Much of the appeal of music lies in its power to convey emotions moods and to evoke them in listeners. In consequence, the past decade witnessed a growing interest in modeling emotions from musical signals in the music information retrieval (MIR) community. In this article, we present a novel generative approach to music emotion modeling, with a specific focus on the valence-arousal (VA) dimension model of emotion. The presented generative model, called (AEG), better accounts for the subjectivity of emotion perception by the use of probability distributions. Specifically, it learns from the emotion annotations of multiple subjects a Gaussian mixture model in the VA space with prior constraints on the corresponding acoustic features of the training music pieces. Such a computational framework is technically sound, capable of learning in an online fashion, and thus applicable to a variety of applications, including user-independent (general) and user-dependent (personalized) emotion recognition and emotion-based music retrieval. We report evaluations of the aforementioned applications of AEG on a larger-scale emotion-annotated corpora, AMG1608, to demonstrate the effectiveness of AEG and to showcase how evaluations are conducted for research on emotion-based MIR. Directions of future work are also discussed.
Early approaches to MER @cite_12 @cite_38 assumed that the perceived emotion of a music piece can be represented as a in the VA space, in which the valence and arousal values are considered as independent numerical values. The ground-truth VA values of a music piece is obtained by averaging the annotations of a number of human subjects, without considering the covariance of the annotations. To predict the VA values of a music piece, a regression model can be applied. Given @math inputs @math , @math , where @math is a @math -dimensional feature vector of the @math -th input segment, @math the number of feature descriptors, and @math the valence or arousal value, a regression model is learned by algorithms such as support vector regression (SVR) @cite_74 that minimize the mismatch (e.g. mean squared loss) between the predicted and the ground-truth VA values.
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The goal of music mood regression is to represent the emotional expression of music pieces as numerical values in a low-dimensional mood space and automatically predict those values for unseen music pieces. Existing studies on this topic usually train and test regression models using music datasets sampled from the same culture source, annotated by people with the same cultural background, or otherwise constructed by the same method. In this study, we explore whether and to what extent regression models trained with samples in one dataset can be applied to predicting valence and arousal values of samples in another dataset. Specifically, three datasets that differ in factors such as cultural backgrounds of stimuli (music) and subjects (annotators), stimulus types and annotation methods are evaluated and the results suggested that cross-cultural and cross-dataset predictions of both valence and arousal values could achieve comparable performance to within-dataset predictions. We also discuss how the generalizability of regression models can be affected by dataset characteristics. Findings of this study may provide valuable insights into music mood regression for nonWestern and other music where training data are scarce. Content-based retrieval has emerged in the face of content explosion as a promising approach to information access. In this paper, we focus on the challenging issue of recognizing the emotion content of music signals, or music emotion recognition (MER). Specifically, we formulate MER as a regression problem to predict the arousal and valence values (AV values) of each music sample directly. Associated with the AV values, each music sample becomes a point in the arousal-valence plane, so the users can efficiently retrieve the music sample by specifying a desired point in the emotion plane. Because no categorical taxonomy is used, the regression approach is free of the ambiguity inherent to conventional categorical approaches. To improve the performance, we apply principal component analysis to reduce the correlation between arousal and valence, and RReliefF to select important features. An extensive performance study is conducted to evaluate the accuracy of the regression approach for predicting AV values. The best performance evaluated in terms of the R 2 statistics reaches 58.3 for arousal and 28.1 for valence by employing support vector machine as the regressor. We also apply the regression approach to detect the emotion variation within a music selection and find the prediction accuracy superior to existing works. A group-wise MER scheme is also developed to address the subjectivity issue of emotion perception. This paper proposes a novel machine learning approach for the task of on-line continuous-time music mood regression, i.e., low-latency prediction of the time-varying arousal and valence in musical pieces. On the front-end, a large set of segmental acoustic features is extracted to model short-term variations. Then, multi-variate regression is performed by deep recurrent neural networks to model longer-range context and capture the time-varying emotional profile of musical pieces appropriately. Evaluation is done on the 2013 MediaEval Challenge corpus consisting of 1000 pieces annotated in continous time and continuous arousal and valence by crowd-sourcing. In the result, recurrent neural networks outperform SVR and feedforward neural networks both in continuous-time and static music mood regression, and achieve an R 2 of up to .70 and .50 with arousal and valence annotations. Mood is a popular access point in music digital libraries and online music repositories, and is often represented as numerical values in a small number of emotion-related dimensions (e.g., valence and arousal). As music mood is recognized as culturally dependent, this study investigates whether regression models built with music data in one culture can be applied to music in another culture. Results indicate that cross-cultural predictions of both valence and arousal values are feasible. Music emotion recognition is concerned with developing predictive models that comprehend the affective content of musical signals. Recently, a growing number of attempts has been made to model the music emotion as a probability distribution in the valence-arousal (VA) space to better account for the subjectivity. In this paper, we present a novel histogram density modeling approach that models the emotion distribution by a 2-D histogram over the quantized VA space and learns a set of latent histograms to predict the emotion probability density of a song from audio. The proposed model is free from parametric distribution assumptions over the VA space, easy to implement, and extremely fast to train. We also extend our model to deal with the temporal dynamics of time-varying emotion labels. Comprehensive performance study on two larger-scale datasets demonstrates that our approach achieves comparable performance to the state-of-the-art ones, but with much better training and testing efficiency. We consider the problem of learning a one-hidden-layer neural network: we assume the input @math is from Gaussian distribution and the label @math , where @math is a nonnegative vector in @math with @math , @math is a full-rank weight matrix, and @math is a noise vector. We first give an analytic formula for the population risk of the standard squared loss and demonstrate that it implicitly attempts to decompose a sequence of low-rank tensors simultaneously. Inspired by the formula, we design a non-convex objective function @math whose landscape is guaranteed to have the following properties: 1. All local minima of @math are also global minima. 2. All global minima of @math correspond to the ground truth parameters. 3. The value and gradient of @math can be estimated using samples. With these properties, stochastic gradient descent on @math provably converges to the global minimum and learn the ground-truth parameters. We also prove finite sample complexity result and validate the results by simulations. Past research in analysis of human affect has focused on recognition of prototypic expressions of six basic emotions based on posed data acquired in laboratory settings. Recently, there has been a shift toward subtle, continuous, and context-specific interpretations of affective displays recorded in naturalistic and real-world settings, and toward multimodal analysis and recognition of human affect. Converging with this shift, this paper presents, to the best of our knowledge, the first approach in the literature that: 1) fuses facial expression, shoulder gesture, and audio cues for dimensional and continuous prediction of emotions in valence and arousal space, 2) compares the performance of two state-of-the-art machine learning techniques applied to the target problem, the bidirectional Long Short-Term Memory neural networks (BLSTM-NNs), and Support Vector Machines for Regression (SVR), and 3) proposes an output-associative fusion framework that incorporates correlations and covariances between the emotion dimensions. Evaluation of the proposed approach has been done using the spontaneous SAL data from four subjects and subject-dependent leave-one-sequence-out cross validation. The experimental results obtained show that: 1) on average, BLSTM-NNs outperform SVR due to their ability to learn past and future context, 2) the proposed output-associative fusion framework outperforms feature-level and model-level fusion by modeling and learning correlations and patterns between the valence and arousal dimensions, and 3) the proposed system is well able to reproduce the valence and arousal ground truth obtained from human coders. The goal of the “Emotion in Music” task in MediaEval 2015 is to automatically estimate the emotions expressed by music (in terms of Arousal and Valence) in a time-continuous fashion. In this paper, considering the high context correlation among the music feature sequence, we study several multiscale approaches at different levels, including acoustic feature learning with Deep Brief Networks (DBNs) followed a modified Autoencoder (AE), bi-directional Long-Short Term Memory Recurrent Neural Networks (BLSTM-RNNs) based multi-scale regression fusion with Extreme Learning Machine (ELM), and hierarchical prediction with Support Vector Regression (SVR). The evaluation performances of all runs submitted are significantly better than the baseline provided by the organizers, illustrating the effectiveness of the proposed approaches. We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . Determining the emotion of a song that best characterizes the affective content of the song is a challenging issue due to the difficulty of collecting reliable ground truth data and the semantic gap between human's perception and the music signal of the song. To address this issue, we represent an emotion as a point in the Cartesian space with valence and arousal as the dimensions and determine the coordinates of a song by the relative emotion of the song with respect to other songs. We also develop an RBF-ListNet algorithm to optimize the ranking-based objective function of our approach. The cognitive load of annotation, the accuracy of emotion recognition, and the subjective quality of the proposed approach are extensively evaluated. Experimental results show that this ranking-based approach simplifies emotion annotation and enhances the reliability of the ground truth. The performance of our algorithm for valence recognition reaches 0.326 in Gamma statistic. Music emotion recognition (MER) is an important topic in music understanding, recommendation, retrieval and human computer interaction. Great success has been achieved by machine learning methods in estimating human emotional response to music. However, few of them pay much attention in semantic interpret for emotion response. In our work, we first train an interpretable model between acoustic audio and emotion. Filter, wrapper and shrinkage methods are applied to select important features. We then apply statistical models to build and explain the emotion model. Extensive experimental results reveal that the shrinkage methods outperform the wrapper methods and the filter methods in arousal emotion. In addition, we observed that only a small set of the extracted features have the key effects to arousal. While, most of our extracted features have small contribution to valence music perception. Ultimately, we obtain a higher average accuracy rate in arousal, compared to that in valence. We study the problem of distribution to real-value regression, where one aims to regress a mapping @math that takes in a distribution input covariate @math (for a non-parametric family of distributions @math ) and outputs a real-valued response @math . This setting was recently studied, and a "Kernel-Kernel" estimator was introduced and shown to have a polynomial rate of convergence. However, evaluating a new prediction with the Kernel-Kernel estimator scales as @math . This causes the difficult situation where a large amount of data may be necessary for a low estimation risk, but the computation cost of estimation becomes infeasible when the data-set is too large. To this end, we propose the Double-Basis estimator, which looks to alleviate this big data problem in two ways: first, the Double-Basis estimator is shown to have a computation complexity that is independent of the number of of instances @math when evaluating new predictions after training; secondly, the Double-Basis estimator is shown to have a fast rate of convergence for a general class of mappings @math . In this paper, we consider regression problems with one-hidden-layer neural networks (1NNs). We distill some properties of activation functions that lead to @math in the neighborhood of the ground-truth parameters for the 1NN squared-loss objective. Most popular nonlinear activation functions satisfy the distilled properties, including rectified linear units (ReLUs), leaky ReLUs, squared ReLUs and sigmoids. For activation functions that are also smooth, we show @math guarantees of gradient descent under a resampling rule. For homogeneous activations, we show tensor methods are able to initialize the parameters to fall into the local strong convexity region. As a result, tensor initialization followed by gradient descent is guaranteed to recover the ground truth with sample complexity @math and computational complexity @math for smooth homogeneous activations with high probability, where @math is the dimension of the input, @math ( @math ) is the number of hidden nodes, @math is a conditioning property of the ground-truth parameter matrix between the input layer and the hidden layer, @math is the targeted precision and @math is the number of samples. To the best of our knowledge, this is the first work that provides recovery guarantees for 1NNs with both sample complexity and computational complexity @math in the input dimension and @math in the precision. The appeal of music lies in its ability to express emotions, and it is natural for us to organize music in terms of emotional associations. But the ambiguities of emotions make the determination of a single, unequivocal response label for the mood of a piece of music unrealistic. We address this lack of specificity by modeling human response labels to music in the arousal-valence (A-V) representation of affect as a stochastic distribution. Based upon our collected data, we present and evaluate methods using multiple sets of acoustic features to estimate these mood distributions parametrically using multivariate regression. Furthermore, since the emotional content of music often varies within a song, we explore the estimation of these A-V distributions in a time-varying context, demonstrating the ability of our system to track changes on a short-time basis. In this paper we describe our approach for the MediaEval's "Emotion in Music" task. Our method consists of deep Long-Short Term Memory Recurrent Neural Networks (LSTM-RNN) for dynamic Arousal and Valence regression, using acoustic and psychoacoustic features extracted from the songs that have been previously proven as effective for emotion prediction in music. Results on the challenge test demonstrate an excellent performance for Arousal estimation (r = 0.613 ± 0.278), but not for Valence (r = 0.026 ± 0.500). Issues regarding the quality of the test set annotations' reliability and distributions are indicated as plausible justifications for these results. By using a subset of the development set that was left out for performance estimation, we could determine that the performance of our approach may be underestimated for Valence (Arousal: r = 0.596 ± 0.386; Valence: r = 0.458 ± 0.551). While emotion-based music organization is a natural process for humans, quantifying it empirically proves to be a very difficult task, and as such no dominant feature representation for music emotion recognition has yet emerged. Much of the difficulty in developing emotion-based features is the ambiguity of the ground-truth. Even using the smallest time window, opinions about emotion are bound to vary and reflect some disagreement between listeners. In previous work, we have modeled human response labels to music in the arousal-valence (A-V) emotion space with time-varying stochastic distributions. Current methods for automatic detection of emotion in music seek performance increases by combining several feature domains (e.g. loudness, timbre, harmony, rhythm). Such work has focused largely in dimensionality reduction for minor classification performance gains, but has provided little insight into the relationship between audio and emotional associations. In this work, we seek to employ regression-based deep belief networks to learn features directly from magnitude spectra. Taking into account the dynamic nature of music, we investigate combining multiple timescales of aggregated magnitude spectra as a basis for feature learning. Interpolators---estimators that achieve zero training error---have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum @math norm ( ridgeless') interpolation in high-dimensional least squares regression. We consider two different models for the feature distribution: a linear model, where the feature vectors @math are obtained by applying a linear transform to a vector of i.i.d. entries, @math (with @math ); and a nonlinear model, where the feature vectors are obtained by passing the input through a random one-layer neural network, @math (with @math , @math a matrix of i.i.d. entries, and @math an activation function acting componentwise on @math ). We recover---in a precise quantitative way---several phenomena that have been observed in large-scale neural networks and kernel machines, including the double descent' behavior of the prediction risk, and the potential benefits of overparametrization. Music as a form of art is intentionally composed to be emotionally expressive. The emotional features of music are invaluable for music indexing and recommendation. In this paper we present a cross-comparison of automatic emotional analysis of music. We created a public dataset of Creative Commons licensed songs. Using valence and arousal model, the songs were annotated both in terms of the emotions that were expressed by the whole excerpt and dynamically with 1 Hz temporal resolution. Each song received 10 annotations on Amazon Mechanical Turk and the annotations were averaged to form a ground truth. Four different systems from three teams and the organizers were employed to tackle this problem in an open challenge. We compare their performances and discuss the best practices. While the effect of a larger feature set was not very apparent in the static emotion estimation, the combination of a comprehensive feature set and a recurrent neural network that models temporal dependencies has largely outperformed the other proposed methods for dynamic music emotion estimation. We consider the problem of learning an unknown function @math on the @math -dimensional sphere with respect to the square loss, given i.i.d. samples @math where @math is a feature vector uniformly distributed on the sphere and @math . We study two popular classes of models that can be regarded as linearizations of two-layers neural networks around a random initialization: (RF) The random feature model of Rahimi-Recht; (NT) The neural tangent kernel model of Jacot-Gabriel-Hongler. Both these approaches can also be regarded as randomized approximations of kernel ridge regression (with respect to different kernels), and hence enjoy universal approximation properties when the number of neurons @math diverges, for a fixed dimension @math . We prove that, if both @math and @math are large, the behavior of these models is instead remarkably simpler. If @math , then RF performs no better than linear regression with respect to the raw features @math , and NT performs no better than linear regression with respect to degree-one and two monomials in the @math . More generally, if @math then RF fits at most a degree- @math polynomial in the raw features, and NT fits at most a degree- @math polynomial. Super-resolution refers to the process of recovering the locations and amplitudes of a collection of point sources, represented as a discrete measure, given @math of its noisy low-frequency Fourier coefficients. The recovery process is highly sensitive to noise whenever the distance @math between the two closest point sources is less than @math . This paper studies the fundamental difficulty of super-resolution and the performance guarantees of a subspace method called MUSIC in the regime that @math . The most important quantity in our theory is the minimum singular value of the Vandermonde matrix whose nodes are specified by the source locations. Under the assumption that the nodes are closely spaced within several well-separated clumps, we derive a sharp and non-asymptotic lower bound for this quantity. Our estimate is given as a weighted @math sum, where each term only depends on the configuration of each individual clump. This implies that, as the noise increases, the super-resolution capability of MUSIC degrades according to a power law where the exponent depends on the cardinality of the largest clump. Numerical experiments validate our theoretical bounds for the minimum singular value and the resolution limit of MUSIC. When there are @math point sources located on a grid with spacing @math , the fundamental difficulty of super-resolution can be quantitatively characterized by a min-max error, which is the reconstruction error incurred by the best possible algorithm in the worst-case scenario. We show that the min-max error is closely related to the minimum singular value of Vandermonde matrices, and we provide a non-asymptotic and sharp estimate for the min-max error, where the dominant term is @math .