CN112784886A - Brain image classification method based on multilayer maximum spanning tree image kernel - Google Patents

Brain image classification method based on multilayer maximum spanning tree image kernel Download PDF

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CN112784886A
CN112784886A CN202110032250.3A CN202110032250A CN112784886A CN 112784886 A CN112784886 A CN 112784886A CN 202110032250 A CN202110032250 A CN 202110032250A CN 112784886 A CN112784886 A CN 112784886A
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张道强
王晓歆
温旭云
马凯
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a brain image classification method based on a multilayer maximum spanning tree image kernel, which comprises the following steps: constructing a functional brain network with n nodes and n-1 edges connecting the two nodes for the rs-fMRI image of the brain of each main body, and setting different labels for each node in the functional brain network; layering the functional brain network constructed in the step 1, and setting a similarity weight for each layer; aggregating the similarity of each layer in the functional brain network to obtain a multilayer maximum spanning tree kernel; calculating to obtain a vector-based maximum spanning tree attribute core by using an RBF (radial basis function) and network attribute characteristics; combining the multilayer maximum spanning tree core and the maximum spanning tree attribute core by utilizing multi-core learning to obtain a maximum spanning tree combination core; and obtaining a brain image classification result by combining the maximum spanning tree with a kernel and an SVM classifier.

Description

Brain image classification method based on multilayer maximum spanning tree image kernel
Technical Field
The invention belongs to the technical field of medical image processing, and particularly relates to a brain image classification method based on a multilayer maximum spanning tree image kernel.
Background
The human brain is a complex system containing abundant structural and functional information. This structural and functional information can be described as a complex network with brain regions as nodes and connections between them as edges. Graph theory provides a variety of metrics to capture the functional integration, isolation, and centrality properties of a graph. A number of graph theory studies use network attributes to accurately identify neurological disease patients from healthy persons. Furthermore, the small world attribute, hub node, in the functional brain network was analyzed using graph theory. However, the graph theory-based approach represents the graph as a feature vector, which results in loss of structural information.
The nuclear approach provides a natural framework to directly measure the similarity between the graphs. Most of the existing graph core methods are to decompose a graph into a plurality of subgraphs and indirectly measure the similarity of the two graphs by calculating the similarity of the subgraphs. This measure requires the size of the subgraph to be controlled to a very small range to ensure the validity of the computation, which is considered to be an NP-hard problem. However, the current solution usually uses paths or step numbers to control the subgraph, but this method destroys the global information of the graph and only emphasizes the local information of the graph.
Furthermore, graph cores based on graph isomorphism, while performing similarity measurements globally, this graph isomorphism approach only applies to traditional graph data. In the brain network, each node represents a different brain area, which means that the label of each node is different, and thus the graph isomorphism problem does not exist. And the image cores designed on the traditional image data do not consider the problem that the edges in the brain network have uncertainty. The brain network is constructed because noise in data processing can cause some false connections in the network, which requires filtering the noise to obtain a sparse brain network. The current image kernel designed on the brain network usually adopts a threshold value strategy to filter noise, but the method ignores the individual difference of the brain network and the difference of edge distribution of different networks.
Disclosure of Invention
The purpose of the invention is as follows: in order to make up for the defects that the traditional image core does not consider the node uniqueness, the network hierarchy and the individual difference of the brain network, the invention provides a brain image classification method based on a multilayer maximum spanning tree image core.
In order to achieve the purpose, the invention is realized by the following technical scheme: a brain image classification method based on a multilayer maximum spanning tree graph core comprises the following steps:
step 1: constructing a functional brain network with n nodes and n-1 edges connecting the two nodes for the rs-fMRI image of the brain of each main body, and setting different labels for each node in the functional brain network;
step 2: layering the functional brain network constructed in the step 1, and setting a similarity weight for each layer;
and step 3: aggregating the similarity of each layer in the functional brain network to obtain a multilayer maximum spanning tree kernel;
and 4, step 4: and obtaining a brain image classification result by utilizing a multilayer maximum spanning tree kernel and an SVM classifier.
In order to achieve the purpose, the invention is realized by the following technical scheme: a brain image classification method based on a multilayer maximum spanning tree graph core comprises the following steps:
step 1: constructing a functional brain network with n nodes and n-1 edges connecting the two nodes for the rs-fMRI image of the brain of each main body, and setting different labels for each node in the functional brain network;
step 2: layering the functional brain network constructed in the step 1, and setting a similarity weight for each layer;
and step 3: aggregating the similarity of each layer in the functional brain network to obtain a multilayer maximum spanning tree kernel;
and 4, step 4: calculating to obtain a vector-based maximum spanning tree attribute core by using an RBF (radial basis function) and network attribute characteristics;
and 5: combining the multilayer maximum spanning tree core and the maximum spanning tree attribute core by utilizing multi-core learning to obtain a maximum spanning tree combination core;
step 6: and obtaining a brain image classification result by combining the maximum spanning tree with a kernel and an SVM classifier.
Further, the step 1 specifically includes:
s110: registering the rs-fMRI image space of the brain of each sample to n interested ROIs according to an AAL template, and taking each ROI as a node in a constructed brain function network;
s120: calculating the arithmetic mean value of the activation signals of all voxels in each ROI at different time points, and taking the set of arithmetic mean values as an average time sequence corresponding to the signal change of each ROI;
s130: for a particular sample, the time series of the ith and j ROIs is represented by xiAnd xjDenotes that x isiAnd xjThe Pearson correlation coefficient between them is taken as the weight of the edge connecting the node i and the node j, and is represented by GijRepresents;
s140: an n × n functional brain network G ═ (V, E, C, L) is constructed for each sample, with V ═ V { (V, E, C, L)1，v2，…，vnSet of nodes, C ═ CijSetting different labels L (v) for each node in the brain network according to different nodes in the brain function network corresponding to different brain regions, wherein | i ═ 1, …, n, j ═ 1, …, n } is an edge weight set, E is an edge set, L is a function of the nodes mapping to discrete labels, andi)＝i。
further, the step 2 specifically includes:
s210: taking the functional brain network G as a forest with n nodes and 0 edge, and marking as T(0)；
S220: sorting all edges in the functional brain network G in a descending order according to the weight, and converting all weighted edges into non-weighted edges, wherein the functional brain network is represented as G ═ V, E, L and O, wherein E is a set of the non-weighted edges, and O is a set of edge sorting results;
s230: selecting the weight at the ith layer from high to low, and if the edge is added into the forest to form a closed loop, selecting the next edge downwards in sequence according to the weight sorting sequence until no closed loop is formed; combining two nodes connected by the newly added edge into one node to form a new forest which is marked as T(i)The forest comprises i edges, T(i)＝(V，E(i)L), where V is the set of nodes of the functional brain network, E)(i)To select the set of weightless edges, | E(i)|＝i；
S240: i ═ i +1, where i ═ 0,1 …, n-1, step S230 continues until forest T(0)N nodes in (2) are merged into one node, which is represented as: t is(n-1)＝(V，E(n-1)L); layering is completed;
s250: a similarity weight is set for each layer of the functional brain network.
Further, the step 3 specifically includes:
for functional brain network G1And G2：
G1＝{T1 (0)，T1 (1)，T1 (2)，...，T1 (n-1)}
Figure BDA0002891794140000031
By calculating T1 (i)And
Figure BDA0002891794140000032
the number of the same edges in the functional brain network is used as the similarity of the ith layer of the functional brain network, and the same edges are defined as that nodes connected by the edges have the same label;
and (3) polymerizing the similarity of each layer to obtain a multilayer maximum spanning tree core:
Figure BDA0002891794140000033
in the formula, λiWeight similarity for each layer
Figure BDA0002891794140000034
Figure BDA0002891794140000035
Representing a node v1And node j, S () is a discriminant function:
Figure BDA0002891794140000036
further, the network attribute feature includes: average path length, node degree, betweenness centrality, and leaf node ratio.
Further, the step 5 specifically includes:
normalizing the multilayer maximum spanning tree core and the maximum spanning tree attribute core;
combining the multi-level maximum spanning tree kernel and the maximum spanning tree attribute kernel according to the following formula:
MK(G1，G2)＝β1K(G1，G2)+β2V(G1，G2) (9)
wherein, K (G)1，G2) For the multi-level maximum spanning tree kernel, V (G)1，G2) Is the maximum spanning tree attribute kernel, beta is a non-negative weight parameter, beta1+β2＝1。
Further, the weight parameter β1And beta2The grid search method is used to determine through cross validation of the training data.
Has the advantages that: compared with the prior art, the invention has the following advantages:
(1) the invention considers the local and global structure information of the graph, and makes up the deficiency that the existing graph core does not consider the hierarchical information and the individual difference of the brain network;
(2) the invention constructs the maximum spanning tree to obtain the sparse brain network by utilizing the advantages of the minimum spanning tree and the characteristics of high relevance connection in the brain network. Layering a brain network in the MST construction process, and under the condition that the size of a sub-graph is not predefined, similarity between a local measurement graph and a global measurement graph is obtained;
(3) the invention combines the multi-layer maximum spanning tree core (ML-MST) and the maximum spanning tree attribute core (MPK) to obtain the multi-layer maximum spanning tree combined core (ML-MCK), and simultaneously considers the combination of the hierarchy information and the topology attribute information of the graph, thereby more comprehensively depicting the structure and the modularization information of the graph.
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FIG. 1 is an overall framework of a multi-level maximum spanning tree kernel;
FIG. 2 is an overall framework of a maximum spanning tree property core;
FIG. 3 is an overall framework of a multi-level maximum spanning tree combining kernel;
fig. 4 is a diagram of a brain region and a pattern of connections between brain regions with significant differences.
Detailed Description
The invention discloses a brain image classification method based on a multilayer maximum spanning tree combined kernel, which comprises the following steps of:
step 1: constructing a functional brain network; the method specifically comprises the following steps:
s110: according to the AAL template, spatially registering the rs-fMRI image of the brain of each sample to n interested areas (ROI), wherein each ROI represents one node in the constructed brain function network;
s120: calculating the arithmetic mean of the activation signals of all voxels in each ROI at different time points, the calculation formula is as follows:
Figure BDA0002891794140000041
in the formula (I), the compound is shown in the specification,
Figure BDA0002891794140000042
represents the activation signal of the nth voxel, | ROIiL represents the number of voxels in the ith region of interest (ROI).
ROIiAverage time series x corresponding to signal changei＝(xi(1)，xi(2)，…，xi(T)), T being the length of the time series;
s130: for a particular sample, the time series of the ith and j ROIs is represented by xiAnd xjDenotes that x isiAnd xjThe Pearson correlation coefficient between them is used as the weight of the edge between the connection node i and the node j, and is represented by CijRepresents:
Figure BDA0002891794140000051
of these, cov (x)i，xj) Is xiAnd xjThe covariance of (a) of (b),
Figure BDA0002891794140000054
is xiStandard deviation of (2).
S140: an n × n functional brain network G ═ (V, E, C, L) is constructed for each sample, where V ═ { V ═ V1，v2，…，vnSet of nodes, C ═ C ij1, …, n, j 1, …, n, is an edge weight set, E is an edge set, L is a function of the mapping of nodes to discrete labels, and a different label L (v) is set for each node in the brain network, considering that different nodes in the brain functional network correspond to different brain regions (v | i ═ 1, …, n, j ═ 1, …, n |)i)＝i。
Step 2: layering functional brain networks; the method specifically comprises the following substeps:
s210: for a given functional brain network G, consider n nodes in the functional brain network G as n trees, which are treated as a forest with n nodes and 0 edges denoted as T(0)；
S220: sorting all edges in the functional brain network G in a descending order according to the weight, only keeping the position information of the edges, discarding the weight information, namely converting all weighted edges into non-weighted edges, wherein the functional brain network G is (V, E, L, O), E is a set of the non-weighted edges, and O is a set of edge sorting results;
s230: and at the ith layer, selecting the edges with the weights ranked from high to low, and if the edges are added into the back forest to form closed loops, sequentially selecting the edges downwards according to the ranking sequence until a closed loop is not formed. The two trees connected by this edge are then merged into one tree, the new forest being denoted T(i)Containing i edges, T(i)＝(V，E(i)L), where V is the set of nodes of the functional brain network, E)(i)To select the set of weightless edges, | E(i)|＝i。
S240: continuing to step S230 until forest T(0)N trees in (1) are merged into one tree, which is denoted as T(n-1)＝(V，E(n-1)，L)。
The invention defines a functional brain network G by calculating the similarity of a spanning tree construction layer1And G2The similarity between them.
And step 3: and calculating a multilayer Maximum Spanning Tree (MST) kernel, wherein the edges of each layer are selected according to the weight of the edges in the functional brain network, the ith layer has i edges, the multilayer MST kernel firstly layers the network and then aggregates the similarity of each layer to calculate the similarity between the two images, and the similarity of each layer is calculated by the number of the same edges. Referring to fig. 1, specifically, the following steps are performed:
since each layer of the functional brain network can be regarded as a group of subtrees, the similarity problem of the hierarchical network is solved by extending subtree cores. For functional brain network G1And G2，G1And G2Can be expressed as:
G1＝{T1 (0)，T1 (1)，T1 (2)，...，T1 (n-1)}
Figure BDA0002891794140000052
calculating T1 (i)And
Figure BDA0002891794140000053
the number of identical edges in (a) is taken as the similarity of the i-th layer of the functional brain network. An identical edge is defined as a node to which this edge connects having the same label.
This may result in very high or very low similarity between the layers, since layering the brain network using the MST construction process results in less network information at the initial layers. Therefore, the invention sets a similarity weight for each layer to make up for the deficiency of the initial layer information. Layer 0, i.e. T1 (0)And
Figure BDA0002891794140000061
the weight of the similarity between the layers is 0, and the weight is increased with the increase of the layer number. Then, the similarity of each layer is polymerized to finally obtain a functional brain network G1And G2Similarity between them:
Figure BDA0002891794140000062
in the formula, λiWeight similarity for each layer
Figure BDA0002891794140000063
Figure BDA0002891794140000064
Representing a node v1And node j, S () is a discriminant function defined as follows:
Figure BDA0002891794140000065
after the MST kernel is obtained through calculation, the traditional SVM classifier can be directly used for realizing medical image classification.
On the basis of the steps 1 to 3, the invention adds the topological attribute characterization characteristics of the network, thereby obtaining the following scheme: the following scheme is that after the steps 1 to 3 are executed, the following steps are executed: and 4, step 4: calculating a Maximum Spanning Tree (MST) attribute core; referring to fig. 2, the method specifically includes:
the topological properties of functional brain networks can be characterized by the network properties in graph theory. The network attributes used in the present method measure the functional separation, aggregation and centrality of the brain network. Brain function separation refers to the ability of interconnected brain regions to process information independently, usually measured by clustering coefficients, defined as the ratio of the number of all closed three-point connected groups to the number of all connected three-point connected groups in the network. Brain function aggregation is the ability to integrate specific information in each region of the brain, usually measured by the average path length, defined as the average of the shortest paths between any two points in the network, and is calculated as follows:
Figure BDA0002891794140000066
wherein d isijIs the shortest path between node i and node j.
Measuring the centrality properties of the brain function network, searching for pivotal nodes that interact with many other areas and play an important role in brain function and network robustness integration. The centrality attribute is usually measured by using a node degree and an betweenness centrality, wherein the node degree is defined as the number of edges connected on a node, and the betweenness centrality is defined as the proportion passing through a node i in the shortest path, and the calculation formula is as follows:
Figure BDA0002891794140000071
where ρ ishjThe number of shortest paths, ρ, between time node h and node jhj(i) The number of paths passing through node i in the shortest path between time node h and node j. Because MST is a tree structure and has no loop and can not calculate a clustering coefficient, the specific attribute leaf node ratio of MST is calculated to describe the overall topological structure of the network, and is defined as the proportion of leaf nodes in the maximum spanning tree to the total node number, wherein the leaf nodes are defined as nodes with the node degree of 0. Network traffic is more dependent on the hub node when the leaf node ratio is high. The average path length, node degree, betweenness centrality and leaf node ratio are therefore calculated as network attribute features according to the above definitions. And then, carrying out feature selection by using an independent sample T test, wherein the independent sample T test is used for testing the data difference of the two groups of samples, the image features of the positive type and the negative type are divided into two groups, and the test statistic is as follows:
Figure BDA0002891794140000072
Figure BDA0002891794140000073
Figure BDA0002891794140000074
is the sample variance, n1And n2And (4) for the number of samples, calculating to obtain statistics, then looking up a corresponding boundary value table, determining a p value, wherein the p value is greater than 0.05, namely that the two have no significance difference, discarding the feature, otherwise, keeping the feature, and realizing feature selection. Finally, using the RBF kernel function:
Figure BDA0002891794140000075
where x is the sample and σ is the adjustable parameter of the kernel function.
A vector-based MST attribute core is implemented.
And 5: a multi-layer maximum spanning tree combining core; referring to fig. 3, the method specifically includes:
because the vector core and the graph core are two different types of cores, normalization is needed, then multi-core learning is utilized to combine the multi-layer MST core and the MST attribute core, and the calculation formula of the multi-core learning is as follows:
MK(G1，G2)＝β1K(G1，G2)+β2V(G1，G2) (9)
wherein, K (G)1，G2) Is the MST structural nucleus, V (G)1，G2) Is MST attribute kernel, beta is non-negative weight parameter, beta1+β2＝1。
Determining optimal beta by cross-validation of training data using a grid search method1And beta2Once the optimal parameters are obtained, the two MST based cores are converted into a graph core. The traditional SVM classifier can be directly used for medical image classification.
The invention is now supported by experimental data.
The experimental data set obtained from the ADNI public database, for a total of 149 subjects' rs-fMRI data, including 99 MCI patients and 50 normal persons. Of the 99 MCI patients, 56 early MCI patients (EMCI) and 43 late MCI patients (LMCI). The data acquisition of this data set is as follows: 34 sheets, 4mm in layer thickness, 64 × 64 in matrix size, 0mm in pitch, 2000ms in TR, 32ms in TE, 77 degrees in flip angle, 256mm in FOV.
The MST kernel method was validated on two classification tasks, mild cognitive impairment classification (MCI vs. nc) and MCI period prediction (EMCI (early MCI) vs. lmci (late MCI)). Cross-validation was performed in this experiment using the leave-one-out method (LOO), and classification performance was validated by calculating classification Accuracy (ACC) and F1-score.
In order to verify the validity of brain network hierarchical information, sequential comparison experiments were performed. The comparison method comprises the following steps:
(1) MST: constructing MST structure core by calculating same edge number of last layer
(2) ML-MST: constructing a multi-layered MST core by computing the similarity of each layer
(3) MPK: MST attribute core
(4) MCK: map kernel for MST and MPK synthesis
(5) ML-MCK: ML-MST and MPK.
TABLE 1 Experimental results of two classification tasks on different methods
Figure BDA0002891794140000081
As can be seen from table 1, the performance of the MSL is higher than MSL _ nensplit, which indicates that the MSL can capture the hierarchical information of the brain network and improve the classification performance. In addition, the performance of the multi-layer maximum spanning tree combined core method is superior to that of MSL and MPK, which shows that the network structure can be better mapped to the feature space by combining the network attribute and the network hierarchy structure information.
Further comparing the method of the present invention with other six graphical kernel methods, the results are shown in table 2, which shows that the method of the present invention achieves better results on both classification tasks.
The comparison method comprises the following steps:
(1)Weisfeiler-LehmanShortest Path Kernel(WL-shortestpath)[1]
(2)Weisfeiler-Lehman Subtree Kernel(WL-subtree)[1]
(3)Weisfeiler-Lehman Edge Kernel(WL-edge)[1]
(4)Shortest path Kernel(Shortest-path)[2]
(5)Truncated Tree Based Graph Kernels(Tree++)[3]
(6)K-core graphlet kernel(Core GR)[4]
[1]Nino Shervashidze，Pascal Schweitzer，Erik Jan，Van Leeuwen，Kurt Mehlhorn，and Karsten M Borgwardt，“Weisfeiler-lehman graph kernels.，”Journal of Machine Learning Research，vol.12，no.9，2011.
[2]K.M.Borgwardt and H.-P.Kriegel.Shortest-path kernels on graphs.In Proceedings of the International Conference on Data Mining，pages 74-81，2005.
[3]Wei Ye，Zhen Wang，Rachel Redberg，and Ambuj Singh，“Tree++：Truncated tree based graph kernels，”IEEE Transactions on Knowledge and Data Engineering，2019.
[4]Giannis Nikolentzos，Polykarpos Meladianos，Stratis Limnios，and Michalis Vazirgiannis，“A degeneracy framework for graph similarity.，”in IJCAI，2018，pp.2595-2601.
TABLE 2 Experimental results of two classification tasks on different methods
Figure BDA0002891794140000091
It can be seen from table 2 that a graph core designed on conventional graph data may not be suitable for a brain network classification with each node being unique and edge uncertainty. In addition, the method combines the global property, the local property and the hierarchical information, and can describe the discrimination information more effectively than the kernel function only considering the unilateral information. In addition, the method adopts the MST method to replace a threshold strategy to obtain the sparse brain network capable of retaining the network global structure information.
Importance of brain regions. Because the method uses the same edge number in the MST construction process as the similarity measurement of the brain network, the significance analysis is carried out on the maximum spanning tree.
Fig. 4 shows all brain regions with significant differences and the connections between them. It can be seen that the hippocampus, amygdala, frontal lobe and tongue gyrus are significant in both analyses, suggesting that these brain regions play a very important role in the recognition of MCI patients. This result is also consistent with previous studies in which the hippocampal structure of MCI patients was severely compromised and amygdala functional connectivity was altered in MCI patients.

Claims (10)

1. A brain image classification method based on a multilayer maximum spanning tree image kernel is characterized in that: the method comprises the following steps:
step 1: constructing a functional brain network with n nodes and n-1 edges connecting the two nodes for the rs-fMRI image of the brain of each sample, and setting different labels for each node in the functional brain network;
step 2: layering the functional brain network constructed in the step 1, and setting a similarity weight for each layer;
and step 3: aggregating the similarity of each layer in the functional brain network to obtain a multilayer maximum spanning tree kernel;
and 4, step 4: and obtaining a brain image classification result by utilizing a multilayer maximum spanning tree kernel and an SVM classifier.
2. The method for classifying the brain image based on the multi-layer maximum spanning tree graph kernel according to claim 1, wherein: the step 1 specifically comprises:
s110: registering the rs-fMRI image space of the brain of each sample to n interested ROIs according to an AAL template, and taking each ROI as a node in a constructed brain function network;
s120: calculating the arithmetic mean value of the activation signals of all voxels in each ROI at different time points, and taking the set of arithmetic mean values as an average time sequence corresponding to the signal change of each ROI;
s130: for a particular sample, the time series of the ith and j ROIs is represented by xiAnd xjDenotes that x isiAnd xjThe Pearson correlation coefficient between them is used as the weight of the edge between the connection node i and the node j, and is represented by CijRepresents;
s140: an n × n functional brain network G ═ (V, E, C, L) is constructed for each sample, with V ═ V { (V, E, C, L)1，v2，…，vnSet of nodes, C ═ CijSetting different labels L (v) for each node in the brain network according to different nodes in the brain function network corresponding to different brain regions, wherein | i ═ 1, …, n, j ═ 1, …, n } is an edge weight set, E is an edge set, L is a function of the nodes mapping to discrete labels, andi)＝i。
3. the method for classifying the brain image based on the multi-layer maximum spanning tree graph kernel according to claim 2, wherein: the step 2 specifically comprises:
s210: taking the functional brain network G as a forest with n nodes and 0 edge, and marking as T(0)；
S220: sorting all edges in the functional brain network G in a descending order according to the weight, and converting all weighted edges into non-weighted edges, wherein the functional brain network is represented as G ═ V, E, L and O, wherein E is a set of the non-weighted edges, and O is a set of edge sorting results;
s230: selecting the weight at the ith layer from high to low, and if the edge is added into the forest to form a closed loop, selecting the next edge downwards in sequence according to the weight sorting sequence until no closed loop is formed; combining two nodes connected by the newly added edge into one node to form a new forest which is marked as T(i)The forest comprises i edges, T(i)＝(V,E(i)L), where V is the set of nodes of the functional brain network, E)(i)To select the set of weightless edges, | E(i)|＝i；
S240: i-i +1, wherein,i-0, 1 …, n-1, and continues to step S230 until forest T(0)N nodes in (2) are merged into one node, which is represented as: t is(n-1)＝(V,E(n-1)L); layering is completed;
s250: a similarity weight is set for each layer of the functional brain network.
4. The method for classifying the brain image based on the multi-layer maximum spanning tree graph kernel according to claim 3, wherein: the step 3 specifically includes:
for functional brain network G1And G2：
G1＝{T1 (0),T1 (1),T1 (2),...,T1 (n-1)}
Figure FDA0002891794130000021
By calculating T1 (i)And
Figure FDA0002891794130000022
the number of the same edges in the functional brain network is used as the similarity of the ith layer of the functional brain network, and the same edges are defined as that nodes connected by the edges have the same label;
and (3) polymerizing the similarity of each layer to obtain a multilayer maximum spanning tree core:
Figure FDA0002891794130000023
in the formula, λiWeight similarity for each layer
Figure FDA0002891794130000024
Figure FDA0002891794130000025
Representing a node v1And between node jS () is a discriminant function:
Figure FDA0002891794130000026
5. a brain image classification method based on a multilayer maximum spanning tree image kernel is characterized in that: the method comprises the following steps:
step 1: constructing a functional brain network with n nodes and n-1 edges connecting the two nodes for the rs-fMRI image of the brain of each sample, and setting different labels for each node in the functional brain network;
step 2: layering the functional brain network constructed in the step 1, and setting a similarity weight for each layer;
and step 3: aggregating the similarity of each layer in the functional brain network to obtain a multilayer maximum spanning tree kernel;
and 4, step 4: calculating to obtain a vector-based maximum spanning tree attribute core by using an RBF (radial basis function) and network attribute characteristics;
and 5: combining the multilayer maximum spanning tree core and the maximum spanning tree attribute core by utilizing multi-core learning to obtain a maximum spanning tree combination core;
step 6: and obtaining a brain image classification result by combining the maximum spanning tree with a kernel and an SVM classifier.
6. The method for classifying the brain image based on the multi-layer maximum spanning tree graph kernel according to claim 5, wherein: the step 1 specifically comprises:
s110: registering the rs-fMRI image space of the brain of each sample to n interested ROIs according to an AAL template, and taking each ROI as a node in a constructed brain function network;
s120: calculating the arithmetic mean value of the activation signals of all voxels in each ROI at different time points, and taking the set of arithmetic mean values as an average time sequence corresponding to the signal change of each ROI;
s130: for a particularGiven the sample, the time series of i and j ROIs is defined by xiAnd xjDenotes that x isiAnd xjThe Pearson correlation coefficient between them is used as the weight of the edge between the connection node i and the node j, and is represented by CijRepresents;
s140: an n × n functional brain network G ═ (V, E, C, L) is constructed for each sample, with V ═ V { (V, E, C, L)1，v2，…，vnSet of nodes, C ═ CijSetting different labels L (v) for each node in the brain network according to different nodes in the brain function network corresponding to different brain regions, wherein | i ═ 1, …, n, j ═ 1, …, n } is an edge weight set, E is an edge set, L is a function of the nodes mapping to discrete labels, andi)＝i。
7. the method for classifying the brain image based on the multi-layer maximum spanning tree graph kernel according to claim 6, wherein: the step 2 specifically comprises:
s210: taking the functional brain network G as a forest with n nodes and 0 edge, and marking as T(0)；
S220: sorting all edges in the functional brain network G in a descending order according to the weight, and converting all weighted edges into non-weighted edges, wherein the functional brain network is represented as G ═ V, E, L and O, wherein E is a set of the non-weighted edges, and O is a set of edge sorting results;
s230: selecting the weight at the ith layer from high to low, and if the edge is added into the forest to form a closed loop, selecting the next edge downwards in sequence according to the weight sorting sequence until no closed loop is formed; combining two nodes connected by the newly added edge into one node to form a new forest which is marked as T(i)The forest comprises i edges, T(i)＝(V,E(i)L), where V is the set of nodes of the functional brain network, E)(i)To select the set of weightless edges, | E(i)|＝i；
S240: i ═ i +1, where i ═ 0,1 …, n-1, step S230 continues until forest T(0)N nodes in (2) are merged into one node, which is represented as: t is(n-1)＝(V,E(n-1)L); go toA component layer;
s250: a similarity weight is set for each layer of the functional brain network.
8. The method for classifying the brain image based on the multi-layer maximum spanning tree graph kernel according to claim 7, wherein: the step 3 specifically includes:
for functional brain network G1And G2：
G1＝{T1 (0),T1 (1),T1 (2),...,T1 (n-1)}
Figure FDA0002891794130000031
By calculating T1 (i)And
Figure FDA0002891794130000032
the number of the same edges in the functional brain network is used as the similarity of the ith layer of the functional brain network, and the same edges are defined as that nodes connected by the edges have the same label;
and (3) polymerizing the similarity of each layer to obtain a multilayer maximum spanning tree core:
Figure FDA0002891794130000041
in the formula, λiWeight similarity for each layer
Figure FDA0002891794130000042
Figure FDA0002891794130000043
Representing a node v1And node j, S () is a discriminant function:
Figure FDA0002891794130000044
9. the method for classifying the brain image based on the multi-layer maximum spanning tree graph kernel according to claim 5, wherein: the network attribute feature in step 4 includes: average path length, node degree, betweenness centrality, and leaf node ratio.
10. The method for classifying the brain image based on the multi-layer maximum spanning tree graph kernel according to claim 9, wherein: the step 5 specifically includes:
normalizing the multilayer maximum spanning tree core and the maximum spanning tree attribute core;
combining the multi-level maximum spanning tree kernel and the maximum spanning tree attribute kernel according to the following formula:
MK(G1,G2)＝β1K(G1,G2)+β2V(G1,G2) (9)
wherein, K (G)1,G2) For the multi-level maximum spanning tree kernel, V (G)1,G2) Is the maximum spanning tree attribute kernel, beta is a non-negative weight parameter, beta1+β2＝1。
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