相关论文: Mathematical Analysis of Melodies: Slope and Discr…

Melodic similarity measurement is of key importance in music information retrieval. In this paper, we use geometric matching techniques to measure the similarity between two melodies. We represent music as sets of points or sets of…

Melody estimation or melody extraction refers to the extraction of the primary or fundamental dominant frequency in a melody. This sequence of frequencies obtained represents the pitch of the dominant melodic line from recorded music audio…

The Frechet distance is often used to measure distances between paths, with applications in areas ranging from map matching to GPS trajectory analysis to handwriting recognition. More recently, the Frechet distance has been generalized to a…

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work,…

This paper focuses on the modeling of musical melodies as networks. Notes of a melody can be treated as nodes of a network. Connections are created whenever notes are played in sequence. We analyze some main tracks coming from different…

We introduce a novel and interpretable path-based music similarity measure. Our similarity measure assumes that items, such as songs and artists, and information about those items are represented in a knowledge graph. We find paths in the…

We propose MelodySim, a melody-aware music similarity model and dataset for plagiarism detection. First, we introduce a novel method to construct a dataset focused on melodic similarity. By augmenting Slakh2100, an existing MIDI dataset, we…

The paper presents a discrete variation of the Frechet distance between closed curves, which can be seen as an approximation of the continuous measure. A rather straightforward approach to compute the discrete Frechet distance between two…

The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…

Melody is one of the most important components in music. Unlike other components in music theory, such as harmony and counterpoint, computable features for melody is urgently in need. These features are highly demanded as data-driven…

The \emph{Fr\'echet distance} is a well studied similarity measures between curves. The \emph{discrete Fr\'echet distance} is an analogous similarity measure, defined for a sequence $A$ of $m$ points and a sequence $B$ of $n$ points, where…

Let M be a bounded domain of a Euclidian space with smooth boundary. We relate the Cheeger constant of M and the conductance of a neighborhood graph defined on a random sample from M. By restricting the minimization defining the latter over…

This paper presents an approach to model melodies (and music pieces in general) as networks. Notes of a melody can be seen as nodes of a network that are connected whenever these are played in sequence. This creates a directed graph. By…

Metric graphs are meaningful objects for modeling complex structures that arise in many real-world applications, such as road networks, river systems, earthquake faults, blood vessels, and filamentary structures in galaxies. To study metric…

In deep learning research, many melody extraction models rely on redesigning neural network architectures to improve performance. In this paper, we propose an input feature modification and a training objective modification based on two…

We introduce new distance measures for comparing straight-line embedded graphs based on the Fr\'echet distance and the weak Fr\'echet distance. These graph distances are defined using continuous mappings and thus take the combinatorial…

The Frechet distance is a metric to compare two curves, which is based on monotonous matchings between these curves. We call a matching that results in the Frechet distance a Frechet matching. There are often many different Frechet…

The criteria for measuring music similarity are important for developing a flexible music recommendation system. Some data-driven methods have been proposed to calculate music similarity from only music signals, such as metric learning…

Notes in a musical piece are building blocks employed in non-random ways to create melodies. It is the "interaction" among a limited amount of notes that allows constructing the variety of musical compositions that have been written in…

Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…