Robust self management classification via sparse representation based discriminative model for mild cognitive impairment associated with diabetes mellitus

Abstract

Diabetes Mellitus combined with Mild Cognitive Impairment (DM-MCI) is a high incidence disease among the elderly. Patients with DM-MCI have considerably higher risk of dementia, whose daily self-care and life management (i.e. self-management) have a significant impact on the development of their condition. Thus, the inclusion and discrimination of subsequent interventions according to their self-management is an urgent issue. A Sparse-representation-based Discriminative Classification model (SDC) is proposed in this paper to correctly classify MCI-DM patients based on their self-management ability. Specifically, an L₁-minimization sparse representation model, an efficient machine learning model, is used to obtain the sparse histogram that encodes the identity of the test sample. Then, the coefficient of determination is adopted to determine the category based on the sparse histogram of the test sample. Extensive experiments on the self-management data of DM-MCI are conducted to verify the effectiveness of SDC. The experimental results show that the accuracy , precision , recall , and F1-score are 94.3%, 95.0%, 94.3%, and 94.5%, respectively, demonstrating the excellent performance of SDC. The model used in this study has high accuracy and can be used for subgroup discrimination. The use of the sparse representation model in this study has supportive implications for the inclusion of research subjects in clinical intervention strategies.

Introduction

Dementia is a neurodegenerative disease and a common serious disease among the elderly. It not only brings inconvenience to patients in daily life but also imposes a heavy burden on caregivers and society ADDIN EN.CITE¹. Therefore, we should pay attention to the cognitive function of the elderly. Mild Cognitive Impairment (MCI) is a disease characterized by decreased memory and executive abilities and is often favored by researchers as a precursor stage of dementia ADDIN EN.CITE². To screen MCI in elderly, researchers explore non-invasive and predictive bio markers for MCI classification³. A research survey has found that MCI has the features of high incidence and low visit rates⁴. In China, the incidence of mild cognitive impairment is 14.7%, and the conversion rate of developing dementia within an average of 3 years is as high as 50%⁵. However, in the survey conducted by our research group, almost no elderly individuals in the community were aware of or recognized this illness, let alone took any steps to address it. Therefore, MCI has become the focus of this study.

MCI is a comorbidity of Diabetes Mellitus (DM), the researcher called it DM-MCI, and self-management ability is an important factor that affects the progression of DM-MCI. Self-management refers to the control of disease development through positive behavior, such as daily care, healthcare, dietary control and so on. MCI results in decreased executive ability due to decreased neurological function, an essential component of self-management ADDIN EN.CITE⁶. When a patient’s executive ability decreases, their self-management ability decreases accordingly ADDIN EN.CITE⁷. Some studies show that when the self-management ability of DM-MCI patients decreases, the self-management behavior related to blood sugar control will be relatively weakened, and patients may have abnormal blood sugar status, such as hypoglycemia, persistent hyperglycemia, and so on⁸. Then, some studies show that persistent hyperglycemia and frequent hypoglycemia can affect the cognitive function of patients, thus affecting blood sugar control again, forming an adverse cycle ADDIN EN.CITE⁶. Therefore, self-management, as an important factor that affects the progression of DM-MCI, should be studied.

Our team have surveyed the self-management ability of 235 DM-MCI patients based on the Diabetes Self-Care Scale (DSCS) with 6 scores⁹. Then, we conducted a cluster analysis based on the self-management ability of DM-MCI patients in the early stage, and observed three clusters with distinct features. Based on their characteristics, the three clusters are called as Disease neglect type, life-oriented type, and medical dependence type ADDIN EN.CITE¹⁰. Disease neglect type patients often do not pay attention to their related diseases, and score lower on the self-management scale in terms of life management, medication adherence, and healthcare. Life-oriented type patients often perform well in life management but pay less attention to medication adherence. They score higher in life-related scales and slightly lower in medicine-related scales on the self-management ability test. Medical dependence type patients are concerned highly about self-management behaviors related to diseases and medical treatment, and have a high degree of compliance with doctors, but pay less attention to lifestyle as diet and exercise. Implementing corresponding intervention measures based on the characteristics of each cluster of self-management can not only improve personalization but also solve the problem of human resource shortage ADDIN EN.CITE¹¹. It is important to stratify the elderly population based on the most impactful diseases to intervene in a targeted manner¹². However, finding a seamless integration method to include new patients without compromising the integrity of the original classification is an urgent challenge that requires our attention. And sparse representation can solve it. The sparse representation algorithm is an unsupervised learning method used to find a set of “over-complete bases” to represent sample data by highlighting the sample feature efficiently. It is characterized by efficiency, robustness, and accuracy, which is widely used in fields such as signal processing¹³, image processing¹⁴, and facial recognition¹⁵. To fully leverage its superiority to enhance the discriminative ability of medical staff on the self-management level of DM-MCI patients, we attempt to use sparse representation to construct a discriminative model based on the clusters of self-management in the previous study to improve the accuracy and efficiency of patient inclusion in the subsequent study cluster.

Related works

DM-MCI is a common disease among older adults, and self-management is critical to controlling disease progression. Self-management is a kind of intervention that can control their motivation, leading to behavioral change. Prior studies have shown positive results. The researcher made self-management therapy that combines diet, physical activity, blood glucose monitoring, first aid training, clinical and stress management, and telephone guidance to conquer the management of blood glucose ADDIN EN.CITE¹⁶. However, controlling blood glucose may influence cognitive function, so we made some reference to MCI’s intervention. Researchers designed self-management therapy based on the human brain’s forgetting pattern, and patients’ cognitive function and capability of daily life improved after 12 weeks¹⁷.

In our previous work ADDIN EN.CITE¹¹, we have developed a stratified support pattern-based internet-assisted self-management intervention therapy method for DM-MCI, and conduct a randomized controlled trial to explore the effectiveness of this personalization intervention method. The experimental results demonstrate that the personalization intervention method has a strong effect on slowing the decline of cognitive function in patients with DM-MCI.

To further explore the effective personalization intervention for DM-MCI patients, our team have surveyed the self-management ability of 235 DM-MCI patients based on the Diabetes Self-Care Scale (DSCS) and conducted a clusters analysis on the self-management feature⁹. The DSCS survey can provide the self-management feature with 6 dimensions, including diet management, blood glucose monitoring, foot care, exercise, medication according to medical advice, prevention and treatment of hyperglycemia and hypoglycemia emergencies. They are the evaluation scores defined by DSCS, whose numeric domains are 6–30, 4–20, 4–20, 4–20, 5–25, and 3–15, respectively. The higher the score, the more obvious the patient’s performance in that dimension, which is conducive to our classification. According to the cluster analysis on the self-management feature data, DM-MCI patients can be classified into three types, i.e. disease neglect type, life-oriented type, and medical dependence type.

Based on the above works, a sparse-representation-based discriminative classification model is proposed in this paper to classify the new DM-MCI patients into the three types for the personalization intervention therapy.

Objective

To incorporate new patients and classify their self-management type for DM-MCI individual nursing, a sparse-representation-based discriminative classification model is proposed in this paper for robust and efficient patient classification.

Methods

Previously, we investigated the self-management data of DM-MCI patients and classified them using cluster analysis. We have published the classified data in relevant articles ADDIN EN.CITE¹⁰. This study is a sequence study of previous research findings.

A basic problem to solve in this paper is to design a sparse-representation-based discriminative classification model to correctly classify patients with DM-MCI based on their self-management, which is beneficial for medical staff to achieve precise intervention to save medical resources and improve treatment efficiency.

This study was approved by the Fujian Provincial Hospital Ethics Committee (K2022-05-012) and complied with the Helsinki Declaration. All methods are carried out in accordance with relevant guidelines and regulations. Patients who will be willing to participate in the study will sign an informed consent form. Registration number is ChiCTR2200061991.

Sparse representation theory for patient self-management classification

Sparse representation has seen a recent surge of interest in statistical signal processing¹⁸, blind signal separation¹⁹ and object tracking²⁰, which is to compute sparse linear representations with respect to an overcomplete dictionary of base elements. Given sufficient training samples of -th type patients that are obtained by the cluster analysis in the early stage, a test sample will lie in the linear space spanned by training samples from the same cluster of -th type patients, which can be formulated as

where is the new sample, is the total number of -th type patients, is the training samples set with -th type of patients, and is the coefficient vector of the new sample.

Since the type of the new patient (test sample) is initially unknown, we adopt the over-complete dictionary matrix with the entire training set consisting of all three types of patients ( is the total number of the patients in the entire training set), which is defined as

where is the self-management feature of the k-th patient with m dimensions. Then, the type-unknown sample with the self-management feature can be rewritten in terms of all training samples as

1

where is a sparse coefficient vector whose elements are almost zero except those are associated with the test sample , and n is the total number of patients in the entire training set.

As only the feature-related elements in the sparse coefficient vector are activated as non-zero, the sparse coefficient vector encodes the identity of the test sample . Therefore, the clusters of patients can be obtained by solving the linear Eq. (1). It is worth noting that the system of Eq. (1) is overdetermined and un-robust when , which means that the number of patients in the training set is at least larger than the dimension of patient feature to make the sparse representation classifier robust to the noise introduced by the individualized differences in patients. Based on the hypothesis above (), the Eq. (1) is underdetermined and its solution is not unique. Conventionally, this problem can be solved by choosing the minimum L₂-norm or L₁-norm solution, which can be formulated respectively as

2

3

where denotes the L₂-norm, which is the Euclidean distance of the vector. And denotes the L₁-norm, which is the absolute distance of the vector. is the regularization parameter.

Recent research in the sparse representation and the compressed sensing reveal that the solution should be sparse enough to make the classifier robust. And the minimum L₁-norm solution in Eq. (3) is sparser than the L₂-norm solution in Eq. (2). The geometric interpretation can be shown in Fig. 1. The geometric graphs of L₁-norm and L₂-norm in 2D space are a square and a circle, respectively. We can see that the linear representation system in Eq. (1) is easier to obtain zero solutions () under the boundary condition of L₁-norm rather than L₂-norm. Therefore, we adopt the L₁-minimization solution as the encoder to recognize the self-management identity of patients in this paper. In fact, the L₁-minimization problem (3) can be solved by standard linear programming methods in polynomial time, which is fast enough to achieve real-time classification²¹.

Fig. 1.

The geometry analysis for the solutions of ℓ₁-norm and ℓ₂-norm in 2D space.

Sparse-representation-based discriminative DM-MCI classification model

Based on the above analysis, we can see that the self-management identity of patients can be obtained by the sparse representation classifier via Eq. (3), namely L1-minimization. L1-minimization is a convex optimization technique widely used to promote sparsity in solutions. Its key properties include the following three points. First, the L1-norm is convex, making the problem solvable by convex optimization techniques. Second, the L1-norm in Eq. (3) promotes sparsity by penalizing large coefficients less aggressively than the L2-norm but enough to shrink small coefficients to zero. Third, under the certain parameter, the solution of L1-minimization is unique and the sparsest. Ideally, the nonzero elements in the solution will be associated with the training samples from the corresponding patient class in the dictionary matrix. However, the noise introduced by the individualized differences in patients and the modeling error caused by the fitting bias and computational approximation may lead to the activation of multiple error classes, which is shown in Fig. 2. Therefore, a category-score mechanism based on the global representation should be designed to solve this problem and obtain the true category of the test patient.

Fig. 2.

The sparse histogram of a sample confused by the noise and the modeling error.

An intuitive idea to solve the above problem is to assign the test sample to the category with the single largest element in the sparse coefficient vector. For instance, the patient category of the test sample in Fig. 2 can be regarded as the type-3 patient due to the location of the largest element in the type-3 area. However, this method is not robust due to the insufficient utilization of the subspace structure.

In this paper, we adopt the coefficient of determination as the category-score mechanism to determine the patient type based on the global representation, which can be defined as

where denotes the mean value of the test patient’s self-management features and . The value range of the coefficient of determination is . The larger the coefficient of -th type determination , the more similar the test sample to the -th type patients. The coefficient of determination is a crucial metric in regression analysis, quantifying reliability of a sample being classified into a category. From the definition of , it can be seen that this category-score mechanism can fully utilize the subspace structure of the global representation and eliminate the model interference introduced by the feature scale differences, which the model obtains more robust classification performance.

In summary, the procedure of the sparse-representation-based discriminative DM-MCI classification model is shown as Algorithm 1, and the workflow illustration of the proposed method is shown Fig. 3.

Fig. 3.

The workflow illustration.

Algorithm 1.

Sparse-representation-based discriminative DM-MCI classification model.

Experiments and results analysis

In this section, extensive experiments on the self-management data of DM-MCI collected in the early stage are conducted to verify the effectiveness of the sparse-representation-based discriminative DM-MCI classification model.

Self-management data of DM-MCI

The self-management data of 235 DM-MCIs from January 2022 to June 2022 in a provincial tertiary A-level general hospital are adopted in this section. The data is collected based on the Diabetes Self-Care Scale (DSCS), which is the standard evaluation of patient self-management ability. The features of patients include 6 dimensions of the diabetes self-management scores (diet management, medication compliance, regular exercise, blood glucose monitoring, feet care, prevention and treatment of hyperglycemia, and hypoglycemia emergencies), which are highly correlated with the effectiveness of the DM-MCI’s healthcare. According to the scores and sorting of each dimension, they are divided into three categories to highlight their cluster characteristics, which are “Disease neglect type”, “Life-oriented type” and “Medical dependence type”, respectively. Based on the previous works of self-management data collection and processing, we verify the proposed sparse-representation-based discriminative DM-MCI classification model on these data.

Experimental setup

The self-management data of 235 DM-MCIs are divided into the validation set and the training set at the class-associated ratio of 0.175, where 35 DM-MCIs are in the validation set and 200 patients are in the training set. We compose the dictionary matrix A with training samples, and solve the identity of all the test samples in the validation set according to the proposed Algorithm 1. Specifically, we calculate the sparse coefficients and the coefficient of determination of 35 test samples in the validation set, and draw the sparse histogram. Based on the coefficient of determination and the sparse histogram, the types of all the patients can be obtained. Then, we adopt four evaluation metrics to verify the proposed model, which are accuracy , precision , recall , and F1-score .

Accuracy is the proportion of the samples classified correctly by the model in the total sample size, which can be formulated as

where TP, TN, FP and FN are the number of the true positive prediction, the true negative prediction, the false positive prediction, and the false negative prediction, respectively. As a holistic metric to evaluate the model, accuracy is hard to obtain judgment results with information content when there are imbalanced categories in the data.

Precision is the ratio of correctly predicted positive samples to all samples predicted as positive, which can be formulated as

The higher the precision, the more credible the model’s judgment of “positive prediction”.

Recall is the ratio of correctly predicted positive samples to all actual positive samples, which can be formulated as

A higher recall rate means that the model has fewer false positives and a lower probability of missed classifications for samples that are actually positive.

F1-score is the weighted harmonic average of precision and recall to measure their overall performance, which can be formulated as

Implementation details

The proposed sparse-representation-based discriminative DM-MCI classification model is implemented with Python. The regularization parameter in Eq. (3) is set to 0.2. According to the split training set, the dictionary matrix has 200 elements, where disease neglect patients account for 9.5%, life orientation patients account for 32%, and medical dependence patients account for 58.5%. The dimension of the self-management feature is 6. Thus, the dictionary matrix is over-completed () to make the solution robust. Based on the above implementation setting, the test samples in the validation set can be processed by Algorithm 1.

Experiment results

To evaluate the classification performance of the sparse-representation-based discriminative DM-MCI classification model, we conduct experiments on the self-management dataset collected in the previous study⁹, where the total number of samples is 235. We randomly divide the entire dataset into a validation set and a training set at a class-associated ratio of 0.175. Specifically, In the training set, there are 19 disease neglect type patients (type 1), 64 life-oriented type patients (type 2) and 117 medical dependence type patients (type 3), with disease neglect patients accounting for 9.5%, life orientation patients accounting for 32%, and medical dependence patients accounting for 58.5%. In the validation set, there are 4 disease neglect type patients (type 1), 13 life-oriented type patients (type 2) and 18 medical dependence type patients (type 3). It is worth noting that the dataset has the problem of class imbalance. Therefore, it is necessary to introduce multiple evaluation metrics to verify the effectiveness of the proposed model. Then, the test results on the validation set can be obtained by constructing a dictionary matrix with the training set and processing the test samples via Algorithm 1.

With the same class-associated ratio of 0.175, we conducted multiple testing experiments based on random data partitioning. The confusion matrices of three experiments are shown in Fig. 4. We can see that the error predictions are mainly in the disease neglect type patients (type 1) and the life-oriented type patients (type 2). These errors can be attributed to insufficient sample size for these two types of patients. According to the confusion matrix, four evaluation metrics can be obtained by the equations in Sect. 3.2. As shown in Table 1, the average accuracy, precision, recall, and F1-score are 88.6%, 90.4%, 88.6%, and 88.9%, respectively. These results demonstrate the effectiveness of the proposed model.

Fig. 4.

The confusion matrices, where DNT-1, LOT-2, MDT-3 denote disease neglect type (type 1), life-oriented type (type 2), and medical dependence type (type 3), respectively.

Table 1.

Evaluation metrics for the model.

Accuracy (%)	Precision (%)	Recall (%)	F1-score (%)
88.6 5.8	90.4 3.1	88.6 5.8	88.9 5.1

To further illustrate the intrinsic mechanism of the proposed model, the sparse histograms of test samples are shown in Fig. 5. In fact, the activated non-zero elements in the sparse coefficients usually lie in the linear space spanned by training samples from the same cluster. Therefore, the classification mechanism of the proposed model can be visualized in the sparse histogram by structuring the dictionary matrix into three blocks (three types of patients). For instance, in Fig. 5a, d,g, the activated non-zero elements of sparse histogram lie in the subspace of the training samples with the same type, which enables these test samples to be easily and accurately predicted. In Fig. 5c, due to the similarity of the test sample’s features in both the type-1 training samples and the type-2 training samples, some elements in the type-2 region are also activated by mistake, which causes the false prediction. Similarly, the test samples in Fig. 5f, j are mis-predicted. In Fig. 5b, e,h, the test samples are predicted correctly via the category-score mechanism of the coefficient of determination , though some elements are activated incorrectly, which demonstrates the superiority of the coefficient of determination in sparse code recognition.

Fig. 5.

Some test results for three types of patients.

Discussion

In our previous study, our team divided patients into three clusters based on machine learning cluster analysis, which belongs to unsupervised learning and is mainly used to discover hidden patterns in grouped data²². In this study, the sparse representation of deep learning belongs to supervised learning, which analyzes training data and generates inference functions to determine the accuracy of clustering²³. The sparse representation was originally used in speech recognition processing and has a long history. With the advancement of technology, there is higher accuracy in sparse representation. That’s why this kind of algorithm method is highly used.

Through team research, we believe that sparse representation has the following advantages in the medical field. The reasons are as follows: Firstly, sparse representation can automatically perform feature selection and preserve the most important features for classification, reducing computational complexity. This is very important for the nursing field, as efficient and convenient calculation methods can maximize work efficiency. Secondly, sparse representation is robust and can somewhat suppress the influence of irrelevant information. This can prevent the extracted features from being disturbed and maintain the original features of the classification. For other algorithms, such as gradient enhancement, the processing efficiency is relatively low on large-scale datasets. This goes against the original intention of efficient nursing. Based on this, we ultimately choose stable and convenient sparse representation learning.

As to the application, Sparse representation can intuitively determine the probability of the category to which the sample belongs, which is similar to traditional discriminant analysis methods. They all use maximum probability to determine the classification of the sample. However, sparse representation can not only show which clusters it belongs to but also show which patients in the training set have similar characteristics (the higher histograms, the higher the similarity). It can refer to the treatment process and efficacy of patients in the training set (individuals in the training set are equivalent to those who have already been treated). And then sparse representation can see the probability ranking of the cluster of samples through the histogram of sparse coefficients. It is characterized by simple and intuitive. When considering the setting of intervention plans, the probability ranking and density of the samples can be directly seen through the sparsity coefficient to determine the cluster of the samples. If the probability of the samples belonging to two categories is relatively close, it is necessary to combine the characteristics of the two clusters for setting. This intuitive judgment is very helpful for setting intervention plans for patients who fall between the two clusters. Interventions can be set by combining the characteristics of two clusters. Finally, as the number of treatment cases increases and the training set continues to expand, the accuracy of the model will also improve. This study uses sparse representation to construct a discriminative model, which not only improves the efficiency of cluster discrimination but also helps to set intervention measures for patients with fuzzy clusters. This method is conducive to achieving a more comprehensive implementation of precision medicine. For example, patients classified as life-oriented, are characterized by focusing on lifestyle behaviors while neglecting medical utility. These patients will receive monitoring and reminder nursing services for follow-up visits. Patients with medical dependence type, believe that they only need to take medication to cure the disease and ignore their self-management behavior. Medical staff will provide self-management guidance for such patients and educate them on the importance of self-management behavior. The core of offering services for patients with Disease Neglect type is to raise disease awareness, identify adverse clinical manifestations caused by blood glucose management, and make them pay attention to disease control. Through precision nursing services, the role of medical care can be further improved and disease-related costs can be reduced.

Supplementary analyses

To explore the impact of the regularization parameter alternation on classification accuracy, we have conducted the sensitivity analysis about the regularization parameter. As show in Fig. 6, the classification accuracy achieves the highest value with the regularization parameter in the range of [0.1, 0.5]. When the parameters are outside this range, the accuracy of the model begins to decrease. Thus, the regularization parameter in Eq. (3) is set to 0.2 to achieve excellent performance.

Fig. 6.

The sensitivity analysis experiment results.

Conclusion

This study used sparse representation to construct a discriminative model for the early classification research of the team, with an accuracy of 88.6% with high accuracy. In the later stage, our team will set intervention plans and conduct a randomized controlled trial based on cluster features. Research members who enter RCT can be included according to the discriminative model of the sparse representation in this study. Therefore, the methods and results of this study have supportive significance for research subjects in clinical intervention strategies.

Limitations

Firstly, a notable challenge faced by the current research lies in the relatively small sample size, which directly constrains the predictive accuracy and generalization capability of our constructed models. In statistics and machine learning, an adequate sample size is the cornerstone for ensuring the robustness and reliability of models. Insufficient samples may lead to overfitting, where the model performs well on training data but significantly loses predictive power on unseen data. Therefore, expanding the sample size by incorporating more representative data points is a crucial step in enhancing model performance.

Secondly, our model’s variable selection is relatively limited, primarily relying on numerical indicators for analysis. Although these numerical indicators can reflect certain physiological or pathological states, they often overlook the multidimensional characteristics of disease complexity. In medical research, especially in the process of neurodegenerative diseases such as mild cognitive impairment (MCI) transitioning to dementia (e.g., Alzheimer’s disease, AD), the diversity of biomarkers is crucial. The current variable selection may fail to comprehensively capture the subtle differences in disease progression, thereby limiting the model’s ability to understand and predict the complexity of the disease.

To overcome these limitations and achieve more personalized classification in future research, we plan to introduce multimodal data, particularly MRI brain network imaging of patients with diabetes-related mild cognitive impairment (DM-MCI). MRI, as a non-invasive imaging technique, can display changes in brain structure and functional networks with high resolution, providing a powerful tool for revealing the impact of diseases on the brain’s microstructure and connectivity patterns. By analyzing MRI data from DM-MCI patients, we can capture fine-grained features related to the disease, such as specific brain region atrophy, white matter lesions, and functional connectivity abnormalities. These features contribute to a deeper understanding of disease mechanisms and provide a scientific basis for formulating personalized treatment plans.

Author contributions

WYX is the first author, WYX and LH processed the data. WYX and LJX designed the study. LR, YYJ, CMF, LH are supervising its implementation and coordinating the study and have critically revised the manuscript. LH is main corresponding author. All authors contributed to manuscript revision, read, and approved the submitted version. All authors reviewed the manuscript.

Data availability

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.