene grouping structures in the brain and the genome, respectively. It avoids resorting to a large number of multiple comparisons while effectively controlling the false discoveries. Validity of the proposed approach is demonstrated by both theoretical investigation and numerical simulations. We apply our proposed method to a brain-GWAS using Alzheimer's Disease Neuroimaging Initiative positron emission tomography (ADNI PET) imaging and genomic data. We confirm previously reported association signals and also uncover several novel SNPs and genes that are either associated with brain glucose metabolism or have their association significantly modified by Alzheimer's disease status.

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Multiclass Linear Discriminant Analysis With Ultrahigh-Dimensional Features

Cited by 13 publications

References 39 publications

A machine-learning approach for detection of local brain networks and marginally weak signals identifies novel AD/MCI differentiating connectomic neuroimaging biomarkers

A machine-learning approach for detection of local brain networks and marginally weak signals identifies novel AD/MCI differentiating connectomic neuroimaging biomarkers

New hard-thresholding rules based on data splitting in high-dimensional imbalanced classification

A structured brain‐wide and genome‐wide association study using ADNI PET images

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