# Spectral information criterion for automatic elbow detection

arXiv: https://arxiv.org/abs/2308.09108 · HTML: https://mlsanity.com/paper/2308.09108/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 17 Aug 2023.

## Builds on (most cited first, 8 of 8)

- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [On the marginal likelihood and cross-validation](https://mlsanity.com/paper/1905.08737/) (2019)
- [Marginal likelihood computation for model selection and hypothesis testing: an extensive review](https://mlsanity.com/paper/2005.08334/) (2020)
- [A Joint introduction to Gaussian Processes and Relevance Vector Machines with Connections to Kalman filtering and other Kernel Smoothers](https://mlsanity.com/paper/2009.09217/) (2020)
- [On the safe use of prior densities for Bayesian model selection](https://mlsanity.com/paper/2206.05210/) (2022)
- [Compressed Monte Carlo with application in particle filtering](https://mlsanity.com/paper/2107.08459/) (2021)
- [An exhaustive variable selection study for linear models of soundscape emotions: rankings and Gibbs analysis](https://mlsanity.com/paper/2207.12743/) (2022)
- [Monte-Carlo Sampling Approach to Model Selection: A Primer](https://mlsanity.com/paper/2209.13203/) (2022)

## Built on by (most cited first, 2 of 2)

- [Effective sample size approximations as entropy measures](https://mlsanity.com/paper/2602.22954/) (2026)
- [Scalable Parameter-Light Spectral Method for Clustering Short Text Embeddings with a Cohesion-Based Evaluation Metric](https://mlsanity.com/paper/2511.19350/) (2025)

## Abstract (arXiv)

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.