By working with high-dimensional representations of covers, modern steganographic methods are capable of preserving a large number of complex dependencies among individual cover elements and thus avoid detection using current best steganalyzers. Inevitably, steganalysis needs to start using high-dimensional feature sets as well. This brings two key problems -construction of good high-dimensional features and machine learning that scales well with respect to dimensionality. Depending on the classifier, high dimensionality may lead to problems with the lack of training data, infeasibly high complexity of training, degradation of generalization abilities, lack of robustness to cover source, and saturation of performance below its potential. To address these problems collectively known as the curse of dimensionality, we propose ensemble classifiers as an alternative to the much more complex support vector machines. Based on the character of the media being analyzed, the steganalyst first puts together a high-dimensional set of diverse "prefeatures" selected to capture dependencies among individual cover elements. Then, a family of weak classifiers is built on random subspaces of the prefeature space. The final classifier is constructed by fusing the decisions of individual classifiers. The advantage of this approach is its universality, low complexity, simplicity, and improved performance when compared to classifiers trained on the entire prefeature set. Experiments with the steganographic algorithms nsF5 and HUGO demonstrate the usefulness of this approach over current state of the art. Today, security of steganographic algorithms designed for empirical cover sources is evaluated using steganalyzers built as binary classifiers trained on cover and stego features. Originally, the features were designed by hand to capture the impact of known steganographic schemes. 12 A cleaner strategy is to obtain the features by adopting a model for individual cover elements and use its sampled form as the feature. 7, 22, 27 Close attention has usually been paid to keep the dimensionality of the feature space low due to potential problems with the Curse of Dimensionality (CoD). However, modern steganography methods, such as HUGO 23 are designed to approximately preserve a high-dimensional representation of covers * and thus many complex dependencies among pixels, as well. With the increased sophistication of steganographic algorithms, steganalysis has already begun using feature spaces of increased dimensionality. The most accurate spatial domain steganalysis of ±1 embedding (LSB matching) uses the 686-dimensional SPAM features 22 while a 1,234-dimensional Cross-Domain Feature (CDF) set was was employed in 18 to attack YASS. 25 Moreover, the recent results of the steganalysis competition BOSS 11 indicate that there is little hope that a human-designed low-dimensional feature space effective against HUGO 23 exists. In this paper, we address both issues -design of useful high-dimensional feature spaces and scalable machine learning approach. We form a high-dimensional feature space of "prefeatures" whose role is to capture as many statistical dependencies among individual cover elements as possible. This is achieved either by merging existing feature sets or by forming the prefeatures from joint statistics of groups of cover elements that exhibit the strongest relationship. The emphasis here is on diversity while one should not be as concerned with dimensionality. Having formed the prefeature space, the steganalyst builds a scalable ensemble classifier by fusing the decisions of a set
Random subspace selection has also been adopted in steganalysis REF , though with a different goal, that is to reduce the problems encountered when working with extremely high-dimensional feature spaces.
Steganalysis in high dimensions: fusing classifiers built on random subspaces
Electronic Imaging
Physics Computer Science Engineering