Weakly supervised classification of objects in images using soft ...

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6 Riwal Lefort, Ronan Fablet, Jean-Marc Boucherfall in the test set T t m . Setting β obeys to a trade-off: for a good assessment ofrandom forest C m , the number of samples in T r m must be high enough. But ifβ is too high, only very few samples will be updated at each iteration leading toa very slow convergence of the algorithm. In practice β is typically set to 0.75.The algorithm is shown in the table 2. In the subsequent, this procedure willbe denoted as IP2 (Iterative Procedure 2).Given a training data set T 1 = {x n, π 1 n} and M iterations,1. for m from 1 to M– Randomly split T m in two groups: T r m = {x n, πn m } and T t m = {x n, πn m }according to a split proportion β.– Learn a classifier C m from subset T r m.– Apply classifier C m to subset T t m.– Update T t m+1 = {x n, πn m+1 } with πnm+1 ∝ πnp(x 1 n|y n = i, C m).– Update training dataset T m+1 as T t m+1: T m+1 = {T r m, T t m+1}.2. Learn the final classifier using T M+1.Table 2. Randomization-based iterative procedure for weakly supervised learning (IP2).4 Application to semi-supervised learningAs a specific case of interest of the proposed weakly supervised strategy, we consideran application to semi-supervised learning. We first briefly review existingapproaches and then detail our contribution.4.1 Related workSemi-Supervised Learning is reviewed in [5]. Four types of methods can be distinguished.The first type includes generative models often exploiting ExpectationMaximization schemes that assess parameters of mono-modal Gaussianmodels [31] [5] or multi-modal Gaussian models [32]. Their advantages are theconsistency of the mathematical framework with the probabilistic setting. Thesecond category refers to discriminative models such as the semi-supervised supportvector machine (S3VM) [33] [5]. Despite a mathematically-sound basis andgood performances, S3VM are subject to local optimization issues and S3VMcan be outperformed by other models depending on the dataset. Graph-basedclassifier is an other well known category in semi-supervised learning [34] [5].The approach is close to the K-nearest-neighbour approach but similarities betweenexamples are also taken in account. The principal drawback is that thisclassifier is mostly transductive: generalization properties are rather weak andperformances decrease with unobserved data. The last family of semi-supervisedmodels is formed by iterative schemes such as the self-training approach [35]or the co-training approach [36] that is applicable if observation features canbe split into two independent groups. The advantage is the good performancereached by these methods and the simplicity of the approach. Their drawbacksmostly lie in the difficulties to characterize convergence properties.
Weakly supervised classification of objects in images 74.2 Self training with soft random forestsA semi-supervised version of the iterative procedure proposed in the previoussection can be derived. Following a self training strategy, it conststs in initiallytraining a random forest from groundtruthed training samples only. Then, ateach iteration, unlabelled data are processed by the current classifier and the Ksamples with the greatest class posteriors are appended to the training databaseto retrain the classifier. If should be stressed that in the standard implementationof semi-supervised learning with SVMs and random forest the new samplesappended to training set at each iteration are assigned class labels. In contrast,we benefit from the proposed weakly supervised decision trees. This is expectedto reduce the propagation of classification errors. The sketch of semi-supervisedlearning is given in table 3.It should be stressed that this semi-supervised procedure can be regarded asa specific case of the iterative weakly supervised learning in which the iteratedrandom sampling of the training and test subsets is replaced by a deterministicsampling initially exploiting the presence of fully groundtruthed samples in theprocessed dataset.Given an initial training data set T = {T L, T U }, where T L contains labelled data andT U unlabelled data, and M iterations.1. For m from 1 to M– Learn a classifier C m from T L.– Apply classifier C m to T U .– For each classes, transfer from T U to T L the most confident examples, withweak label, according to the probabilistic classification.2. Generate the final classifier using T L.Table 3. Soft self-training procedure for semi-supervised learning.5 Experiments5.1 Simulation protocolIn this section, we compare four classification models: IP1 using soft randomforests, IP2 using soft random forests, soft random forests alone, and the generativemodel proposed in [6] for weakly labelled data.Given a supervised dataset, a weakly supervised training dataset is built.We distribute all the training examples in several groups according to predefinedtarget class proportions (table 4). All the instances in a given group areassigned the class proportion of the group. In table 4, we show an example oftarget class proportions for a three-class dataset. In this example, we can creategroups containing from one class (supervised learning) to three classes. For eachcase of class-mixture, different mixture complexities can be created: from oneclass dominating the mixture, i.e. the prior of one class being close to one, toequiprobable class, i.e. equal values for non-zeros class priors.
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