CN110298364B - Multi-threshold-value multi-task-based feature selection method for functional brain network - Google Patents

Multi-threshold-value multi-task-based feature selection method for functional brain network Download PDF

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CN110298364B
CN110298364B CN201910591933.5A CN201910591933A CN110298364B CN 110298364 B CN110298364 B CN 110298364B CN 201910591933 A CN201910591933 A CN 201910591933A CN 110298364 B CN110298364 B CN 110298364B
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接标
王正东
王咪
卞维新
丁新涛
左开中
陈付龙
罗永龙
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Anhui Normal University
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Abstract

A multi-threshold-oriented multi-task-based feature selection method for a functional brain network extracts multi-level network features by adopting a multi-threshold mode, and extracts multi-level features for the thresholded network by utilizing a multi-core multi-task learning mode for further classification processing. Overcomes the defects of the existing method, and further learns more discriminative and explanatory characteristics. The gk-MTFS method takes feature learning under each threshold as a task, adopts a graph core (a core constructed on the graph) to retain the structural information of the network for each task, and adopts multi-task learning to explore the internal relevance among the tasks, thereby learning features with more discriminative power and interpretability. Finally, verification is carried out on a real brain disease data set, and experimental results show that compared with the existing method, the method has better classification characteristics on the brain diseases.

Description

Multi-threshold-value multi-task-based feature selection method for functional brain network
Technical Field
The invention belongs to the field of machine learning and medical image analysis, and particularly relates to a multi-task-based feature selection method under multiple thresholds for a functional brain network.
Background
With the rapid development of the current biotechnology, brain imaging technologies, such as the modern Magnetic Resonance Imaging (MRI) technology including functional MRI, provide a non-invasive way to explore the human brain, and reveal the mechanism of the brain structure and function that was not known before. Brain network analysis can depict the interaction between brain and brain regions on a connection level, and becomes a new research hotspot in medical image analysis and neuroimaging.
More recently, methods of machine learning have been used in the analysis and classification of brain networks. For example, researchers have taken advantage of the brain network for early brain disease diagnosis and classification, and have achieved very good performance. In these studies, it is typical to extract local measures of the brain (e.g., clustering coefficients) from the brain network as features for disease classification. And the feature selection is to filter out redundant and unimportant features, thereby improving the classification performance. For example, Chen et al use the weights of edges as features for the classification of AD (Alzheimer's disease) and MCI (millicognitive impact). Wee et al extracted clustering coefficients from functional brain networks as features for classification of MCI. Zanin et al used 16 network measurements as features for classification of MCI and normal. Since the locality measures only the characteristics of the local structure of the network, the overall topology of the network is lost during the classification process, which may affect the classification performance.
In brain network analysis, the two feature selection methods most frequently used are the t-test method and the Lasso method. In the t-test method, the discriminativity of each feature is first measured using a standard t-test, and the features are sorted according to the discriminativity, and finally a set of most discriminative feature subsets is selected. Previous studies have shown that good performance is generally obtained with the t-test method in small samples. Unlike the t-test method, the Lasso method does feature selection by minimizing an objective function, and studies have shown that the Lasso method works well when there are a large number of uncorrelated features but only a small number of samples. At present, most feature selection methods mainly aim at vector data and cannot be directly used for processing complex structured data such as brain network data.
Feature selection can not only improve the performance of the classifier, but also help to find some disease-sensitive biomarkers. Existing methods typically extract local measures (such as edge weights or clustering coefficients) from the network data as features and combine them into a long feature vector for subsequent feature selection and classification, while some useful network structure information (such as the overall topology of the network) is lost, which may degrade the final classification performance. In addition, the functional brain network is generally a fully connected weighted network, and thresholding preprocessing is required to characterize the structural characteristics of the network. However, on the one hand, there is no good criterion to select a specific threshold, and on the other hand, different thresholds generally result in different network structures, which may contain complementary information, possibly further improving network analysis performance.
Based on the method, the multi-threshold mode is adopted to extract multi-level network features, and multi-core multi-task learning is utilized to extract multi-level features for further classification processing of the thresholded network. Overcomes the defects of the existing method, and further learns more discriminative and explanatory characteristics. The proposed gk-MTFS method takes feature learning under each threshold as a task, adopts a graph core (a core constructed on the graph) to retain the structural information of the network for each task, and adopts multi-task learning to explore the internal relevance among the tasks, thereby learning features with more discriminative power and interpretability. Finally, verification is carried out on a real brain disease data set, and experimental results show that compared with the existing method, the method has better classification characteristics on the brain diseases.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a multi-task-based feature selection method under multiple thresholds for a functional brain network. The gk-MTFS method first utilizes L21And the paradigm group sparsizes the terms, so that more discriminative features can be selected. And further using a Laplacian regularization item based on a graph kernel under multiple thresholds, and reserving the topological structure information of the functional brain network connection. And finally, performing optimization solution on the objective function by using multi-core feature joint learning and using an approximate acceleration gradient algorithm.
In order to achieve the purpose, the invention adopts the following technical scheme:
the feature selection method based on multiple tasks under the multiple threshold values facing the functional brain network is characterized by comprising the following steps:
step one, preprocessing fMRI data to construct a functional brain network;
step two, adopting R thresholds to carry out thresholding treatment on the constructed functional brain network at the same time;
step three, extracting the clustering coefficient of the brain area of each thresholding network as a characteristic for measuring the local topological structure of the network;
step four, calculating the similarity of the overall topological structure among the networks by utilizing the graph cores for each thresholding network;
step five, based on the step three and the step four, establishing a target function of the brain network-oriented multi-threshold gk-MTFS feature selection method;
and step six, optimizing the proposed objective function by utilizing an accelerated approximation gradient algorithm.
In order to optimize the technical scheme, the specific measures adopted further comprise:
further, in the first step, the brain space is divided into 116 brain areas, a time sequence of the brain areas is obtained, a Pearson correlation coefficient is used for constructing a functional brain network, and the constructed brain network is a weighted fully-connected network and is used for subsequent brain network analysis.
Further, in the second step, for the fully-connected network with the weight constructed in the first step, R given thresholds are simultaneously utilized to convert the weight network into a plurality of binarized networks, and a multi-level topological structure is depicted for subsequent feature extraction and structural feature selection.
Further, in the third step, for each thresholded brain network in the second step, the local clustering coefficient of each brain region is extracted as a feature, and the features from all brain regions form a feature vector together to depict the local topology of the brain network.
Further, in the fourth step, a graph core is used to define the similarity of the two networks, and in order to retain the topology information of the functionally connected network data, the graph core is used to directly define the overall structural similarity of the two network data, that is, the two brain networks under the r threshold value
Figure BDA0002109960910000031
And
Figure BDA0002109960910000032
the definition of similarity is:
Figure BDA0002109960910000033
wherein the content of the first and second substances,
Figure BDA0002109960910000034
representing two brain networks below the r-th threshold
Figure BDA0002109960910000035
And
Figure BDA0002109960910000036
the similarity of (a) to (b) is,
Figure BDA0002109960910000037
is a defined graph core, and the method of Weisfeiler-Lehman subtree is used to construct the corresponding graph core.
Further, in the fifth step, order
Figure BDA0002109960910000038
r＝1，2，...，R，XrRepresenting the feature matrix extracted in step three from N samples under R thresholds,
Figure BDA00021099609100000313
n denotes the feature vector extracted from the ith sample under the r-th threshold, d is each feature dimension;
let Y be [ Y1，y2…，yN]∈RNY denotes a response vector corresponding to N samples, YiN denotes the class label of the sample, classifying two classes of problems, yiE { +1, -1}, which can be expressed as patient and normal person, respectively;
based on the above, the objective function of the multi-threshold gk-MTFS feature selection method for the brain network is provided as follows:
Figure BDA0002109960910000039
wherein W ═ W1，w2，…，wR]∈Rd*NIs a weight matrix, wrDenotes the weight under the r-th threshold, Mr＝Cr-SrIs a Laplacian matrix, SrRepresenting a similarity matrix defined at the r-th threshold (i.e. task), using equation (1) to define the similarity of two networks, i.e. let
Figure BDA00021099609100000310
i＝1，2，...N，j＝1，2，...N，CrIs a diagonal matrix, and
Figure BDA00021099609100000311
Figure BDA00021099609100000312
representing the element on the ith diagonal;
the target function comprises three terms, wherein the first term is a loss function term and adopts a square loss function, the second term is a group-sparsity regularization term which is used for selecting common features from different tasks, the third term is a Laplacian regularization term which is used for retaining structural information of a network and distribution information of network data, and lambda and beta are constants which are used for balancing relative contribution between the three terms and are larger than 0.
The invention has the beneficial effects that: complementary information of threshold networks under different thresholds (tasks) is explored in a multi-task mode aiming at multiple thresholds, sample characteristics are fully extracted, the overall structure information and the self topological information of brain network data are reserved, and the gk-MTFS provided by the method is verified to have better classification performance on two real public data sets (an attention deficit hyperactivity disorder data set and an senile dementia data set).
Drawings
Fig. 1a to 1c show the curves of the classification accuracy results with different regularization parameters λ and β over three classification tasks, wherein fig. 1a shows the 1MCI vs. eMCI classification, fig. 1b shows the eMCI vs. hc classification, and fig. 1c shows the ADHD vs. hc classification.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
The invention provides a multi-task-based feature selection method under multi-threshold for a functional brain network, which comprises the following steps:
step one, preprocessing fMRI data to construct a functional brain network;
step two, adopting R thresholds to carry out thresholding treatment on the constructed functional brain network at the same time;
step three, extracting the clustering coefficient of the brain area of each thresholding network as a characteristic for measuring the local topological structure of the network;
step four, calculating the similarity of the overall topological structure among the networks by utilizing the graph cores for each thresholding network;
establishing a target function of the brain network-oriented multi-threshold gk-MTFS feature selection method;
and step six, optimizing the proposed objective function by utilizing an accelerated approximation gradient algorithm.
Order to
Figure BDA0002109960910000041
R1, 2.., R, which represents a feature matrix extracted from N samples under R thresholds in step three, where d is each feature dimension, let Y ═ Y ·1，y2…，yN]∈RNRepresenting a response vector corresponding to N samples, where yiClass labels representing samples, classifying two classes of problems, i.e. yiE { +1, -1}, which can be expressed as patient and normal person, respectively; based on the above, the objective function of the multi-threshold gk-MTFS feature selection method for the brain network is provided as follows:
Figure BDA0002109960910000042
wherein W ═ W1，w2，…，wR]∈Rd*NIs a matrix of weights that is a function of,
Figure BDA0002109960910000043
is a L2，1The paradigm is to encourage multiple rows of 0 vectors in the weight matrix W, and features corresponding to non-0 elements will be selected. By using L2，1An exemplary approach would have a small number of features to be jointly selected from multiple threshold tasks. Mr＝Cr-SrIs a Laplacian matrix, order SrRepresenting a similarity matrix defined at the r-th threshold (i.e. task), using equation (1) to define the similarity of two networks, i.e. let
Figure BDA0002109960910000044
i＝1，2，...N，j＝1，2，...N，CrIs a diagonal matrix, and
Figure BDA0002109960910000045
the target function comprises three terms, wherein the first term is a loss function term, a square loss function is adopted, the second term is a group-sparsity regularization term used for selecting common characteristics from different tasks, and the third term is a Laplacian regularization term used for retaining structural information of a network and distribution information of network data. λ and β are constants greater than 0 that are used to balance the relative contribution between the three terms.
In order to reserve the self topological structure information of the functional connection network data, a graph core is introduced, and the structural similarity of the two network data is directly defined, namely the two brain networks under the r threshold value
Figure BDA0002109960910000046
And
Figure BDA0002109960910000047
the definition of similarity is:
Figure BDA0002109960910000051
wherein, k represents a kernel function,
Figure BDA0002109960910000052
is a defined graph core, and the method of Weisfeiler-Lehman subtree is used to construct the corresponding graph core.
According to the Laplacian regular term defined above, when two samples are very similar, the two samples are as close as possible after mapping, and then the similarity of network data can be calculated through the graph kernel. This ensures that the structured information of the network is preserved, and the spatial distribution information of the whole network data is preserved.
For the solution of the defined objective function, the accelerated approximate gradient optimization which is widely applied at present is adopted. Experimental results on two real public datasets, namely adhd (attention default hyper activity disorder) dataset and ADNI (the Alzheimer's Disease neuroactive Initiative) demonstrate the effectiveness of the proposed method.
The technical solution of the present invention will be further described in detail with reference to the application examples below:
one embodiment of the present invention, enumerates the evaluation of the effectiveness of the proposed method on two published fMRI datasets. Table 1 gives the characteristics of these data sets.
Table 1: statistical information of samples of two data sets
Figure BDA0002109960910000053
MMSE＝Mini-Mental State Examination
For the ADHD dataset, using already pre-processed time series data from the NYU (New York university) site, detailed pre-processing steps can be performed in http: v/www.nitrc.org/plugs/mwiki/index php/neuroboureau: athena finds. The preprocessed data divides the brain into 90 brain areas according to AAL (automated Anatomical laboratory), each brain area comprises 172 time point data, and a Pearson correlation coefficient is used for constructing a functional brain network.
For the ADNI dataset, standard pre-processing pipelines were used, including time-slicing (rectification and cephalorectification). Image pre-processing was done using SPM8(Statistical Parametric Mapping software package) (http:// www.fil.ion.ucl.ac.uk.spm). For each sample, the first 10 fMRI images were discarded to ensure magnetization balance. The remaining images are corrected for inter-slice acquisition time delay first, followed by head motion correction to eliminate the effects of head motion. Since ventricular (ventricle) and White Matter (WM) regions contain relatively high noise, the Gray Matter (GM) is used to extract the Blood Oxygen Level Dependent (BOLD) signal to construct a functionally connected network, and each sample GM tissue is further used to mask (mask) their corresponding fMRI images in order to eliminate the possible effects of WM and CSF. The first scan of the fMRI time series is registered to the T1 weighted image of the same sample, and the estimated transformation is applied to other time series of the same sample. The rectified fMRI image is first registered to the same template space using the deformed registration method of HAMMER, and divided into 90 regions of interest (ROIs) using the AAL template. Finally, for each ROI, the mean fMRI time-series over all voxels (voxels) is taken as the time-series for that ROI. The same Pearson correlation coefficients are also used to construct functional brain networks.
The originally constructed brain network data is a fully-connected weighted graph, and in order to depict a topological structure in multiple levels, a multi-threshold mode is adopted to carry out thresholding on the data, so that a plurality of thresholded binary networks are obtained. And then extracting local clustering coefficients as features for each binary network according to a classical graph theory correlation algorithm. Finally, the feature selection is executed by adopting the proposed gk-MTFS method, and a multi-kernel support vector machine (multi-SVM) is adopted for classification in the classification step.
Table 2, table 3, table 4 show the experimental results of the proposed gk-MTFS method in three classification tasks, respectively, and are used as a comparison with the other three mainstream feature selection methods and the method without performing feature selection (Baseline). Specifically, the accuracy of our proposed method on three classification tasks of 1MCI and eMCI, eMCI and HC, and ADHD and HC was 76.5%, 76.9%, and 68.0%, respectively, and AUC values were 0.81, 0.79, and 0.70. The effectiveness of the proposed method is further verified.
Table 2: performance of all methods when classifying 1MCI and eMMC
Figure BDA0002109960910000061
Table 3: performance of all methods in eMMC vs. HC classification
Figure BDA0002109960910000062
Table 4: classification Performance of the method used in ADHD vs. HC Classification
Figure BDA0002109960910000063
Figure BDA0002109960910000071
All these results verify the validity of the gk-MTFS method in feature selection. From tables 2-4, it can be seen that the methods for performing feature selection (i.e., gk-MTFS, MMT-LASSO, and MMT-LASSO) can obtain better performance than the methods without feature selection (i.e., Baseline), which indicates the important contribution of feature selection to the improvement of brain disease classification performance. In addition, fig. 1a, 1b, 1c show the accuracy variation obtained with two regularization parameters λ, β varying. It can be observed that a smaller lambda value indicates that more sub-threshold features will be jointly selected, indicating that the classification performance of the multi-tasking feature selection method is largely influenced by the lambda values in the three classification tasks. This means that it is important to choose the optimal lambda value in the gk-MTFS method proposed by the present invention, probably due to the sparsity of the solution in the parametric lambda control equation.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.
It should be noted that the terms "upper", "lower", "left", "right", "front", "back", etc. used in the present invention are for clarity of description only, and are not intended to limit the scope of the present invention, and the relative relationship between the terms and the terms is not limited by the technical contents of the essential changes.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (2)

1. The feature selection method based on multiple tasks under the multiple threshold values facing the functional brain network is characterized by comprising the following steps:
preprocessing fMRI data to construct a functional brain network, wherein the constructed brain network is a weighted fully-connected network;
step two, adopting R thresholds to carry out thresholding treatment on the constructed functional brain network at the same time; for the fully-connected network with the weight constructed in the step one, simultaneously converting the weight network into a plurality of binary networks by utilizing R given threshold values for depicting a multi-level topological structure;
step three, extracting the clustering coefficient of the brain area of each thresholding network as a characteristic for measuring the local topological structure of the network; for each thresholded brain network in the step two, extracting a local clustering coefficient of each brain area as a feature, and forming a feature vector by the features from all the brain areas together for depicting a local topological structure of the brain network;
step four, calculating the similarity of the overall topological structure among the networks by utilizing the graph cores for each thresholding network; using graph kernels to directly define the overall similarity in structure of two network data, i.e. two brain networks for the mth threshold
Figure FDA0003022202270000011
And
Figure FDA0003022202270000012
the definition of similarity is:
Figure FDA0003022202270000013
wherein the content of the first and second substances,
Figure FDA0003022202270000014
representing two brain networks below the r-th threshold
Figure FDA0003022202270000015
And
Figure FDA0003022202270000016
the similarity of (a) to (b) is,
Figure FDA0003022202270000017
the method is characterized in that the method is a defined graph core, and a Weisfeiler-Lehman subtree method is used for constructing a corresponding graph core;
step five, based on the step three and the step four, establishing a target function based on a multitask feature selection method under a brain network-oriented multi-threshold value; order to
Figure FDA0003022202270000018
XrRepresenting the feature matrix extracted in step three from N samples under R thresholds,
Figure FDA0003022202270000019
representing the feature vectors extracted from the ith sample under the r threshold, d being each feature dimension;
let Y be [ Y1，y2…，yN]∈RNY denotes a response vector corresponding to N samples, YiN denotes the class label of the sample, classifying two classes of problems, yi∈{+1,-1}；
Based on the above, the objective function based on the multitask feature selection method under the multi-threshold facing brain network is provided as follows:
Figure FDA00030222022700000110
wherein W ═ W1,w2,…,wR]∈Rd*NIs a weight matrix, wrDenotes the weight under the r-th threshold, Mr＝Cr-SrIs a Laplacian matrix, SrRepresenting a similarity matrix defined below an r-th threshold,
Figure FDA0003022202270000021
Cris a diagonal matrix, and
Figure FDA0003022202270000022
Figure FDA0003022202270000023
representing the element on the ith diagonal;
the target function comprises three items, wherein the first item is a loss function item and adopts a square loss function, the second item is a group sparsity regularization item and is used for selecting common characteristics from different tasks, the third item is a Laplacian regularization item and is used for retaining structural information of a network and distribution information of network data, and lambda and beta are constants which are used for balancing relative contribution of the three items and are larger than 0;
and sixthly, performing optimization solution on the proposed objective function by using multi-core feature joint learning and using an accelerated approximation gradient algorithm to complete feature selection.
2. The functional brain network-oriented multi-threshold multi-task based feature selection method of claim 1, wherein: in the first step, the brain space is divided into 116 brain areas, the time sequence of the brain areas is obtained, and a functional brain network is constructed by using Pearson correlation coefficients.
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