Alzheimer’s disease (AD) is a neurodegenerative disease. Compared to cognitively normal individuals, the AD patient’s brain undergoes morphological or functional changes. For example, Kazemifar et al. (2014) found significant atrophy of the temporal cortex in AD patients. Supekar et al. (2008) used resting-state fMRI to find reduced local efficiency of functional brain networks in AD patients. Buckner et al. (2009) used resting-state fMRI data to find that the distribution of core nodes in the functional brain network overlaps highly with the brain regions where Aß amyloid is deposited in AD patients. It means that the brain connection hub area is vulnerable to receive attacks. Zhou et al. (2012) used resting-state functional brain networks to predict the course of developmental changes in AD pathology. These studies above not only provide experimental evidence for the brain region disconnection hypothesis of AD from the perspective of functional integration, but also provide an explanation for the abnormalities in functional integration of the AD brain.

The AD Neuroimaging Initiative (ADNI), led by Dr. Weiner, was launched in 2004. This is a long-term research plan jointly composed of several institutions. It integrates the database of multi-center and cross-disciplinary longitudinal studies carried out by various methods. Such as clinical cognitive function evaluation, neuroimaging examination, and detection of molecular biological markers of cerebrospinal fluid and blood (Susanne et al., 2005). Its primary goal is to explore the patterns of relationships between clinical, cognitive, imaging, genetic and biomarker features as the disease progresses. It also has the goal of establishing standardized methods for imaging/biomarker collection and analysis, and ultimately for use in clinical research.

In 2004, Huang et al. (2004) proposed the Extreme Learning Machine (ELM). ELM generates random input weights and uses the Moore-Penrose pseudo-inverse (MPP) to calculate the output weights. It is a feed-forward neural network based on randomization(RFNN). The RFNN was introduced by Schmidt et al. (1992) and Suganthan and Katuwal (2021). Methods using random input weights and MPP also include random vector function linked neural networks (RVFL) (Pao et al., 1994), and a method proposed by Guo et al. (1995).

The ELM be widely used in many fields such as disease diagnosis, traffic sign recognition, image quality assessment and so on (Chyzhyk et al., 2015; Huang et al., 2016; Wang et al., 2016). ELM strives to solve the research problems in machine learning fields such as regression, classification, supervised learning and unsupervised learning under a single framework (Huang et al., 2014). From the perspective of learning efficiency, ELM is concise to implement, with extremely high learning speeds and less human intervention. From the perspective of theoretical studies, ELM can still maintain SLFN’s interpolation ability (Huang et al., 2016), general approximation ability (Huang and Chen, 2007) and classification ability (Huang et al., 2012) even in the case of randomly generating hidden layer neuron parameters. From the perspective of structural risk minimization, the VC dimensionality (Vapnik-Chervonenkis dimensionality) of ELM depends on the number of neurons in the hidden layer (Liu et al., 2012). The size of the VC dimensionality can be controlled by adjusting the number of neurons in the hidden layer of ELM, to make a compromise between training error and model complexity, and get the optimal generalization performance. ELM has also been extended to a deep learning model (Tang et al., 2015; Kim et al., 2017), and made a lot of research results.

In recent years, RFNN has also been gradually used for AD studies based on medical images. Sharma et al. (2021) proposed that the FAF-DRVFL method achieved 86.67% accuracy in classifying AD with CN. Malik et al. (2022) proposed the IFRVFL method for diagnosing AD. Its performance is better than standard ELM and RVFL. Lama and Kwon (2021) proposed the ElM+Graph embedding method achieved 90.93% accuracy in classifying AD, MCI, CN. Nguyen et al. (2019) proposed the MVPA+ELM method achieved 98.86% accuracy in classifying AD, MCI, CN. The RFNN is often used as a classifier in these studies. It is mainly used to process selected low-dimensional features. Few studies have used RFNN as a feature screening method.

The ELM classifier has redundant hidden layer nodes when the number of hidden layer nodes is large enough. Rong et al. (2008) proposed the method Pruned-Extreme Learning Machine (P-ELM), as well as Miche et al. (2010, 2011) improved the P-ELM method, which was used to pruning of the hidden layer nodes with the aim of making the ELM classifier more compact, with high speed and more robustness. But it cannot improve the accuracy of the classifier. In ELM classifiers with high feature dimensionality, some input nodes have no positive effect on classification. Useless input nodes are removed using the idea of P-ELM. It can screen features that have an impact on the classification. It may even improve the accuracy of the classifier.

We analyzed the state of machine learning techniques in diagnosing AD (Tanveer et al., 2020). We found no method to prune the network to extract key features. Some of the work involving AD feature extraction (Bi et al., 2018; Richhariya et al., 2020; Hao et al., 2021; Sadiq et al., 2021) have achieved good results in terms of classification accuracy, but none have assigned weights to the importance of these features. In this study, we propose a novel key features screening method based on extreme learning machine (KFS-ELM) to screen key features of AD. It is a data-driven approach that is not based on empirical assumptions or prerequisites. It prunes the ELM classifier to determine the relationship between each feature and AD, screens the key features, and identifies their importance. This will make the key features more intuitive, facilitate the study of the patterns behind AD, and benefit the construction of better classifiers to diagnose AD. The KFS-ELM can be used not only for studying AD, but also for other research fields where the studied subjects have a high dimension of features.

The rest of this article is organized as follows. The section “Materials and Methods” describes the “Brain Functional Connectivity Network,” “ELM,” and “KFS-ELM method.” The section “Experiment” introduces the experimental procedure, experimental environment, data preparation, screening of key features by the KFS-ELM method, and validation of key features. The section “Results” presents the streamlining ability of the KFS-ELM method, the distribution of the screened key features, and the effect of the key features on the classification of the ELM classifier. The section “Discussion” discusses the limitations of the ELM method and the advantages of the KFS-ELM method, and analyzes the key features. The section “Conclusion” summarizes the work of this study.

According to the KFS-ELM method, the accuracy of ELM classification constructed using the key feature set corresponding to W* is no longer improved when screening to the 17th group Wⁱ. The accuracy of the 17 ELM classifiers is shown in Table 1. The average training accuracy is 100%, the average verification accuracy is 97.84%, and the average test accuracy is 92.35%.

The accuracy of the 17 ELM classifiers after pruning is shown in Table 2. After pruning, the average training accuracy of all ELM classifiers remained 100%. the average validation accuracy increased from 97.84% to 99.8%. And the average test accuracy decreased from 92.35 to 84.71%. The number of input nodes and the number of hidden nodes are drastically reduced. The average number of input nodes decreases from 4005 to 106.24, which is 2.65% of the original number of input nodes. The average number of remaining hidden nodes decreased from 64,000 to 1042.53, which is 1.63% of the original number of hidden nodes.

The key features corresponding to the pruned ELM classifier are shown in Figure 2 by the functional connectivity matrix. Figures 2A–C are the image representations of the key features (functional connectivity matrix) of the 1st, 2nd, and 3rd ELM classifier, respectively. Figure 2D is the image representation of W*. The horizontal and vertical coordinates of the image correspond to the serial numbers of the 90 brain regions of the AAL template. The colors of the points correspond to the weights of the key features. The total number of key features corresponding to W* is 920. where the highest weight is 12. That is, the intersection of 17 Wⁱ is empty.

Table 3 shows the performance of testing the classification (diagnosis) ability of key features with different weights versus full features for AD. Perform ten times 10 fold cross-validation and calculate the average of their accuracy rates. The ELM classifier trained using the full amount of features had a test accuracy of 95.33% with a standard deviation of 0.0035. The ELM classifier trained with all key features (920 features, 22.97% of the total number of features) had the highest test accuracy of 99.20% with a standard deviation of 0.0021. When the number of key features is 199 (4.97% of the total number of features), its test accuracy is 95.24%, which is only 0.09% lower than the accuracy of the full number of features. That is, the number of selected features was reduced from 4005 to 199, and the accuracy of the constructed ELM classifier test did not decrease significantly. When the number of selected features is 45 (1.12% of all features), its verification accuracy can still reach 100%, and the test accuracy is 87.84%. When the selected features are further reduced, the accuracy of the ELM classifier is also further reduced. When the number of selected features is 4 or 1, the ELM test accuracy is close to 50%. It is no longer practical to do classification using only these features.

Considering the visualization effect, this paper takes 45 key features with weights greater than or equal to 6 as an example to show their distribution. Table 4 shows the features (functional connectivity) and their corresponding weights. Table 5 shows the brain regions corresponding to the features and their weights. Its weight is the sum of the weights of all functional connections involving that brain region. Figure 3 is a demonstration of these key features. The visualization tool used is BrainNet Viewer (Xia et al., 2013).

Comparing the ELM classifier before and after pruning (according to Tables 2, 3), a significant decrease in the number of input nodes was observed. The average number of input nodes decreased from 4005 to 106.24. Its corresponding number of key features accounts for 2.65% of the total number of features. According to the constraints of Inequality (12) and Inequality (13), removing any of the key nodes will lead to a decrease in the accuracy of the classifier. It shows that all these features are important. The KFS-ELM feature screening experiments yielded 17 groups of key features whose intersection is empty. This indicates that the key features that contribute differently in different classifiers. Therefore, the union of these key feature groups can describe AD more comprehensively.

The performance of the full amount of features and key features in building ELM classifiers was tested in the experiments. The ELM classifier trained using the full amount of features (4,005 features) has a test accuracy of 95.33%. The ELM classifier trained using all key features (920 features) has a test accuracy is 99.20%. It indicates that, training the ELM classifier with fewer features results in higher test accuracy, the 3,085 (4,005 − 920 = 3,085) features that were excluded had a negative effect in classification. Therefore, the KFS-ELM is effective in screening key features.

In this experiment, the weights assigned to the features by KFS-ELM are from 0 to 12, and the bigger the weights, the more important they are. In the testing section, we divided the features into 13 groups according to their weights and gradually excluded the group with the lowest feature weights to test the diagnostic ability of the remaining features for AD. For example, in Table 3, the row where “Weight ≥ 1” indicates the diagnostic ability of all key features (excluding features with weights equal to 0) for AD. Comparing the results of “Weight ≥ 0” and “Weight ≥ 1,” the features with weight equal to 0 play a negative role in AD diagnosis. The row where “Weight ≥ 2” indicates that the key features “Weight = 0” and “Weight = 1” are excluded. Comparing the results of “Weight ≥ 2” and “Weight ≥ 1,” we can judge the effect of the “Weight = 1” feature group on the diagnosis of AD. Adding the feature group of “Weight = 1” to the feature group of “Weight ≥ 2” increased the number of features by 523 (920 - 397), and the training and validation accuracy did not change, while the test accuracy increased by 2.28% (99.20 - 96.92%). That is, the 523 features(“Weight = 1”) contributed 2.28% to the test accuracy of AD. In this way, the effect of the features with weight = 10 on the diagnosis of AD can be shown by comparing the experimental results of “Weight ≥ 10” and “Weight ≥ 11.” The feature group with Weight = 10 contributed 6.10% (87.75 - 81.65%) to the validation accuracy and 8.45% (60.14 - 51.69%) to the test accuracy in AD diagnosis. According to this rule, the effect of feature groups with different weights on AD diagnosis was calculated based on the results in Table 3, as detailed in Table 6. In addition, according to Table 3, the accuracy of the training set was 58.05% when “Weight ≥ 12”, which means that the group of features with Weight = 12 is not enough to distinguish AD from normal people, so this result is not adopted as the basis for Table 6. Therefore, in Table 6, the impact of AD diagnosis can only be assessed for the feature groups with weights from 0 to 10.

Each row in Table 6 indicates the effect of a key feature group on the accuracy of AD diagnosis for a given weight. The first column indicates the weights of the feature group. The second column indicates the number of features in the group. The third column indicates the contribution of the feature group to the validation accuracy. The fourth column indicates the average contribution of each feature in the group to the validation accuracy. The fifth column indicates the contribution of the feature group to the test accuracy. The sixth column indicates the average contribution of each feature in the group to the test accuracy.

According to Table 6, in terms of the contribution of single feature to the validation accuracy (column 4), basically the higher the weight of the feature, the more it contributes to the AD diagnosis (except weight = 9). In terms of the contribution of single feature to the test accuracy (column 6), basically the higher the weight of the feature, the more it contributes to the AD diagnosis (except weight = 8 and weight = 9). Basically, it can be considered that the higher weight the feature has, the greater contribution it makes to the AD diagnosis.

According to the pattern in column 2 of Table 6, the lower the weight of the feature group, the higher amount of features it contains. However, the group with a weight of 9 has fewer features than expected and the group with a weight of 8 has more features than expected. This also caused the contribution of features to diagnose AD deviated when the weight equals 8 and 9. We consider that this is due to the ELM classifier’s randomness in the utilization of features (refer to Figure 2). There are some deviations in the results of feature screening from the probability distribution of the features. Features with weights of 8, 9, 10, 11, and 12 account for 0.27, 0.07, 0.10, 0.07, and 0.02% of all features, respectively, and there are only 22 of these features in total, accounting for 0.55% of the total number of features. If there is a deviation of 0.1% in the feature screening, the results may deviate from the expected pattern, as it happens in Table 6 when the weights are equal to 8 and 9. When the number of features in the feature set is greater than or equal to 17 (0.42% of the total features), no such deviation occurs.

We have taken four references with similar work for comparison, as shown in Table 7. They all use functional connectivity as a feature measure, and they all screen for features as well. All the five studies used different feature screening methods. Bi et al. (2018) obtains feature sets by clustering, without assigning weights. It selects a class with the best classification performance from a large number of classes. Nguyen et al. (2019) set thresholds on the original values of the features. These values do not have a clear relationship with classification. Sadiq et al. (2021) and Hao et al. (2021) have in common that the features are given new weights by the feature screening method. They are both selected the top N features according to the weight. Hao et al. (2021) did not test the effects of different numbers of features on classification. It cannot be shown that there is a clear relationship between the weights of the features and the classification. Sadiq et al. (2021) used the ReliefF method to screen for features. This is a method that is widely used for feature screening. They tried 100, 200, 300, 400, 500 features for classification, respectively. The accuracy did not show a positive correlation with the number of features. Our experimental results show a clear positive correlation between the accuracy and the number of features.

In summary, the KFS-ELM method can rationally identify the weights of key features. The higher the weights of the features, the greater the impact in AD diagnosis.

Extreme learning machine is linearly transformed between the hidden and output layers. The KFS-ELM method has achieved good performance based on ELM. Some other representative RFNN methods may achieve high classification accuracies in scenarios with high-dimensional features, such as RVFL, where it is non-linearly transformed between the hidden and output layers. In the future, we will attempt to use the idea of key feature screening for research on the RVFL. We will also apply the proposed method to explore patterns in AD-like diseases or other brain sciences.

The experimental results and discussion analysis showed that, the KFS-ELM method can effectively screen key features related to the diagnosis of AD, and can assign rational weights to the features to identify their importance for the diagnosis of AD. The KFS-ELM can be used to construct better classifiers for the diagnosis of AD, and can also be used as a feature analysis tool to study the patterns inherent in the brains of AD patients. We consider that the KFS-ELM is also applicable to the classification and the study of feature patterns of the other objects with high feature dimensions, even with small sample sizes.

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

The studies involving human participants were reviewed and approved by ADNI. All the fMRI data used in this manuscript are from LONI’s ADNI database ADNI2 project. It can be downloaded from http://adni.loni.usc.edu. All ADNI participants signed an informed consent form at the time of fMRI and related information collection, and the protocol for consent was approved by the institutional review board at each site. The ethical approval was obtained by ADNI and can be found at http://www.loni.usc.edu/ADNI/. All studies in this manuscript were conducted in accordance with the relevant guidelines.

JL and WZ contributed to the conception of the study. JL performed the experiment and data analyses and wrote the manuscript. JL and LZ contributed significantly to the analysis and manuscript preparation. YS helped to perform the analysis with constructive discussions. All authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.