Research on soundscapes has shifted the focus of environmental acoustics from noise levels to the perception of sounds, incorporating contextual factors. Soundscape emotion recognition (SER) models perception using a set of features, with arousal and valence commonly regarded as sufficient descriptors of affect. In this work, we blend \emph{graph learning} techniques with a novel \emph{information criterion} to develop a feature selection framework for SER. Specifically, we estimate a sparse graph representation of feature relations using linear structural equation models (SEM) tailored to the widely used Emo-Soundscapes dataset. The resulting graph captures the relations between input features and the two emotional outputs. To determine the appropriate level of sparsity, we propose a novel \emph{generalized elbow detector}, which provides both a point estimate and an uncertainty interval. We conduct an extensive evaluation of our methods, including visualizations of the inferred relations. While several of our findings align with previous studies, the graph representation also reveals a strong connection between arousal and valence, challenging common SER assumptions.

An index of an effective number of variables (ENV) is introduced for model selection in nested models. This is the case, for instance, when we have to decide the order of a polynomial function or the number of bases in a nonlinear regression, choose the number of clusters in a clustering problem, or the number of features in a variable selection application (to name few examples). It is inspired by the idea of the maximum area under the curve (AUC). The interpretation of the ENV index is identical to the effective sample size (ESS) indices concerning a set of samples. The ENV index improves drawbacks of the elbow detectors described in the literature and introduces different confidence measures of the proposed solution. These novel measures can be also employed jointly with the use of different information criteria, such as the well-known AIC and BIC , or any other model selection procedures. Comparisons with classical and recent schemes are provided in different experiments involving real datasets. Related Matlab code is given.

We introduce a generalized information criterion that contains other well-known information criteria, such as Bayesian information Criterion (BIC) and Akaike information criterion (AIC), as special cases. Furthermore, the proposed spectral information criterion (SIC) is also more general than the other information criteria, e.g., since the knowledge of a likelihood function is not strictly required. SIC extracts geometric features of the error curve and, as a consequence, it can be considered an automatic elbow detector. SIC provides a subset of all possible models, with a cardinality that often is much smaller than the total number of possible models. The elements of this subset are “elbows” of the error curve. A practical rule for selecting a unique model within the sets of elbows is suggested as well. Theoretical invariance properties of SIC are analyzed. Moreover, we test SIC in ideal scenarios where provides always the optimal expected results. We also test SIC in several numerical experiments: some involving synthetic data, and two experiments involving real datasets. They are all real-world applications such as clustering, variable selection, or polynomial order selection, to name a few. The results show the benefits of the proposed scheme. Matlab code related to the experiments is also provided. Possible future research lines are finally discussed.

In the last decade, soundscapes have become one of the most active topics in Acoustics, providing a holistic approach to the acoustic environment, which involves human perception and context. Soundscapes-elicited emotions are central and substantially subtle and unnoticed (compared to speech or music). Currently, soundscape emotion recognition is a very active topic in the literature. We provide an exhaustive variable selection study (i.e., a selection of the soundscapes indicators) to a well-known dataset (emo-soundscapes). We consider linear soundscape emotion models for two soundscapes descriptors: arousal and valence. Several ranking schemes and procedures for selecting the number of variables are applied. We have also performed an alternating optimization scheme for obtaining the best sequences keeping fixed a certain number of features. Furthermore, we have designed a novel technique based on Gibbs sampling, which provides a more complete and clear view of the relevance of each variable. Finally, we have also compared our results with the analysis obtained by the classical methods based on p-values. As a result of our study, we suggest two simple and parsimonious linear models of only 7 and 16 variables (within the 122 possible features) for the two outputs (arousal and valence), respectively. The suggested linear models provide very good and competitive performance, with$R^{2}>0.86$and$R^{2}>0.63$(values obtained after a cross-validation procedure), respectively.