【免费】2019-InceptionGCN，ReceptiveFieldAwareGraph-基于矩阵+图表示-rrr1

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InceptionGCN: Receptive Field Aware Graph

Convolutional Network for Disease Prediction

Anees Kazi

, Shayan Shekarforoush

, S.Arvind krishna

, Hendrik Burwinkel

Gerome Vivar

1,4

, Karsten Kort

, Seyed-Ahmad Ahmadi

, Shadi

Albarqouni

, and Nassir Navab

1,6

Computer Aided Medical Procedures (CAMP), Technical University of Munich,

Munich, Germany

Sharif University of Technology, Tehran, Iran

Department of Computer Science and Engineering, National Institute of Technology

Tiruchirappalli, India

German Center for Vertigo and Balance Disorders, Ludwig Maximilians Universit

unchen, Germany

Augenklinik der Universit

at, Klinikum der Universit

at M

unchen, Germany

Whiting School of Engineering, Johns Hopkins University, Baltimore, USA

Abstract. Geometric deep learning provides a principled and versatile

manner for integration of imaging and non-imaging modalities in the

medical domain. Graph Convolutional Networks (GCNs) in particular

have been explored on a wide variety of problems such as disease pre-

diction, segmentation, and matrix completion by leveraging large, multi-

modal datasets. In this paper, we introduce a new spectral domain archi-

tecture for deep learning on graphs for disease prediction. The novelty lies

in deﬁning geometric ’inception modules’ which are capable of captur-

ing intra- and inter-graph structural heterogeneity during convolutions.

We design ﬁlters with different kernel sizes to build our architecture. We

show our disease prediction results on two publicly available datasets.

Further, we provide insights on the behaviour of regular GCNs and our

proposed model under varying input scenarios on simulated data.

1 Introduction

There is an increasing focus on applying deep learning on unstructured data in

the medical domain, especially using Graph Convolutional Networks (GCNs)

[1]. Multiple applications have been demonstrated so far, including Autism

Spectrum Disorder prediction with manifold learning to distinguish between

diseased and healthy brains [2], matrix completion to predict the missing val-

ues in medical data [3], and ﬁnding drug similarity using graph auto encoders

[4]. In this paper, we study the task of Alzheimer and Autism disease prediction

with complementary imaging and non-imaging multi-modal data.

In above works, GCNs had a remarkable impact on the usage of multi-

modal medical data. One key difference to previous learning-based methods

is to set patients in relation to each other with a neighborhood graph, often by

arXiv:1903.04233v1 [cs.LG] 11 Mar 2019

2 A. Kazi et al.

associating them through non-imaging data like gender, age, clinical scores or

other meta-information. On this graph, patients can be considered as nodes, pa-

tient similarities are represented as edge weights and features from e.g. imag-

ing modalities are incorporated through graph signal processing. GCNs then

provide a principled manner for learning optimal graph ﬁlters that minimize a

objective. Here, we use node-level classiﬁcation for our disease prediction task.

A simple analogy to node-based classiﬁcation of the population is image

segmentation with CNNs, where each pixel is a node and the image grid is the

graph. In such domains, ﬁlters with a constant size can manage to acquire se-

mantic features over the whole grid domain, given convolutions over a constant

number of equidistant neighbors. In the case of irregular graphs, the number of

neighbors and their distance from each other leads to heterogeneous density

and local structure. Applying ﬁlters with constant kernel size over the whole

grid domain might not produce semantic and comparable features.

In medical datasets, graphs deﬁned on patient’s data observe similar het-

erogeneity, as each patient may have a distinct combination of non-imaging

data and different number of neighbors. A concrete example is shown in Fig.

1 (left), which depicts a population graph of 150 subjects for Alzheimer’s dis-

ease classiﬁcation, who are arranged in clusters of varying density and local

topology (regions a, b and c). Such heterogeneity in the graph structure should

be considered to learn cluster-speciﬁc features. A model capable of producing

similar intra-cluster and different inter-cluster features can be designed by ap-

plying multi-sized kernels on the same input. To this end, we propose Incep-

tionGCN, inspired by the successful inception [5] architecture for CNNs. Our

model leverages spectral convolutions with different kernel sizes and chooses

optimal features to solve the classiﬁcation problem.

To the best of our knowledge, there is not much related literature that fo-

cuses on receptive ﬁelds of GCN ﬁlters. Earlier works [1,6] use GCNs with

constant ﬁlter size for the node-based classiﬁcation task and show the supe-

riority of GCN but do not address the problem of heterogeneity of the graph.

In [7], a method is proposed that determines a receptive path for each node

rather than a ﬁeld for performing the convolutions for representation learn-

ing. Irrespective of nearest neighbors, the aim is to perform convolutions with

selective nodes in the receptive ﬁeld. In [8], a DenseNet-like architecture [9] is

proposed, in which outputs from consecutive layers are concatenated. Here, the

receptive ﬁeld is addressed in an indirect way since the output features of suc-

cessive layers depend on multiple previous layers through skip connections.

Another work [10] uses features that are either ﬁxed, hand-designed or based

on aggregator-functions. Moreover, the method needs a pre-deﬁned order of

nodes which is difﬁcult to obtain.

In this paper we show that InceptionGCN is an improvement in terms of

performance and convergence. Our contributions are: (1) we analyze the inter-

dependence of graph structure and ﬁlter sizes on one artiﬁcial and two public

medical datasets and in doing so, we motivate the need for multiple kernel

size. (2) We propose our novel InceptionGCN model with multiple ﬁlter kernel

InceptionGCN 3

Fig. 1. Left: Afﬁnity graph with clusters for TADPOLE dataset, different cluster sizes are

depicted at points (a), (b) and (c). Right: Setup of InceptionGCN, feature matrix X is pro-

cessed by several GC-layers with considered neighborhood k

, · · · , k

in each inception

module. The output of each layer is used in the aggregator function.

sizes. We validate it on artiﬁcial and clinical data and the show improved per-

formance over regular GCN architectures. (3) We demonstrate the robustness

of our model towards different approaches for constructing graph adjacency

from non-imaging data.

2 Methodology

Traditional models [11] use a constant ﬁlter size throughout all layers, which

forces the features of every node to be learned using neighbors at a ﬁxed num-

ber of hops away without consideration of cluster size and shape. Our pro-

posed InceptionGCN model overcomes this limitation by varying the ﬁlters’

size across the GC-layers in order to produce class separable output features.

This property of our model is highly desirable when each class distribution has

distinct variance and/or when the classes are heavily overlapping. Utilizing

this setting, we target to solve the disease classiﬁcation task by incorporating

semantics of varied associations coming from different graphs within the popu-

lation. We provide a detailed description of the model starting from the afﬁnity

graph construction followed by the mathematical background and a discussion

of the proposed model architecture.

2.1 Afﬁnity graph construction

The construction of an afﬁnity graph is crucial to accurately model the interac-

tions among the patients and should be designed carefully. The afﬁnity graph

G =

(

V, E, W

)

is constructed on the entire population (including training and

testing samples) of the patients, where

= N vertices, E are the edge connec-

tions of the graph and W are the weights of the edges. Considering each patient

as a node n

in the graph, G incorporates the similarities between the patients

with respect to the non-imaging data η. The features x

∈ R

at every node

are fetched from imaging data. First, we construct a binarized edge graph

E ∈ R

N×N

representing the connections. Mathematically, E can be deﬁned as

i,j



1 i f



− η



< β

0 otherwise

(1)

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