Bump hunting by topological data analysis

Sommerfeld, Max; Heo, Giseon; Kim, Peter; Rush, Stephen; Marron, J. S.

doi:10.1002/sta4.167

Cited by 6 publications

(8 citation statements)

References 37 publications

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“…However, the deviation of each data point from a cluster centroid is measured instead of variance. -Various methods for density modes (equivalently zero-dimensional density ridges or degree zero homological features) have been recently proposed (Chacón, 2020;Chaudhuri & Marron, 1999;Chazal et al, 2018;Chen et al, 2016;Comaniciu & Meer, 2002;Fasy et al, 2014;Genovese et al, 2014;Genovese et al, 2016;Sommerfeld et al, 2017;Zhang & Ghanem, 2021).…”

Section: Deviation) [Dimensionless]mentioning

confidence: 99%

Globally, songs and instrumental melodies are slower and higher and use more stable pitches than speech: A Registered Report

Ozaki¹,

Tierney²,

Pfordresher³

et al. 2022

Preprint

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What, if any, similarities and differences between song and speech are consistent across cultures? Both song and speech are found in all known human societies and are argued to share evolutionary roots and cognitive resources, yet no studies have compared similarities and differences between song and speech across languages on a global scale. We will compare sets of matched song/speech recordings produced by our 81 coauthors whose 1st/heritage languages span 23 language families. Each recording set consists of singing, recited lyrics, and spoken description, plus an optional instrumental version of the sung melody to allow us to capture a “musi-linguistic continuum” from instrumental music to naturalistic speech. Our literature review and pilot analysis using five audio recording sets (by speakers of Japanese, English, Farsi, Yoruba, and Marathi) led us to make six predictions for confirmatory analysis comparing song vs. spoken descriptions: three consistent differences and three consistent similarities. For differences, we predict that: 1) songs will have higher pitch than speech, 2) songs will be slower than speech, and 3) songs will have more stable pitch than speech. For similarities, we predict that 4) pitch interval size, 5) timbral brightness, and 6) pitch declination will be similar for song and speech. Because our opportunistic language sample (approximately half are Indo-European languages) and unusual design involving coauthors as participants (approximately 1/5 of coauthors had some awareness of our hypotheses when we recorded our singing/speaking) could affect our results, we will include robustness analyses to ensure our conclusions are robust to these biases, should they exist. Other features (e.g., rhythmic isochronicity, loudness) and comparisons involving instrumental melodies and recited lyrics will be investigated through post-hoc exploratory analyses. Our sample size of n=80 people providing sung/spoken recordings already exceeds the required number of recordings (i.e. 60) to achieve 95% power with the alpha level of 0.05 for the hypothesis testing of the selected six features. Our study will provide diverse cross-linguistic empirical evidence regarding the existence of cross-cultural regularities in song and speech, shed light on factors shaping humanity’s two universal vocal communication forms, and provide rich cross-cultural data to generate new hypotheses and inform future analyses of other factors (e.g., functional context, sex, age, musical/linguistic experience) that may shape global musical and linguistic diversity.

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Section: Deviation) [Dimensionless]mentioning

confidence: 99%

Globally, songs and instrumental melodies are slower and higher and use more stable pitches than speech: A Registered Report

Ozaki¹,

Tierney²,

Pfordresher³

et al. 2022

Preprint

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“…For this single‐bandwidth case, Fasy et al () showed that it is possible to construct a band above the diagonal to identify the significant modes, in the sense that all the modes with death–birth pairs lying on this low persistence band can be considered to be caused by random fluctuation. On the other hand, Sommerfeld et al () suggested to inspect all the persistence diagrams as the bandwidth varies to evaluate the significance of the modes across different degrees of smoothing. They showed through simulated and real data examples that such an approach appears to be more powerful than SiZer.…”

Section: Many Modesmentioning

confidence: 99%

“…In contrast, the remaining three modes appear to be really there, and besides, they have death-birth levels which are very similar to those of the true density modes. For this single-bandwidth case, Fasy et al (2014) showed that it is possible to construct a band above the diagonal to identify the significant modes; on the other hand, Sommerfeld et al (2017) suggested to inspect all the persistence diagrams as the bandwidth varies to evaluate the significance of the modes across different degrees of smoothing.…”

Section: Many Modesmentioning

confidence: 99%

The Modal Age of Statistics

Chacón

2020

Int Statistical Rev

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Summary Recently, a number of statistical problems have found an unexpected solution by inspecting them through a ‘modal point of view'. These include classical tasks such as clustering or regression. This has led to a renewed interest in estimation and inference for the mode. This paper offers an extensive survey of the traditional approaches to mode estimation and explores the consequences of applying this modern modal methodology to other, seemingly unrelated, fields.

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“…In turn, modes have paved the way to introduce related concepts in data structures such as bumps, components, clusters, or classes, among others. However, chasing modes has proven to be extremely difficult in large and even not‐so‐large dimensions, so huge amounts of statistical research are devoted to improve already existing methods or developing new ones to allow a more efficient way to tackle the problem . In this paper, we are primarily concerned with the particular case of mode hunting.…”

Section: Introductionmentioning

confidence: 99%

“…However, chasing modes has proven to be extremely difficult in large and even not-so-large dimensions, so huge amounts of statistical research are devoted to improve already existing methods or developing new ones to allow a more efficient way to tackle the problem. [1][2][3][4] In this paper, we are primarily concerned with the particular case of mode hunting. Thus, we propose here Active Information Mode Hunting (AIMH), a multivariate algorithm to chase modes based on information theory.…”

Section: Introductionmentioning

confidence: 99%

Mode hunting through active information

Díaz–Pachón

Sáenz

Rao

et al. 2019

Appl Stoch Models Bus & Ind

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We propose a new method to find modes based on active information. We develop an algorithm called active information mode hunting (AIMH) that, when applied to the whole space, will say whether there are any modes present and where they are. We show AIMH is consistent and, given that information increases where probability decreases, it helps to overcome issues with the curse of dimensionality. The AIMH also reduces the dimensionality with no resource to principal components. We illustrate the method in three ways: with a theoretical example (showing how it performs better than other mode hunting strategies), a real dataset business application, and a simulation.

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Bump hunting by topological data analysis

Cited by 6 publications

References 37 publications

Globally, songs and instrumental melodies are slower and higher and use more stable pitches than speech: A Registered Report

Globally, songs and instrumental melodies are slower and higher and use more stable pitches than speech: A Registered Report

The Modal Age of Statistics

Mode hunting through active information

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