Music Emotion Detection Using Hierarchical Sparse Kernel Machines

For music emotion detection, this paper presents a music emotion verification system based on hierarchical sparse kernel machines. With the proposed system, we intend to verify if a music clip possesses happiness emotion or not. There are two levels in the hierarchical sparse kernel machines. In the first level, a set of acoustical features are extracted, and principle component analysis (PCA) is implemented to reduce the dimension. The acoustical features are utilized to generate the first-level decision vector, which is a vector with each element being a significant value of an emotion. The significant values of eight main emotional classes are utilized in this paper. To calculate the significant value of an emotion, we construct its 2-class SVM with calm emotion as the global (non-target) side of the SVM. The probability distributions of the adopted acoustical features are calculated and the probability product kernel is applied in the first-level SVMs to obtain first-level decision vector feature. In the second level of the hierarchical system, we merely construct a 2-class relevance vector machine (RVM) with happiness as the target side and other emotions as the background side of the RVM. The first-level decision vector is used as the feature with conventional radial basis function kernel. The happiness verification threshold is built on the probability value. In the experimental results, the detection error tradeoff (DET) curve shows that the proposed system has a good performance on verifying if a music clip reveals happiness emotion

On the probability distribution of a moving target. Asymptotic and non-asymptotic results

International audienceThe problem addressed here is the probability distribution of the position of a moving target, and especially of its distance to the starting point. The trajectory is made of leg segments with random length and random change of direction, and it is assumed that the target has a known constant velocity. Earlier results have been obtained in the literature in the simple case where the change of direction is uniformly distributed on the circle and the length of leg is exponentially distributed. These results are generalized for an arbitrary (non-necessarily uniformly distributed) change of direction and an arbitrary (non-necessarily exponentially distributed) length of leg. Explicit expressions are obtained for the non-asymptotic mean and covariance matrix of the position, and a central limit theorem is obtained for the normalized position, with an explicit expression for the asymptotic variance, hence a limiting Rayleigh distribution for the normalized distance to the starting point