Dual-Curriculum Contrastive Multi-Instance Learning for Cancer Prognosis Analysis with Whole Slide Images
Abstract
The multi-instance learning (MIL) has advanced cancer prognosis analysis withwhole slide images (WSIs).
However, current MIL methods for WSI analysis stillconfront unique challenges.
Previous methods typically generate instance representations via a pre-trained model or a model trained by the instances with bag-levelannotations, which, however, may not generalize well to the downstream task dueto the introduction of excessive label noises and the lack of ﬁne-grained information across multi-magniﬁcation WSIs.
Additionally, existing methods generallyaggregate instance representations as bag ones for prognosis prediction and haveno consideration of intra-bag redundancy and inter-bag discrimination.
To addressthese issues, we propose a dual-curriculum contrastive MIL method for cancerprognosis analysis with WSIs.
The proposed method consists of two curriculums,i.e., saliency-guided weakly-supervised instance encoding with cross-scale tilesand contrastive-enhanced soft-bag prognosis inference.
Extensive experimentson three public datasets demonstrate that our method outperforms state-of-the-artmethods in this ﬁeld.
The code is available.
Introduction
Cancer prognosis analysis is of great signiﬁcance for risk-beneﬁt assessment and clinical decision [1].
Computational whole slide image (WSI), which entails the quantitative proﬁling of spatial patternsand tumor microenvironments in tissue slides, has advanced the application of deep learning in cancerprognosis analysis [2, 3].
However, deep learning in WSIs is often hindered by the gigapixel sizeand the lack of pixel-level annotations [4].
Recently, multi-instance learning (MIL) methods haveattracted increasing attention to performing inference in a weakly-supervised manner and have beensuccessfully applied to WSI analysis [5, 6, 7].
In general, the MIL consists of two stages, i.e., instance encoding and aggregation stages [8, 9].
In theencoding stage, several methods have utilized the pre-trained model (e.g., ResNet on ImageNet) toextract instance representations in an unsupervised way (i.e., without the reference of outcome labels)[10, 11, 12].
However, recent studies have demonstrated that the pre-trained model may not generalizewell to the downstream tasks as it is task-agnostic 1 and inclined to overﬁt the pretraining objective[13, 14, 15].
Alternatively, some studies directly assigned each instance the bag-level annotation (i.e.,the survival time of the patient) for network training, which introduces task-speciﬁc 1 supervision and improves model’s generalisability [16, 17, 18].
Actually, the prognosis evaluation is primarily andcomprehensively determined by certain representative regions, yet those regions might only occupy asmall portion of WSI [17].
As a result, the strong supervision on all instances, especially on prognosisirrelevant tiles, will introduce excessive label noises and limit model’s performance [19, 20].
Foralleviating this issue, a feasible way is to supervise the instance encoding in a weak and easy-to-hardmanner.
On the other hand, existing methods often generate mono-scale instance representations[11, 21] or typically concatenate multi-scale information from multi-magniﬁcation WSIs [22, 23],which may result in feature redundancy and ignore ﬁne-grained details across multi-magniﬁcationimages.
In the aggregation stage, most previous studies aggregate instance representations within a bag forprognosis estimation by certain fusion strategies (e.g., pooling operation and attention mechanism)[24, 25].
However, it may overwhelm prognosis-relevant information, cause intra-bag redundancy,and reduce inter-bag discrimination, if many instances from irrelevant regions are enrolled [12, 26].
To address the above-mentioned issues, we arm MIL with a dual-curriculum strategy and propose adual-curriculum contrastive MIL method for cancer prognosis analysis with WSIs.
The proposedmethod consists of two easy-to-hard curriculums, i.e., saliency-guided weakly-supervised instanceencoding with cross-scale tiles and contrastive-enhanced soft-bag prognosis inference.
The maincontributions are summarized as follows:
1 ) We present a dual-curriculum contrastive MIL method which includes two easy-to-hard curriculums.
We ﬁrst conduct a preliminary task to learn instance representations by considering risk stratiﬁcationstatus (degraded from survival time) as the annotation, followed by the prognosis inference withsurvival time as supervision.2 )
We design the ﬁrst curriculum of saliency-guided weakly-supervised instance encoding withcross-scale tiles.
It is supervised by the relatively weak annotations so as to reduce label noises and maintain prognosis related guidance.
Additionally, to imitate the reviewing procedure of pathologists
we leverage the low magniﬁcation saliency map to guide
the
encoding of high-magniﬁcation instances
for exploring ﬁne grained information across multi-magniﬁcation WSIs
3 ) We develop the second curriculum of contrastive-enhanced soft- bag prognosis inference
Instead of enrolling all instances, we adaptively identify and integrate representative instances within a bag(as the soft-bag) for prognosis inference and leverage the constrained self-attention strategy to obtainextra sparseness for soft-bag representations, which can help reduce intra-bag redundancy in bothinstance and feature levels.
Meanwhile, we improve the Cox loss with two-tier contrastive learningfor enhancing intra-bag and inter-bag discrimination
We evaluate the proposed method on three
public cancer datasets and extensive experiments demonstrate that our method outperforms state-of-the-art methods in cancer prognosis analysis with
WSIs.  Related Work2.1 WSI-based Cancer Prognosis Model
In recent years, many methods, especially convolutional neural networks (CNNs), have been proposedfor cancer prognosis evaluation with WSIs [27, 28, 29].
Due to the gigapixel size of WSI, somemethods took small-size ROIs selectively sampled from WSIs as the input of the network for trainingand inference, in which all ROIs were assigned with patient-level outcome labels [30, 31].
However,these methods generally require prior knowledge from pathologists, which are experience-dependentand may suffer from high inter-observer variation.
Therefore, current researches have proposedto crop the entire WSI into many tiles for the model’s input so as to make full use of availableinformation contained by WSI [10, 32, 33].
However, these methods often confront the lack oftile-level annotations and may result in a sub-optimal solution.
To this end, MIL methods havebeen proposed to perform cancer prognosis analysis in a weakly-supervised manner and have shownpromising performance in this ﬁeld [5, 28].
2.2 Multi-instance Learning in WSI Analysis
The MIL methods in WSI analysis can be roughly divided into two categories according to the wayinstances are leveraged in the model [12, 17].
The one infers bag-level ones from instance-level prediction via average pooling, maximum pooling, or other ensemble strategies [34, 35].
In contrast,the other one, referred to as the bag embedding method, aggregates instance representations as bagones, upon which a model is constructed for bag-level prediction [36, 37].
The former is simpleand straightforward but empirically proven to be inferior to the latter in terms of generalizationperformance.
Therefore, the bag embedding method has attracted extensive attention in WSI analysis[17].
For example, Courtiol et al.
[6] developed a MIL method based on CNN, called MesoNet,to accurately predict the overall survival of mesothelioma patients with WSIs.
Yao et al.
[5]proposed deep attention multiple instance survival learning to efﬁciently learn features from the
WSI and aggregated them for prognosis prediction.
Our method essentially belongs to the bagembedding method.
Different from previous methods, the proposed method consists of two easyto-hard curriculums, in which ﬁne-grained information across multi-magniﬁcation WSIs, intra-bagredundancy, and inter-bag discrimination are comprehensively considered.
Method3.1 Problem Formulation
Denote the triplet { X n , T n , δ n } Nn =1 as the dataset consisting of N patients, where X n is the n -thpatient with one or more WSIs, T n and δ n are its observed survival time and event indicator (viz.equals to 1 and 0 for uncensored and censored samples, respectively).
Prognosis analysis is an ordinalregression task that models time-to-event distribution, which is formulated as
[Equation]
(1) where S and ˆ T n denote the prognosis inference function and the estimated survival time, respectively.
In practice, it is difﬁcult to directly feed the whole WSI into the model due to its gigapixel size.
Accordingly, many studies [10, 32, 33] have cropped WSIs into many tiles and generated bag
X n = { x n,i } N n i =1 which contains N n instances (tiles) for the n -th patient.
Then, MIL is leveraged toconstruct the prognosis model as follows:
[Equation]
where E is an instance encoding function that extracts feature representation for each instance, and 106 A is a permutation-invariant instance aggregation function that pools the instance representationsinto the bag ones.
However, previous studies [10, 11, 12, 16, 17, 18] typically generate instancerepresentations via a pre-trained model or a model trained by the instances with bag-level annotations,which may not generalize well to the downstream task.
As a result, we decompose the model intotwo easy-to-hard curriculums, including (1) Curriculum I (C-I): instance encoding (via E ) duringpreliminary risk stratiﬁcation (via C , a risk stratiﬁcation function), and (2) Curriculum II (C-II):prognosis inference (via S ) after instance aggregation (via A ).
Formally, the optimization process canbe formulated as
[Equation]
where † ( · ) outputs 1 (0) if true (false), and L I and L II denote the loss functions for C-I and C-II,respectively.
The risk stratiﬁcation status Y n is determined by { T n , δ n } with a three-year timethreshold (denoted as T r ) as follows:
[Equation]
3.2 Curriculum I: Saliency-guided Weakly-supervised Instance Encoding with Cross-scale
Tiles
In this section, we introduce the ﬁrst curriculum of saliency-guided weakly-supervised instanceencoding with cross-scale tiles, as shown in Figure 1.
Given the input instance with S magniﬁcations { x sn,i } Ss =1 ( S = 3 in this work), the proposed method contains S branches and each branch takesdifferent-magniﬁcation tiles as input, which aims to explore multi-scale information from multimagniﬁcation images.
For the s -th branch, it mainly consists of a feature extractor F s , a featureaggregator G s and a classiﬁer C s .
And { F s } Ss =1 and { G s } Ss =1 form E , while { C s } Ss =1 constitute Cin Eq.(3).
The feature extractor F s contains s residual modules with the parameters { θ 1 F s , · · · , θ s F s } ,and the ﬁrst s − 1 {+modules share the same architecture with F s − 
+}
if s > 1 .
Figure 2 illustrates thearchitecture details 2 .
Different from previous studies [22, 23] that separately feed { x sn,i } Ss =1 into thenetwork and ignore ﬁne-grained details across multi-magniﬁcation images, we encourage the networkto focus on salient regions by utilizing the prior knowledge of the ( s − 1 )-th branch to highlight theinput x sn,i , which can be formulated as
[Equation]
where ⊗ denotes the element-wise multiplication operator, and m s − 1 n,i is the salient mask indicatinghigh-risk regions. For convenience, we introduce how to acquire m sn,i , which is easily generalized tom s − 1 n,i . Speciﬁcally, m sn,i is computed by Class Activation Map [38] as follows:
[Equation]
where (cid:12) is the channel-wise multiplication operator, and ω s indicates the importance of channel offeature maps for risk stratiﬁcation prediction in the s -th branch.
To obtain ω s , we ﬁrst generate aninstance embedding vector z sn,i by
[Equation]
where G s is a feature aggregator that performs channel-direction attention (as shown in Figure 2).
Incorporating comprehensive information from current and previous branches, we subsequently feedinstance embeddings { z jn,i } sj =1 into the classiﬁer C s for predicting high-risk probability p sn,i , whichis computed by
[Equation]
where C s is implemented by a linear layer with the parameters { ω s , ω s } (as shown in Figure 2), andφ and T denote softmax activation function and transposition operation, respectively.
We introduce a hierarchical transfer strategy to leverage the prior from different-magniﬁcation images,accelerate network convergence, and maintain the speciﬁcity of current branch.
Speciﬁcally, as shownin Figure 1, the parameter θ s F s (for any s ) of the s -th module in F s is completely learnable and hasnot any constraints, while θ s − 1 F s (for s > 1 ) is also learnable but constrained to approximate θ s − 1 F s − 1 bythe structural loss L Ω as follows: [Equation] For the remaining parameters { θ 1 F s , · · · , θ s − 2 F s } (for s > 2 ) in F s , they are ﬁrst initialized with{ θ 1 F s − 1 , · · · , θ s − 2 F s − 1 } , and then are frozen.
Furthermore, we propose a hybrid loss function L I thatcontains two parts, i.e., empirical loss L (cid:96) and structural loss L Ω , to train the network:
[Equation]
(10) where β Ω is the weight coefﬁcient, and the empirical loss L (cid:96) is deﬁned as
[Equation]
where y sn,i ∈ Y n denotes the risk stratiﬁcation status of the i -th instance in the n -th bag.
Finally, we can obtain the multi-scale instance representation z n,i for subsequent prognosis inferencetask by z n,i =
[ z 1 n,i , · · · , z Sn,i ] .
3.3 Curriculum II: Contrastive-enhanced Soft-bag Prognosis Inference
In this section, we develop the second curriculum of contrastive-enhanced soft-bag prognosis inference, as shown in Figure 1.
Given a set of instance representations from the n -th bag, i.e.,
Z n =
[ z n, 1 ; z n, 2 ; · · · ; z n,N n ] T ∈ R N n × C , where C denotes the feature dimension, the proposedmethod mainly consists of a soft-bag learning module B , a constrained self-attention module D , acontrastive-enhanced prognosis inference function S , where B and D form A in Eq.(3).
For the soft-bag learning module B (as shown in Figure 2), it ﬁrst learns new bag representation
E n ∈ R N n × D (where D denotes the feature dimension) from Z n via a linear layer.
Instead ofenrolling all instances, we adaptively identify and integrate representative instances within a bag byintroducing the function H :
[Equation]
(12) where ˆ E n ∈ R N B × D ( N B is the number of selected instances in each bag, and N B (cid:28) N n ) is thefeature representation of those selected instances, and W n ∈ R N n × N B denotes the weight matrixthat is generated by feeding E n into two linear layers (as shown in Figure 2).
And ˆ h n ∈ R N n × 1 is an indicator vector that adaptively selects N B representative instances and is computed by
[Equation]
The constrained self-attention module D and contrastive-enhanced prognosis inference function S areintroduced below.
We leverage D to obtain extra sparseness for soft-bag representations.
Given the input ˆ E n , it ﬁrstlinearly projects ˆ E n into three feature spaces (i.e., Q n ∈ R N B × ˆ D , K n ∈ R N B × ˆ D , and V n ∈
R N B × ˆ D , and ˆ D is the feature dimension) via three mapping matrices (i.e., W Q ∈ R D × ˆ D , W K ∈ R D × ˆ D , and W V ∈ R D × ˆ D ), in which the mapping matrices are constrained by
[Equation]
Then, the sparse soft-bag representation B n ∈ R 1 × D B (where D B is the feature dimension) can beobtained by the correlation-based activation mechanism [39], as illustrated in Figure 2.
It is worthmentioning that the collaboration of B and D can signiﬁcantly help reduce intra-bag redundancy inboth instance and feature levels so as to improve the model’s generalization.
For S , it takes B n as input to infer the relative risk ˆ T n via a linear projection matrix W S ∈ R D B × 1 ,as shown in Figure 2.
In order to improve the ability of soft-bag inference, we perform two-tiercontrastive learning (TCL) to enhance intra-bag and inter-bag discrimination.
We assume that a bag B n is sampled from the distribution O
=
{O + , O − } , where the positive source O + denotes thedistribution of high-hazard samples (i.e. those with survival time ≤ T r ), while the negative source O − presents the distribution of low-hazard samples (i.e. those with survival time > T r ).
We ﬁrstfocus on the inter-bag discrimination.
Let B n = { B 1 , · · · , B N Bn } / B n present the collection ofbags (expect B n ) from the same source O + (or O − ) with B n , where N B n denotes the number ofsuch bags.
We can obtain the representation of B n (denoted as ˆ B n ) by merging the representations ofall bags in B n via a attention function K (as illustrated in Figure 2).
Inspired by [40], the inter-bagdiscrimination can be enhanced by maximally preserving the mutual information between B n andˆ B n as follows:
[Equation]
According to Eq.(12), partial instances within a bag are adaptively discarded and the rest remained.
However, all instances within the bag belong to homologous tissues sampled from the same patient,which means that it should show potential correlation among these instances.
Therefore, similar to Eq.(15), we maximize the following mutual information to improve the intra-bag discrimination:(cid:88)
[Equation]
where B n is obtained via K to merge the representation of those discarded instances E n that hasthe deﬁnition of E n = H ( E n , 1 − ˆ h n ) , as illustrated in Figure 2.
To this end, we propose to jointlymaximize Eq.(15) and (16), i.e., max ( (cid:80) n ∈ [ N ] I ( B n , ˆ B n ) + I ( B n , B n )) , which is formulated bymax ( (cid:88)
[Equation]
Instead of constructing a generative model p ( B n | ˆ B n ) p ( B n | B n ) [Equation] we leverage a log-bilinear function 199 L to model the density ratio which preserves the mutual information:
[Equation]
[Table]
where W L and V L are trainable parameters.
Motivated by [41] [Table] we design the TCL loss based on the
InfoNCE function, which has the following deﬁnition:
[Equation]
where B denotes the collection of all bags.
Additionally, we utilize the negative log partial likelihood 203 of Cox proportional hazard regression model [42] to train the network, which is computed by
[Equation]
where W S is the linear projection matrix in S , and R ( T n )
= { i : T i ≥ T n } is the collection ofall samples (including censored and uncensored samples) with survival time being longer than T n .
Finally, the loss function L II for the second curriculum can be deﬁned as
[Equation]
where β s is the weight coefﬁcient.
Experiments and Results
In this section, we brieﬂy describe the datasets, preprocessing, and implementation details, followedby experimental results.
4.1 Datasets and Preprocessing
In this work, we evaluated the proposed method on three datasets from the Cancer Genome Atlas(TCGA) database, including colon adenocarcinoma (COAD)( N = 365 ), hepatocellular carcinoma(LIHC)( N = 334 ), and bladder urothelial carcinoma (BLCA)( N = 396 ).
Each dataset contains WSIs stained with hematoxylin and eosin (H&E) and clinical information of survival time and eventstatus.
After segmenting tissue areas by the Otsus method, a set of tiles under different magniﬁcations( 20 × , 10 × , 5 × ) were non-overlappingly sampled from each segmented tissue area, and the windowsizes were set to 512 × 512 , 256 × 256 , and 128 × 128 , respectively.
4.2 Implementation Details
In our experiments, we adopted the 5-fold cross-validation strategy to comprehensively evaluate ourproposed method and the ratio of training and validation sets was set to 4:1.
Speciﬁcally, we dividedthe entire dataset into ﬁve folds, among which four folds for model training and ﬁne-tuning whilethe remaining one for model evaluation.
Notably, the cross-validation strategy was conducted onpatient level to prevent data leakage, which means that the WSI of each patient only appears in oneof these subsets.
During training stage, we selected the best model in terms of two speciﬁc evaluationmetrics for different curriculums.
That is, the model with the highest accuracy was selected for Curriculum I, while the model with the highest C-index for Curriculum II. The concordance index(CI), the receiver operating characteristic (ROC) curve, the area under the ROC curve (AUC), and
Kaplan-Meier (KM) curve were used to assess the performance of model. We chose three-year timeas threshold for risk stratiﬁcation status and AUC calculation, which lies on two reasons as follows:1) Three -year survival time is
an very important
indicator
for clinically evaluating the prognosis ofpatients, especially for these three cancer types studied in our work [45, 46, 47]. For the used [Table]
datasets, using three-year survival time as threshold can make the distribution of positive and negativesamples relatively balanced, which is beneﬁcial to network training.
We implemented all competingmethods using Pytorch1.9 library on Python3.6.
All intensive calculations were ofﬂoaded to a 12 GB NVIDIA Pascal Titan X GPU.
Curriculum I. We adopted Adam optimizer with the weight decay of 0.2 for network training. Fordifferent magniﬁcations s ∈ { 1 , 2 , 3 } , the learning rate, batch size and epoch number were set to{ 10 − 5 , 3 × 10 − 6 , 3 × 10 − 6 } , { 32 , 16 , 16 } and { 50 , 50 , 50 } , respectively.
The weight coefﬁcient β Ωwas set to 10 − 5 .
Curriculum II.
We adopted SGD optimizer with the momentum of 0.9. The learning rate, batch sizeand epoch number were set to 10 − 4 , 16 and 1000, respectively.
The soft-bag size was set to 3 and theweight coefﬁcient β s was set to 10 − 3 .
4.3 Comparison with State-of-the-Art Methods
We compared our method with other weakly-supervised methods in cancer prognosis analysis,including clustering approaches [43], graph networks [10, 44], and multi-instance learning methods [5,6]. Table 1 presents the 5-fold cross-validation results (in terms of CI and AUC) of all competingmethods.
The KM curves as well as p -values are provided in Figure S1.
We can observe that theproposed method outperforms others in head-to-head comparisons, achieving overall CI of 0.698and AUC of 0.74.
It may beneﬁt from several potential advantages in DC_MIL: 1) Unlike somemethods that leverage the dimension reduction technique [43] or pre-trained model [5, 6, 10, 44],it encodes instances in a weakly-supervised manner so as to reduce label noises and maintainprognosis-related guidance. 2) It utilizes the low-magniﬁcation saliency map to guide the encoding ofhigh-magniﬁcation instances for exploring ﬁne-grained information across multi-magniﬁcation WSIs.3) It introduces a soft-bag learning method and a constrained self-attention strategy to help reduceintra-bag redundancy in both instance and feature levels, respectively.
4) It equips the Cox loss withtwo-tier contrastive learning for enhancing intra-bag and inter-bag discrimination.
Additionally, it alsocan be observed that WSISA [43], MesoNet [6], and DeepAttnMISL [5] outperform DeepGraphSurv[44] and Patch-GCN [10], which may owe the selection of discriminant tiles.
More results can referto Appendix.
4.4 Ablation Study
Abaltion on Curriculum I. We validated the efﬁcacy of each crucial component in Curriculum
I. From Table 2, we can observe several key points: 1) Compared with pre-trained ResNet-34(regardless with MM or not), the proposed model shows signiﬁcant performance improvement,which demonstrates the effectiveness of Curriculum I. 2)
The model with MM outperforms the onewithout MM and gets CI gain of 0.039 and AUC gain of 0.061, which beneﬁts from the utilization ofmulti-magniﬁcation information. The model without SG or FT suffers from performance reduction R I S
K L o w
(average CI drops of 0.028 and 0.011 and AUC drops of 0.039 and 0.028). It indicates that ﬁne-gainedinformation across multi-scale tiles and hierarchical transfer strategy can help signiﬁcantly improvethe performance of model. More results can refer to Appendix.
Abaltion on Curriculum II.
We also validated the efﬁcacy of each key component in Curriculum II.
From Table 2, we have the following observations: 1) The baseline method performed prognosisprediction with the Cox model, which achieves average CI of 0.642 and AUC of 0.669.
Comparedto the baseline method, the model with soft-bag strategy achieves average CI gain of 0.024 and AUC gain of 0.031, which mainly proﬁts by adaptively identifying and integrating the representativeinstances within a bag.
The models with CSA, TCL, and both of them show better performancewith average CI gains of 0.006, 0.024, and 0.032 and AUC gains of 0.011, 0.02, and 0.04, respectively,which beneﬁts from the reduction of intra-bag redundancy and the enhancement of intra-bag andinter-bag discrimination.
More results can refer to Appendix.
4.5 Visualization
In this section, we show the salient maps output by the proposed method for some samples.
As shownin Figure 3, the model mainly focuses on the ﬁne-grained regions (under 20 × WSIs) that is wrappedby the salient regions under 10 × WSIs, which indicates that the proposed method can effectivelyguide the encoding of high-magniﬁcation instances so as to encourage the network to focus on moreﬁne-grained information. We have provided more intuitive results and analyses in Appendix.
Conclusion
In this paper, we propose a dual-curriculum contrastive MIL method for cancer prognosis analysiswith WSIs, which contains two easy-to-hard curriculums, i.e., saliency-guided weakly-supervisedinstance encoding with cross-scale tiles and contrastive-enhanced soft-bag prognosis inference.
Theproposed network is easy to train in each curriculum, and can be applied to gigapixel WSI analysiswith good visualization.
Besides, the proposed method outperforms the state-of-the-art methods incancer prognosis analysis over three public datasets.
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