Nonlinear Supervised Dimensionality Reduction via Smooth Regular Embeddings

The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing methods primarily focus on the embedding of the training data, and the generalization of the embedding to initially unseen test data is rather ignored. In this work, we build on recent theoretical results on the generalization performance of supervised manifold learning algorithms. Motivated by these performance bounds, we propose a supervised manifold learning method that computes a nonlinear embedding while constructing a smooth and regular interpolation function that extends the embedding to the whole data space in order to achieve satisfactory generalization. The embedding and the interpolator are jointly learnt such that the Lipschitz regularity of the interpolator is imposed while ensuring the separation between different classes. Experimental results on several image data sets show that the proposed method outperforms traditional classifiers and the supervised dimensionality reduction algorithms in comparison in terms of classification accuracy in most settings

Naturalistic Affective Expression Classification by a Multi-Stage Approach Based on Hidden Markov Models

In naturalistic behaviour, the affective states of a person change at a rate much slower than the typical rate at which video or audio is recorded (e.g. 25fps for video). Hence, there is a high probability that consecutive recorded instants of expressions represent a same affective content. In this paper, a multi-stage automatic affective expression recognition system is proposed which uses Hidden Markov Models (HMMs) to take into account this temporal relationship and finalize the classification process. The hidden states of the HMMs are associated with the levels of affective dimensions to convert the classification problem into a best path finding problem in HMM. The system was tested on the audio data of the Audio/Visual Emotion Challenge (AVEC) datasets showing performance significantly above that of a one-stage classification system that does not take into account the temporal relationship, as well as above the baseline set provided by this Challenge. Due to the generality of the approach, this system could be applied to other types of affective modalities