WO2021103287A1 - 基于弱监督多任务矩阵补全的脑疾病进程预测方法及系统 - Google Patents

基于弱监督多任务矩阵补全的脑疾病进程预测方法及系统 Download PDF

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WO2021103287A1
WO2021103287A1 PCT/CN2020/070259 CN2020070259W WO2021103287A1 WO 2021103287 A1 WO2021103287 A1 WO 2021103287A1 CN 2020070259 W CN2020070259 W CN 2020070259W WO 2021103287 A1 WO2021103287 A1 WO 2021103287A1
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matrix
task
feature
prediction
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陈蕾
王凌胜
查思明
李平
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南京邮电大学
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    • G16H50/00—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
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  • the present invention relates to the fields of artificial intelligence and machine learning, and in particular to a method for predicting the course of brain diseases based on a weakly-supervised multi-task matrix completion model.
  • AD Alzheimer’s disease
  • MMSE Mini-mental State Examination
  • ADAS-Cog Alzheimer’s disease assessment Scale-Cognitive subscale
  • MMSE has been shown to be associated with the progressive deterioration of underlying AD pathology and function.
  • ADAS-Cog is the main criterion for evaluating cognitive function in AD drug trials.
  • RVR correlation vector regression
  • PCA Principal Component Analysis
  • Objective of the invention In order to overcome the problem of sample overfitting and feature noise in the existing disease process prediction research, to propose a brain disease process prediction method and system based on weakly supervised multi-task matrix completion, which can be effectively used
  • the internal relevance of disease states at multiple time points fully mining the low-rank and structural distribution information between samples, selecting task-share features and task-specific features, solving the problem of overfitting, and denoising the samples , So as to obtain a higher prediction accuracy rate.
  • a brain disease process prediction method based on weakly-supervised multi-task matrix completion including the following steps:
  • Step 1 Preprocess the measured values of magnetic resonance imaging MRI, positron emission tomography PET and cerebrospinal fluid CSF measured when the subject goes to the hospital for examination for the first time to obtain magnetic resonance imaging characteristics and positron emission tomography Imaging characteristics, cerebrospinal fluid characteristics.
  • Step 2 Using the multi-task direct push matrix completion model, the disease state prediction at each time point after going to the hospital for examination for the first time is regarded as a single-task regression task, so as to predict the disease state at multiple time points It is modeled as a multi-task regression problem, and the feature matrix is denoised, and the cognitive scoring matrix is predicted in the absence of part of the mark.
  • Step 2 specifically includes the following steps:
  • the formula is as follows:
  • Step 2-2 the purpose of disease progression prediction is to predict the subject’s disease state for a period of time after going to the hospital for examination for the first time, and for specific time points at regular intervals after going to the hospital for examination for the first time
  • the disease state is predicted.
  • the cognitive scores of the Simple Mental State Scale MMSE and the Alzheimer's Disease Assessment Scale-Cognitive Subscale ADAS-Cog were used to indicate the disease state of the subjects.
  • Step 3 Use the hybrid sparse group Lasso feature selection method to select the task-share features shared by all tasks and the unique task-specific features of each task, and use the task-share features and task-specific features to further improve the prediction of the scoring matrix Accuracy rate, so as to complete the prediction of the disease process.
  • Step 3 specifically includes the following steps:
  • Step 3-1 the coefficient matrix Use the l 2,1 norm constraint to make W rows sparse, and obtain W through training, where each row of W corresponds to a feature, and each column corresponds to a task, and the feature corresponding to the non-zero row of W is the task-share feature .
  • Step 3-2 the coefficient matrix Use the l 1 norm constraint to make W arbitrarily sparse, so that random zero values appear in the non-zero rows of W, so the feature corresponding to the non-zero row of W is the task-specific feature of the task corresponding to the non-zero value in the non-zero row .
  • Step 3-3 introduce a time series smoothing regularization term to punish the large deviation of the score prediction at adjacent times.
  • Step 3-4 combining the norm constraints in step 3-1, step 3-2, and step 3-3, the feature selection items for task-share features and task-specific features, also known as mixed sparse group Lasso items:
  • Step 3-5 combine the direct matrix completion model and the mixed sparse group Lasso term in step 3-1 and step 3-4 to obtain the following model:
  • Step 3-6 improve the model in step 3-4 into the following non-convex multi-task regression form:
  • Step 3-7 combining the fast iterative shrinkage threshold algorithm and the DC planning method to design the solution method of the model proposed in step 3-6.
  • F(Z,W) represents the set of derivable terms except the kernel norm in formula (5).
  • ⁇ 1 ( ⁇ ) represents the largest singular value of the matrix in the brackets
  • T represents the transpose of the matrix
  • I d ⁇ d represents the unit matrix with the dimension d ⁇ d.
  • ⁇ X and ⁇ Y respectively represent the set of Z Y element subscripts in Z X, W k-1 and Respectively represent the values of Z X , W and Z Y during the k-1th iteration.
  • Sub-problem 2 in formula (6) is a non-convex optimization problem.
  • the DC programming method is used to approximate the non-convex formula with convex relaxation.
  • the basic principles of the DC programming method are briefly described as follows:
  • l(W) and h(W) represent functions of general formula
  • l(W) and h(W) are convex
  • Equation (11) is expressed in the form of the difference between f(W) and g(h(W)):
  • Formula (6) corresponds to the convex relaxation form of formula (14):
  • W k+1 represents the value of W during the k+1 iteration
  • ⁇ is a small constant term to avoid zero denominator
  • w i represents the i-th row of matrix W
  • w i(t) represents the value of w i in the k-th iteration
  • ⁇ 4 represents the hyperparameter of the feature selection item
  • d Represents the number of features.
  • the method for obtaining magnetic resonance imaging characteristics, positron emission tomography characteristics, and cerebrospinal fluid characteristics in step 1 is as follows:
  • Step 1-1 use anterior commissure AC-posterior commissure PC correction, intensity non-uniformity correction, skull dissection, cerebellectomy based on Atlas registration, and space segmentation for magnetic resonance imaging MRI in sequence, and get the Jacobian
  • the template has 93 manually marked ROI marked images, and the gray matter volume of the 93 manually marked ROIs is calculated as the magnetic resonance imaging feature.
  • Step 1-2 for each positron emission tomography PET, use affine registration to align the positron emission tomography PET image with its respective magnetic resonance imaging MRI, and then use the corresponding magnetic resonance brain mask to obtain the skull The image was stripped, and the average intensity of each manually marked ROI in the PET image was calculated as the positron emission tomography feature.
  • Steps 1-3 for the cerebrospinal fluid CSF, the measured values of CSF A ⁇ 42, CSF t-tau and CSF p-tau are used as cerebrospinal fluid characteristics.
  • demographic characteristics which include the subject’s age, education, and gender.
  • step 2-2 specific time points at regular intervals after the first visit to the hospital for examination include 06 months, 12 months, 24 months, 36 months after the first visit to the hospital for examination, 48 months.
  • a brain disease process prediction system based on weakly supervised multi-task matrix completion including a data acquisition unit, an offline processing unit, and a process prediction unit that are sequentially connected, wherein:
  • the data collection unit is used to collect the measured values of magnetic resonance imaging MRI, positron emission tomography PET and cerebrospinal fluid CSF measured when the subject goes to the hospital for examination for the first time.
  • the offline processing unit includes a data preprocessing module and a model building module, wherein the data preprocessing module is used to preprocess the collected magnetic resonance imaging MRI, positron emission tomography PET and cerebrospinal fluid CSF measurement values, Obtain the characteristics of magnetic resonance imaging, positron emission tomography and cerebrospinal fluid.
  • the model building module is used to use the preprocessed data to train the proposed brain disease process prediction model based on weakly supervised multi-task matrix completion.
  • the process prediction unit is used to predict the brain disease process of the newly-diagnosed subject according to the trained brain disease process prediction model based on weakly supervised multi-task matrix completion.
  • the present invention has the following beneficial effects:
  • MTMC multi-task direct interpolation matrix completion
  • our model is based on the idea of weakly supervised learning, combining labeled training samples and unlabeled test samples to establish the geometric structure of the sample manifold.
  • Figure 1 is a schematic diagram of the system structure of the present invention.
  • Figure 2 is a process flow chart of the present invention.
  • a brain disease process prediction method based on weakly-supervised multi-task matrix completion includes the following steps:
  • Step 1 Preprocess multiple modal data such as magnetic resonance imaging (MRI), positron emission tomography (PET) and cerebrospinal fluid (CSF) measured values measured by multiple subjects on the baseline, Specifically include the following steps:
  • MRI magnetic resonance imaging
  • PET positron emission tomography
  • CSF cerebrospinal fluid
  • Step 1-1 use anterior commissure (AC)-posterior commissure (PC) correction, intensity unevenness correction, skull dissection, cerebellectomy based on Atlas registration for magnetic resonance imaging (MRI) in sequence, Space segmentation and other techniques are used to obtain labeled images with 93 manually labeled regions of interest (ROI) based on the Jacob template, and the gray matter volumes of these 93 ROIs are respectively calculated as features.
  • the baseline refers to the time when the subject went to the hospital for an examination for the first time.
  • Step 1-2 for each positron emission tomography (PET), we first use affine registration to align the PET image with its respective MRI. Then, the corresponding MRI brain mask is used to obtain the skull dissection image, and the average intensity of each ROI in the PET image is calculated as a feature.
  • PET positron emission tomography
  • Steps 1-3 for cerebrospinal fluid (CSF), we use the measured values of CSF A ⁇ 42, CSF t-tau and CSF p-tau as CSF characteristics.
  • Steps 1-4 you can also add some demographic characteristics, such as the subject’s age, education, gender, etc. Studies have shown that demographic characteristics also have a certain impact on the process of brain disease.
  • Step 2 Using the multi-task direct push matrix completion model, the disease state prediction at each time point after the baseline is regarded as a single-task regression task, so that the disease state prediction at multiple time points is modeled as a multi-task Regression problem, denoising the feature matrix, and predicting the cognitive scoring matrix in the absence of part of the marker, specifically including the following steps:
  • the kernel norm constraint on the Z matrix and using the F norm constraint as the fidelity term between the feature matrix X before completion and the feature matrix Z X after completion, the formula is as follows:
  • d represents the number of features
  • n represents the number of samples
  • t represents the number of tasks
  • W represents the weight matrix
  • ⁇ 1 , ⁇ 2 and ⁇ 3 are regularization parameters
  • Step 2-1 the purpose of disease progression prediction is to predict the subject’s disease state for a period of time after the baseline.
  • we calculate the specific time points at regular intervals after the baseline such as 06, 12, 24 after the baseline). , 36, 48 months, etc.).
  • many clinical/cognitive measures have been designed and used as important criteria for the clinical diagnosis of possible AD, such as the Mini Mental State Scale (MMSE) and Alzheimer’s Disease Assessment Scale-Cognitive Subscale (ADAS-Cog)
  • MMSE Mini Mental State Scale
  • ADAS-Cog Alzheimer’s Disease Assessment Scale-Cognitive Subscale
  • the present invention uses these two cognitive scores to indicate the disease state of the subject.
  • the number of training samples is often insufficient, and there is a phenomenon that part of the scoring data is missing.
  • Step 3 At the same time, use the hybrid sparse group Lasso feature selection strategy to select the task-share features shared by all tasks and the task-specific features unique to each task, and use these two features to further improve the prediction accuracy of the scoring matrix To complete the prediction of the disease process, it specifically includes the following steps:
  • Step 3-1 in order to obtain the task-share feature shared by all tasks, the coefficient matrix Using the l 2,1 norm constraint, the W rows are sparse, and W is obtained through training, where each row of W corresponds to a feature, and each column corresponds to a task, and the feature corresponding to the non-zero row of W is the task-share feature.
  • Step 3-2 At the same time, in order to obtain the unique task-specific characteristics of each task, the coefficient matrix Use the l 1 norm constraint to make W arbitrarily sparse, so that random zero values appear in the non-zero rows of W, so the feature corresponding to the non-zero row of W is the task-specific feature of the task corresponding to the non-zero value in the non-zero row .
  • Step 3-3 in order to make full use of the common prior characteristics of time series smoothing in the disease process prediction problem, that is, the clinical cognition scores of adjacent time points should be similar, we introduce the time series smoothing regularization term into the disease process modeling, and compare the relative Adjacent time points out the larger deviation of the forecast and penalizes it.
  • Step 3-4 combining the norm constraints in step 3-1, step 3-2, and step 3-3, the feature selection items for task-share features and task-specific features, also known as mixed sparse group Lasso items:
  • Step 3-5 combine the direct matrix completion model in (3-1) and (4-4) and the Lasso feature selection items of the mixed sparse group to obtain the following model:
  • Steps 3-7 Combine Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) and DC programming method (difference of convex programming techniques) to design a solution method for the model proposed by the present invention.
  • FISTA Fast Iterative Shrinkage-Thresholding Algorithm
  • DC programming method difference of convex programming techniques
  • sub-problem 1 in formula (5) can be solved by the FISTA method, and its convergence has been proved by Beck et al. Specifically, we make:
  • sub-problem 1 can be solved in the following way:
  • ⁇ X and ⁇ Y respectively represent the index set of Z Y elements in Z X.
  • Sub-problem 2 in formula (6) is a non-convex optimization problem, so we use the well-known DC programming method to approximate the non-convex formula with convex relaxation.
  • the formula (6) can be expressed as:
  • Equation (11) can be expressed in the form of the difference between f(W) and g(h(W)):
  • Formula (6) corresponds to the convex relaxation form of formula (14):
  • a brain disease process prediction system based on weakly-supervised multi-task matrix completion includes a data acquisition unit, an offline processing unit, and a process prediction unit connected in sequence, in which:
  • the data collection unit is used to collect the measured values of magnetic resonance imaging MRI, positron emission tomography PET and cerebrospinal fluid CSF measured when the subject goes to the hospital for examination for the first time.
  • MRI magnetic resonance imaging
  • positron emission tomography PET positron emission tomography PET
  • cerebrospinal fluid CSF cerebrospinal fluid CSF measured when the subject goes to the hospital for examination for the first time.
  • MRI and positron tomography were performed with MRI and positron scanner, respectively, and the original MRI and PET brain image data were obtained.
  • a doctor performs a lumbar puncture operation to obtain a cerebrospinal fluid sample. This operation is simple and less dangerous, and is most commonly used in clinical practice.
  • the offline processing unit includes a data preprocessing module and a model building module, wherein the data preprocessing module is used to preprocess the collected magnetic resonance imaging MRI, positron emission tomography PET and cerebrospinal fluid CSF measurement values, Obtain the characteristics of magnetic resonance imaging, positron emission tomography and cerebrospinal fluid.
  • the model building module is used to use the preprocessed data to train the proposed brain disease process prediction model based on weakly supervised multi-task matrix completion (formula (4)).
  • the process prediction unit is used to predict the brain disease process of the newly-diagnosed subject according to the trained brain disease process prediction model based on weakly supervised multi-task matrix completion.
  • For new subjects to be diagnosed we collect data according to the method in the data collection unit, and then preprocess the collected data using the method in the offline processing unit, and finally use the brain disease process prediction trained in the offline processing unit Model to predict the brain disease process of the subject to be diagnosed.
  • the data acquisition unit is used to collect the original data, and then the data preprocessing module in the offline processing unit is used to preprocess the original data to obtain the sample characteristics of the new subject.
  • the sample data of the new subject is used as the test sample and input into the brain disease process prediction model trained by the model building module in the offline processing unit.
  • the row in the score matrix corresponding to the sample is the process prediction result.

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Abstract

一种基于弱监督多任务矩阵补全的脑疾病进程预测方法及系统，包括依次连接的数据采集单元、离线处理单元、进程预测单元，通过对由多位受试者在baseline时测得的多个模态数据进行预处理；利用多任务直推式矩阵补全模型，将多个时间点的疾病状态预测建模为一个多任务回归问题；选择出task-share特征和task-specific特征，利用这两种特征进一步提高评分矩阵的预测准确率，从而完成对疾病进程的预测。

Description

基于弱监督多任务矩阵补全的脑疾病进程预测方法及系统 技术领域
本发明涉及人工智能和机器学习领域，具体涉及一种基于弱监督多任务矩阵补全模型的脑疾病进程预测方法。
背景技术
阿尔茨海默病(Alzheimer’s disease,AD)是一种不可逆的神经退行性疾病，其特征是神经元及其连接受损，导致患者渐进性记忆丧失和认知能力下降，最终死亡。最近的研究表明，全世界大约有2660万名AD患者，到2050年，每85人中将有1人将受到AD的影响。准确地预测AD的疾病进程，便能根据预测结果，及时对患者进行有效的针对性治疗，较大地延缓和改善病情，对于AD的临床诊断和预后具有重要意义。
许多临床/认知测量被设计用来评估患者的认知状态，并作为可能的AD临床诊断的重要标准，例如简易精神状态量表(Mini-mental State Examination,MMSE)和阿尔茨海默病评估量表-认知子量表(Alzheimer’s Disease Assessment Scale-Cognitive section,ADAS-Cog)。MMSE已被证明与潜在的AD病理学和功能的逐步恶化相关。ADAS-Cog则是评估AD药物试验认知功能的主要标准。在传统的疾病进程预测研究中，大部分人采用回归模型进行预测，如Stonnington等人，使用了相关向量回归(relevance vector regression，RVR)方法来测量结构变化和神经心理学测试之间的相互作用关系。另一部分人采用生存模型，如Pearson等人，将疾病进程预测建模成典型的生存分析问题。这些方法在样本维度较小时取得了较好的效果，但是当维度较高，如使用医学影像作为输入特征时，他们的效果并不理想。为此，研究者通常采用降维技术来处理高维问题，如Duchesne等人，使用主成分分析(Principal Component Analysis，PCA)技术将高维数据映射到低维空间中。周涛等人将高维基因型数据和表现型图像数据共同映射到由诊断标签引导的联合潜在特征空间来处理高维问题。同时，现有研究大多集中在对单个时间点，如baseline(患者第一次到医院接受检查的时间)或者baseline一年以后的状态预测上，但是，对多个时间点的数据进行联合分析可以利用其之间的关联性提高预测效果，尤其是当样本数较少且样本维度较大时。
为了充分利用多个时间点疾病状态的关联性，许多人将多任务学习思想应用到疾病进程预测上。多任务学习的目的是通过同时学习多个相关任务，挖掘任务之间的内在关联性，提高泛化性能。由于神经影像学数据的珍贵和稀少，Jabason等人将弱监督学习思想与疾病进程预测相结合，充分挖掘样本潜在的结构信息。同时，现有的大部分论文在进行特征选择时仅考虑了选择与所有任务相关的公共特征子集，并没有考虑到每个任务所独有的特征，也没 有考虑到样本存在噪声。
发明内容
发明目的：为了克服现有疾病进程预测研究中存在的样本过拟合问题和特征含噪问题，提出一种基于弱监督多任务矩阵补全的脑疾病进程预测方法及系统，该方法能有效利用多个时间点疾病状态的内在关联性，充分挖掘出样本之间的低秩性及结构分布信息，选择出task-share特征和task-specific特征，解决过拟合问题，并对样本进行去噪，从而获得较高的预测准确率。
技术方案：为实现上述目的，本发明采用的技术方案为：
一种基于弱监督多任务矩阵补全的脑疾病进程预测方法，包括以下步骤：
步骤1：对受试者在第一次去医院接受检查时测得的磁共振成像MRI、正电子发射断层显像PET和脑脊液CSF测量值进行预处理，得到磁共振成像特征、正电子发射断层显像特征、脑脊液特征。
步骤2：利用多任务直推式矩阵补全模型，将对第一次去医院接受检查之后每个时间点的疾病状态预测都视作一个单任务回归任务，从而多个时间点的疾病状态预测建模为一个多任务回归问题，并对特征矩阵进行去噪，在标记部分缺失的情况下预测出认知评分矩阵。
步骤2具体包括如下步骤：
步骤2-1，基于特征矩阵X的低秩性假设和X与Y之间的线性关联假设，补全后得到的矩阵Z＝[Z X,Z Y]也是低秩的，其中，矩阵Z X是对应于矩阵X的真实潜在的特征矩阵，Z Y是对应于矩阵Y的真实潜在的评分矩阵。通过对Z矩阵使用核范数约束，并对补全前的特征矩阵X和补全后的特征矩阵Z X之间使用F范数约束作为保真项，其公式如下：
Figure PCTCN2020070259-appb-000001
其中，
Figure PCTCN2020070259-appb-000002
Z是一个维度为n×(d+t)的矩阵，
Figure PCTCN2020070259-appb-000003
表示实数，d代表特征数，n代表样本数，t代表任务数，W表示权重矩阵，λ 1,λ 2和λ 3是正则化参数，‖Z‖ *表示矩阵Z的核范数，P是一个mask矩阵，P ij表示矩阵P中第i行第j列的元素，当第i个样本在第j个时间点的认知评分缺失时，P ij＝0,反之则为1，⊙表示哈达玛积。
步骤2-2，疾病进程预测的目的是预测出受试者在第一次去医院接受检查后一段时间的疾病状态，对第一次去医院接受检查后每隔一定时间间隔的特定时间点的疾病状态进行预测。采用简易精神状态量表MMSE和阿尔茨海默病评估量表-认知子量表ADAS-Cog的认知评分来表示受试者的疾病状态。
步骤3：利用混合稀疏组Lasso特征选择方法选择出所有任务共享的task-share特征和每个任务所独有的task-specific特征，利用task-share特征、task-specific特征进一步提高评分矩阵的预测准确率，从而完成对疾病进程的预测。
步骤3具体包括如下步骤：
步骤3-1，对系数矩阵
Figure PCTCN2020070259-appb-000004
使用l 2,1范数约束，使得W行稀疏，通过训练得到W，其中，W的每一行对应一个特征，每一列对应一个任务，W的非零行所对应的特征即为task-share特征。
步骤3-2，对系数矩阵
Figure PCTCN2020070259-appb-000005
使用l 1范数约束，使得W任意稀疏，使得W的非零行中出现随机的零值，所以W的非零行对应的特征即为非零行中非零值对应任务的task-specific特征。
步骤3-3，引入时序平滑正则化项对相邻时间点评分预测的较大偏差进行惩罚。
步骤3-4，结合步骤3-1、步骤3-2、步骤3-3中的范数约束，关于task-share特征和task-specific特征的特征选择项，又称混合稀疏组Lasso项：
Figure PCTCN2020070259-appb-000006
步骤3-5，结合步骤3-1和步骤3-4中的直推式矩阵补全模型和混合稀疏组Lasso项，得到如下模型：
Figure PCTCN2020070259-appb-000007
步骤3-6，将步骤3-4中的模型改进为如下的非凸多任务回归形式：
Figure PCTCN2020070259-appb-000008
Figure PCTCN2020070259-appb-000009
步骤3-7，结合快速迭代收缩阈值算法和DC规划方法设计步骤3-6所提出模型的求解方法。
通过交替迭代以下两个子问题来求解出W和Z：
Figure PCTCN2020070259-appb-000010
其中，公式(5)中的子问题1用FISTA方法来求解，令：
Figure PCTCN2020070259-appb-000011
其中，F(Z,W)表示公式(5)中除了核范数的可导项的集合。
那么子问题1就用如下方式求解：
Figure PCTCN2020070259-appb-000012
其中，
Figure PCTCN2020070259-appb-000013
表示核范数的近邻算子，
Figure PCTCN2020070259-appb-000014
表示步长，而Lipschitz连续常数
Figure PCTCN2020070259-appb-000015
求解如下:
Figure PCTCN2020070259-appb-000016
其中，σ 1(·)表示括号中矩阵的最大奇异值，T表示矩阵的转置，I d×d表示维度为d×d的单位矩阵。
此外，梯度
Figure PCTCN2020070259-appb-000017
计算如下:
Figure PCTCN2020070259-appb-000018
其中，ΔX和ΔY分别表示Z X中Z Y元素下标集合，
Figure PCTCN2020070259-appb-000019
W k-1和
Figure PCTCN2020070259-appb-000020
分别表示在第k-1次迭代过程中Z X,W和Z Y的值。
公式(6)中的子问题2是一个非凸优化问题，利用DC规划方法来利用凸松弛近似非凸公式，DC规划方法基本原理简述如下：
Figure PCTCN2020070259-appb-000021
其中，l(W)和h(W)表示一般式的函数，l(W)和h(W)是凸的，很容易证明
Figure PCTCN2020070259-appb-000022
形式也是凸的，接着设f(W)＝l(W)+h(W)和
Figure PCTCN2020070259-appb-000023
公式(11)表示成f(W)和g(h(W))之差的形式：
min Wf(W)-g(h(W))     (12)
然后利用在许多非凸问题中常用的CCCP理论，将函数g(h(W))在当前的点W′处一阶泰勒展开：
Figure PCTCN2020070259-appb-000024
这是非凸问题的凸上界，接下来，在每次迭代中使用CCCP算法最小化凸上界：
Figure PCTCN2020070259-appb-000025
公式(6)对应于公式(14)凸松弛形式：
Figure PCTCN2020070259-appb-000026
其中，W k+1表示第k+1次迭代过程中W的值，
Figure PCTCN2020070259-appb-000027
ε是一个避免分母为零的较小常数项，w i表示矩阵W的第i行，w i(t)表示第k次迭代中w i的值，λ 4表示特征选择项的超参数，d表示特征数。
优选的：步骤1中得到磁共振成像特征、正电子发射断层显像特征、脑脊液特征的方法如下：
步骤1-1，对磁共振成像MRI依次使用前连合AC–后连合PC矫正、强度不均匀性校正、头骨剥离、基于阿特拉斯配准的小脑摘除术、空间分割，得到基于Jacob模板的具有93个手动标记感兴趣区ROI的标记图像，并分别计算这93个手动标记感兴趣区ROI的灰质体积作为磁共振成像特征。
步骤1-2，对于每个正电子发射断层显像PET，使用仿射配准将正电子发射断层显像PET图像与其各自的磁共振成像MRI对齐，然后，利用相应的磁共振脑掩模得到颅骨剥离图像，并计算出正电子发射断层显像PET图像中每个手动标记感兴趣区ROI的平均强度作为正电子发射断层显像特征。
步骤1-3，对于脑脊液CSF，使用CSF Aβ42,CSF t-tau和CSF p-tau三项的测量值作为脑脊液特征。
优选的：在预测时，加入人口统计学特征，人口统计学特征包括受试者的年龄、受教育情况、性别。
优选的：步骤2-2中第一次去医院接受检查后每隔一定时间间隔的特定时间点包括第一次去医院接受检查后06个月、12个月、24个月、36个月、48个月。
一种基于弱监督多任务矩阵补全的脑疾病进程预测系统，包括依次连接的数据采集单元、离线处理单元、进程预测单元，其中：
所述数据采集单元用于采集受试者在第一次去医院接受检查时测得的磁共振成像MRI、正电子发射断层显像PET和脑脊液CSF测量值。
所述离线处理单元包括数据预处理模块和构建模型模块，其中，所述数据预处理模块用于对采集到的磁共振成像MRI、正电子发射断层显像PET和脑脊液CSF测量值进行预处理，得到磁共振成像特征、正电子发射断层显像特征、脑脊液特征。所述构建模型模块用于利用预处理后的数据来训练所提出的基于弱监督多任务矩阵补全的脑疾病进程预测模型。
所述进程预测单元用于根据训练好的基于弱监督多任务矩阵补全的脑疾病进程预测模型对新待诊断的受试者进行脑疾病进程预测。
本发明相比现有技术，具有以下有益效果：
(1)能够解决脑疾病诊断所常需要面临的过拟合问题
我们使用多任务直推式矩阵补全MTMC来解决过拟合问题。它可以充分利用特征矩阵潜在的低秩特性，同时对特征矩阵进行去噪，以此来得到更好的预测精度。在挖掘不同任务之间固有的关联性方面，MTMC也具有多任务学习共同的优点。
(2)能够处理样本含噪和标记部分缺失问题
由于获取充足的带标记数据昂贵且耗时，为了解决这个问题，我们的模型基于弱监督学习思想，联合使用带标记训练样本和无标记测试样本来建立样本流形内蕴的几何结构。
(3)能够选择出对阿尔茨海默病进程预测有较高判别性的生物标志物特征。
我们通过对系数矩阵进行l 1/2范数正则化来选择出task-share特征和task-specific特征。这对于神经退行性疾病的诊断尤其重要，因为我们是从大脑的不同区域提取特征，但实际上只有某些特定的区域与AD相关。因此，通过结合混合稀疏组Lasso特征选择方法，我们的模型可以选择出对疾病进程中不同时间点的疾病状态预测最具判别性的特征。
附图说明
图1是本发明系统结构示意图。
图2是本发明处理流程图。
具体实施方式
下面结合附图和具体实施例，进一步阐明本发明，应理解这些实例仅用于说明本发明而不用于限制本发明的范围，在阅读了本发明之后，本领域技术人员对本发明的各种等价形式的修改均落于本申请所附权利要求所限定的范围。
一种基于弱监督多任务矩阵补全的脑疾病进程预测方法，如图2所示，包括以下步骤：
步骤1：在对由多位受试者在baseline时测得的磁共振成像(MRI)、正电子发射断层显像(PET)和脑脊液(CSF)测量值等多个模态数据进行预处理，具体包括如下步骤：
步骤1-1，对磁共振成像(MRI)依次使用前连合(AC)–后连合(PC)矫正、强度不均匀性校正、头骨剥离、基于阿特拉斯配准的小脑摘除术、空间分割等技术，得到基于Jacob模板的具有93个手动标记感兴趣区(ROI)的标记图像，并分别计算这93个ROI的灰质体积作为特征。其中，baseline指的是受试者第一次去医院接受检查的时间。
步骤1-2，对于每个正电子发射断层显像(PET)，我们首先使用仿射配准将PET图像与其各自的MRI对齐。然后，利用相应的磁共振脑掩模得到颅骨剥离图像，并计算出PET图像中每个ROI的平均强度作为特征。
步骤1-3，对于脑脊液(CSF)，我们使用CSF Aβ42,CSF t-tau和CSF p-tau三项的 测量值作为CSF特征。
步骤1-4，同时也可以加入一些人口统计学特征，如受试者的年龄，受教育情况，性别等，有研究表明，人口统计学特征对于脑疾病进程也有一定的影响。
步骤2：利用多任务直推式矩阵补全模型，将对baseline之后每个时间点的疾病状态预测都视作一个单任务回归任务，从而多个时间点的疾病状态预测建模为一个多任务回归问题，并对特征矩阵进行去噪，在标记部分缺失的情况下预测出认知评分矩阵，具体包括如下步骤：
步骤2-1，根据多任务直推式矩阵补全理论，首先，它假设X和Y之间存在线性关联，即Y＝XW，其中
Figure PCTCN2020070259-appb-000028
是一个隐式的系数矩阵。其次，它假设矩阵X是低秩的，即原始高维数据实际位于低维流形结构上。并且，根据rank(Z)≤rank(X)，可以得出矩阵Z＝[Z X,Z Y]同样是低秩的，其中，矩阵Z X是对应于矩阵X的真实潜在的特征矩阵，Z Y是对应于矩阵Y的真实潜在的评分矩阵。通过对Z矩阵使用核范数约束，并对补全前的特征矩阵X和补全后的特征矩阵Z X之间使用F范数约束作为保真项，其公式如下：
Figure PCTCN2020070259-appb-000029
其中，
Figure PCTCN2020070259-appb-000030
d代表特征数，n代表样本数，t代表任务数，W表示权重矩阵，λ 1,λ 2和λ 3是正则化参数，P是一个mask矩阵，当第i个样本在第j个时间点的认知评分缺失时，P ij＝0,反之则为1，⊙表示哈达玛积(Hadamard product)。
步骤2-1，疾病进程预测的目的是预测出受试者在baseline后一段时间的疾病状态，本发明中我们对baseline后每隔一定时间间隔的特定时间点(如baseline后06、12、24、36、48个月等)的疾病状态进行预测。而对于受试者疾病状态的评价方法，许多临床/认知测量已被设计出来，并作为可能的AD的临床诊断的重要标准，如简易精神状态量表(MMSE)和阿尔茨海默病评估量表-认知子量表(ADAS-Cog)，本发明用这两种认知评分来表示受试者的疾病状态。在实际研究中，训练样本的数量往往不足，且存在评分数据部分缺失的现象。
步骤3：与此同时，利用混合稀疏组Lasso特征选择策略选择出所有任务共享的task-share特征和每个任务所独有的task-specific特征，利用这两种特征进一步提高评分矩阵的预测准确率，从而完成对疾病进程的预测，具体包括如下步骤：
步骤3-1，为了得到所有任务共享的task-share特征，对系数矩阵
Figure PCTCN2020070259-appb-000031
使用l 2,1范数约束，使得W行稀疏，通过训练得到W，其中W的每一行对应一个特征，每一列对应一个任务，W的非零行所对应的特征即为task-share特征。
步骤3-2，与此同时，为了得到每个任务所独有的task-specific特征，对系数矩阵
Figure PCTCN2020070259-appb-000032
使用l 1范数约束，使得W任意稀疏，使得W的非零行中出现随机的零值，所以W的非零行对应的特征即为非零行中非零值对应任务的task-specific特征。
步骤3-3，为了充分利用疾病进程预测问题中常见的时序平滑先验特性，即相邻时间点的临床认知评分应该相近，我们将时序平滑正则化项引入疾病进程建模中，对相邻时间点评分预测的较大偏差进行惩罚。
步骤3-4，结合步骤3-1，步骤3-2和步骤3-3中的范数约束，关于task-share特征和task-specific特征的特征选择项，又称混合稀疏组Lasso项：
Figure PCTCN2020070259-appb-000033
步骤3-5，结合(3-1)和(4-4)中的直推式矩阵补全模型和混合稀疏组Lasso特征选择项，得到如下模型：
Figure PCTCN2020070259-appb-000034
步骤3-6，许多先前的研究表明，将l 1正则化项和l 2,1正则化项进行简单的组合并不是最优的，而且，众所周知，稀疏惩罚会导致有偏估计。为了解决这一问题，我们将步骤3-4中的模型改进为如下的非凸多任务回归形式：
Figure PCTCN2020070259-appb-000035
步骤3-7，结合快速迭代收缩阈值算法(Fast Iterative Shrinkage-Thresholding Algorithm,FISTA)和DC规划方法(difference of convex programming techniques)设计本发明所提出模型的求解方法，求解方法的详细过程如下：
通过交替迭代以下两个子问题来求解出W和Z：
Figure PCTCN2020070259-appb-000036
其中，公式(5)中的子问题1可以用FISTA方法来求解，其收敛性由已Beck等人证明。具体来说，我们令：
Figure PCTCN2020070259-appb-000037
那么子问题1就可以用如下方式求解：
Figure PCTCN2020070259-appb-000038
其中
Figure PCTCN2020070259-appb-000039
表示核范数的近邻算子，
Figure PCTCN2020070259-appb-000040
表示步长，而Lipschitz连续常数
Figure PCTCN2020070259-appb-000041
求解如下:
Figure PCTCN2020070259-appb-000042
此外，梯度
Figure PCTCN2020070259-appb-000043
计算如下:
Figure PCTCN2020070259-appb-000044
其中ΔX和ΔY分别表示Z X中Z Y元素下标集合。
公式(6)中的子问题2是一个非凸优化问题，因此我们利用著名的DC规划方法来利用凸松弛近似非凸公式。具体地说，公式(6)中可以表示为：
Figure PCTCN2020070259-appb-000045
其中，l(W)和h(W)是凸的，很容易证明
Figure PCTCN2020070259-appb-000046
形式也是凸的。接着设f(W)＝l(W)+h(W)和
Figure PCTCN2020070259-appb-000047
公式(11)可以表示成f(W)和g(h(W))之差的形式：
min Wf(W)-g(h(W))    (12)
然后利用在许多非凸问题中常用的CCCP理论(convex-concave procedure algorithm)，将函数g(h(W))在当前的点W′处一阶泰勒展开：
Figure PCTCN2020070259-appb-000048
这是非凸问题的凸上界。接下来，我们在每次迭代中使用CCCP算法最小化凸上界：
Figure PCTCN2020070259-appb-000049
公式(6)对应于公式(14)凸松弛形式：
Figure PCTCN2020070259-appb-000050
一种基于弱监督多任务矩阵补全的脑疾病进程预测系统，如图1所示，包括依次连接的数据采集单元、离线处理单元、进程预测单元，其中：
所述数据采集单元用于采集受试者在第一次去医院接受检查时测得的磁共振成像MRI、正电子发射断层显像PET和脑脊液CSF测量值。对于多位受试者，我们在baseline时间点对受试者进行核磁共振检查，正电子发射断层现象检查和脑脊液测量，从而获得受试者的MRI、PET脑图像，以及三种脑脊液的测量值，我们将这三个模态的数据作为训练数据。
分别用核磁共振仪和正子扫描仪进行核磁共振和正电子断层显像，得到原始的MRI和PET脑图像数据。由医生进行腰椎穿刺操作来获得脑脊液样本，此操作简单且危险性小，临床最为常用。
所述离线处理单元包括数据预处理模块和构建模型模块，其中，所述数据预处理模块用于对采集到的磁共振成像MRI、正电子发射断层显像PET和脑脊液CSF测量值进行预处理，得到磁共振成像特征、正电子发射断层显像特征、脑脊液特征。所述构建模型模块用于利用预处理后的数据来训练所提出的基于弱监督多任务矩阵补全的脑疾病进程预测模型(公式(4))。
所述进程预测单元用于根据训练好的基于弱监督多任务矩阵补全的脑疾病进程预测模型对新待诊断的受试者进行脑疾病进程预测。对于新的待诊断的受试者，我们按照数据采集单元中的方法采集数据，然后离线处理单元中的方法对采集到的数据进行预处理，最后利用离线处理单元中训练出的脑疾病进程预测模型来预测出待诊断受试者的脑疾病进程。
对于新的待诊断的受试者，利用数据采集单元采集得到原始数据，然后利用离线处理单元中数据预处理模块对原始数据进行预处理，得到新受试者的样本特征。将新受试者的样本数据作为测试样本，输入到离线处理单元中构建模型模块训练出的脑疾病进程预测模型中，该样本对应的评分矩阵中的那一行即为进程预测结果。
以上所述仅是本发明的优选实施方式，应当指出：对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也应视为本发明的保护范围。

Claims (5)

  1. 一种基于弱监督多任务矩阵补全的脑疾病进程预测方法，其特征在于，包括以下步骤：
    步骤1：对受试者在第一次去医院接受检查时测得的磁共振成像MRI、正电子发射断层显像PET和脑脊液CSF测量值进行预处理，得到磁共振成像特征、正电子发射断层显像特征、脑脊液特征；
    步骤2：利用多任务直推式矩阵补全模型，将对第一次去医院接受检查之后每个时间点的疾病状态预测都视作一个单任务回归任务，从而多个时间点的疾病状态预测建模为一个多任务回归问题，并对特征矩阵进行去噪，在标记部分缺失的情况下预测出认知评分矩阵；
    步骤2具体包括如下步骤：
    步骤2-1，基于特征矩阵X的低秩性假设和X与Y之间的线性关联假设，补全后得到的矩阵Z＝[Z X,Z Y]也是低秩的，其中，矩阵Z X是对应于矩阵X的真实潜在的特征矩阵，Z Y是对应于矩阵Y的真实潜在的评分矩阵；通过对Z矩阵使用核范数约束，并对补全前的特征矩阵X和补全后的特征矩阵Z X之间使用F范数约束作为保真项，其公式如下：
    Figure PCTCN2020070259-appb-100001
    其中，
    Figure PCTCN2020070259-appb-100002
    Z是一个维度为n×(d+t)的矩阵，
    Figure PCTCN2020070259-appb-100003
    表示实数，d代表特征数，n代表样本数，t代表任务数，W表示权重矩阵，λ 1,λ 2和λ 3是正则化参数，‖Z‖ *表示矩阵Z的核范数，P是一个mask矩阵，P ij表示矩阵P中第i行第j列的元素，当第i个样本在第j个时间点的认知评分缺失时，P ij＝0,反之则为1，⊙表示哈达玛积；
    步骤2-2，疾病进程预测的目的是预测出受试者在第一次去医院接受检查后一段时间的疾病状态，对第一次去医院接受检查后每隔一定时间间隔的特定时间点的疾病状态进行预测；采用简易精神状态量表MMSE和阿尔茨海默病评估量表-认知子量表ADAS-Cog的认知评分来表示受试者的疾病状态；
    步骤3：利用混合稀疏组Lasso特征选择方法选择出所有任务共享的task-share特征和每个任务所独有的task-specific特征，利用task-share特征、task-specific特征进一步提高评分矩阵的预测准确率，从而完成对疾病进程的预测；
    步骤3具体包括如下步骤：
    步骤3-1，对系数矩阵
    Figure PCTCN2020070259-appb-100004
    使用l 2,1范数约束，使得W行稀疏，通过训练得到W，其中，W的每一行对应一个特征，每一列对应一个任务，W的非零行所对应的特征即为task-share特征；
    步骤3-2，对系数矩阵
    Figure PCTCN2020070259-appb-100005
    使用l 1范数约束，使得W任意稀疏，使得W的非零行中 出现随机的零值，所以W的非零行对应的特征即为非零行中非零值对应任务的task-specific特征；
    步骤3-3，引入时序平滑正则化项对相邻时间点评分预测的较大偏差进行惩罚；
    步骤3-4，结合步骤3-1、步骤3-2、步骤3-3中的范数约束，关于task-share特征和task-specific特征的特征选择项，又称混合稀疏组Lasso项：
    Figure PCTCN2020070259-appb-100006
    步骤3-5，结合步骤3-1和步骤3-4中的直推式矩阵补全模型和混合稀疏组Lasso项，得到如下模型：
    Figure PCTCN2020070259-appb-100007
    其中，稀疏矩阵
    Figure PCTCN2020070259-appb-100008
    定义如下：
    Figure PCTCN2020070259-appb-100009
    其他元素为零；
    步骤3-6，将步骤3-4中的模型改进为如下的非凸多任务回归形式：
    Figure PCTCN2020070259-appb-100010
    步骤3-7，结合快速迭代收缩阈值算法和DC规划方法设计步骤3-6所提出模型的求解方法；
    通过交替迭代以下两个子问题来求解出W和Z：
    Figure PCTCN2020070259-appb-100011
    其中，公式(5)中的子问题1用FISTA方法来求解，令：
    Figure PCTCN2020070259-appb-100012
    其中，F(Z,W)表示公式(5)中除了核范数的可导项的集合；
    那么子问题1就用如下方式求解：
    Figure PCTCN2020070259-appb-100013
    其中，
    Figure PCTCN2020070259-appb-100014
    表示核范数的近邻算子，
    Figure PCTCN2020070259-appb-100015
    表示步长，而Lipschitz连续常数
    Figure PCTCN2020070259-appb-100016
    求解如下:
    Figure PCTCN2020070259-appb-100017
    其中，σ 1(·)表示括号中矩阵的最大奇异值，T表示矩阵的转置，I d×d表示维度为d×d的 单位矩阵；
    此外，梯度
    Figure PCTCN2020070259-appb-100018
    计算如下:
    Figure PCTCN2020070259-appb-100019
    其中，ΔX和ΔY分别表示Z X中Z Y元素下标集合，
    Figure PCTCN2020070259-appb-100020
    W k-1和
    Figure PCTCN2020070259-appb-100021
    分别表示在第k-1次迭代过程中Z X,W和Z Y的值；
    公式(6)中的子问题2是一个非凸优化问题，利用DC规划方法来利用凸松弛近似非凸公式，包括如下步骤：
    Figure PCTCN2020070259-appb-100022
    其中，l(W)和h(W)表示一般式的函数，l(W)和h(W)是凸的，很容易证明
    Figure PCTCN2020070259-appb-100023
    形式也是凸的，接着设f(W)＝l(W)+h(W)和
    Figure PCTCN2020070259-appb-100024
    公式(11)表示成f(W)和g(h(W))之差的形式：
    min Wf(W)-g(h(W))   (12)
    然后利用在许多非凸问题中常用的CCCP理论，将函数g(h(W))在当前的点W′处一阶泰勒展开：
    Figure PCTCN2020070259-appb-100025
    这是非凸问题的凸上界，接下来，在每次迭代中使用CCCP算法最小化凸上界：
    Figure PCTCN2020070259-appb-100026
    公式(6)对应于公式(14)凸松弛形式：
    Figure PCTCN2020070259-appb-100027
    其中，W k+1表示第k+1次迭代过程中W的值，
    Figure PCTCN2020070259-appb-100028
    ε是一个避免分母为零的较小常数项，w i表示矩阵W的第i行，w i(t)表示第k次迭代中w i的值，λ 4表示特征选择项的超参数，d表示特征数。
  2. 根据权利要求1所述基于弱监督多任务矩阵补全的脑疾病进程预测方法，其特征在于：步骤1中得到磁共振成像特征、正电子发射断层显像特征、脑脊液特征的方法如下：
    步骤1-1，对磁共振成像MRI依次使用前连合AC–后连合PC矫正、强度不均匀性校正、 头骨剥离、基于阿特拉斯配准的小脑摘除术、空间分割，得到基于Jacob模板的具有93个手动标记感兴趣区ROI的标记图像，并分别计算这93个手动标记感兴趣区ROI的灰质体积作为磁共振成像特征；
    步骤1-2，对于每个正电子发射断层显像PET，使用仿射配准将正电子发射断层显像PET图像与其各自的磁共振成像MRI对齐，然后，利用相应的磁共振脑掩模得到颅骨剥离图像，并计算出正电子发射断层显像PET图像中每个手动标记感兴趣区ROI的平均强度作为正电子发射断层显像特征；
    步骤1-3，对于脑脊液CSF，使用CSF Aβ42,CSF t-tau和CSF p-tau三项的测量值作为脑脊液特征。
  3. 根据权利要求1所述基于弱监督多任务矩阵补全的脑疾病进程预测方法，其特征在于：在预测时，加入人口统计学特征，人口统计学特征包括受试者的年龄、受教育情况、性别。
  4. 根据权利要求1所述基于弱监督多任务矩阵补全的脑疾病进程预测方法，其特征在于：步骤2-2中第一次去医院接受检查后每隔一定时间间隔的特定时间点包括第一次去医院接受检查后06个月、12个月、24个月、36个月、48个月。
  5. 一种基于弱监督多任务矩阵补全的脑疾病进程预测系统，其特征在于：包括依次连接的数据采集单元、离线处理单元、进程预测单元，其中：
    所述数据采集单元用于采集受试者在第一次去医院接受检查时测得的磁共振成像MRI、正电子发射断层显像PET和脑脊液CSF测量值；
    所述离线处理单元包括数据预处理模块和构建模型模块，其中，所述数据预处理模块用于对采集到的磁共振成像MRI、正电子发射断层显像PET和脑脊液CSF测量值进行预处理，得到磁共振成像特征、正电子发射断层显像特征、脑脊液特征；所述构建模型模块用于利用预处理后的数据来训练所提出的基于弱监督多任务矩阵补全的脑疾病进程预测模型；
    所述进程预测单元用于根据训练好的基于弱监督多任务矩阵补全的脑疾病进程预测模型对新待诊断的受试者进行脑疾病进程预测。
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