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We simulate the errors in label proportion by adding noise n k of a normal distribution with mean μ=0 and standard deviation σ=0.05∼0.20 to the existing label proportion p k.

Then, the noisy label proportion is p k =p k +n k, where n k ∼ N μ,σ 2).

When w and b are fixed, ω can be updated according to label agreement and label proportion constraints.

Influence of label proportion errors on classification accuracy for the two SAR images is presented in Fig. 7.

The unknown sample weight ω can be seen as a link between supervised learning loss L and label proportion loss L p in Eq. (4).

Fig. 7 Influence of label proportion errors on classification accuracy using GL+LpcSVM for SAR images of Tianjin and Rosenheim areas.

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Similar(46)

Thus, we introduce proportional grid labeling (proportional GL) by combining grid labeling with label proportions to implement rapid training set definition for SAR images.

Then, proportional GL can be presented in three forms by giving label proportions for each class or the major class in a cell during the sample labeling process, 1) Multiclass GL: The task of multiclass GL is to estimate the proportion p k (l i ) for each ({{l}_{i}}in mathcal {L})(i=1,…,M) in a grid cell C k by a human expert.

We compared our method (label-proportion-constrained SVM with grid labeling, GL+LpcSVM) with the traditional SVM classifier with pixel labeling (PL+SVM), the traditional SVM classifier with naive grid labeling (GL+SVM), and ∝SVM, which is also based on learning from label proportions.

It combines boosting-based SVM and label proportions for efficient learning from uncertain labels.

So grid labeling outputs label proportions of each cell in the training data.

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