Universal and Automatic Elbow Detection for Learning the Effective Number of Components in Model Selection Problems

We design a Universal Automatic Elbow Detector (UAED) for deciding the effective number of components in model selection problems. The relationship with the information criteria widely employed in the literature is also discussed. The proposed UAED does not require the knowledge of a likelihood function and can be easily applied in diverse applications, such as regression and classification, feature and/or order selection, clustering, and dimension reduction. Several experiments involving synthetic and real data show the advantages of the proposed scheme with benchmark techniques in the literature.

Spectral information criterion for automatic elbow detection

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.

An exhaustive variable selection study for linear models of soundscape emotions: rankings and Gibbs analysis

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.