Sweepline the Music

Audio Cover Song Identification and Similarity: Background, Approaches, Evaluation, and Beyond

“…The most typical algorithms for dynamic programming alignment/similarity are dynamic time warping algorithms [65,69] and edit distance variants [31]. Their main drawback is that they are computationally expensive (i.e., quadratic in the length of the song representations), but several fast implementations may be derived [31,56,83]. This is a preliminary draft.…”

Transposition and Time-Scale Invariant Geometric Music Retrieval

“…To this end, several authors have recently used geometric-based modeling of music [1,3,4,5]. Geometric representations usually also take into account another feature intrinsic to the problem: the matching process ignores extra intervening notes in the database that do not appear in the query pattern.…”

“…We give an algorithm for finding exact occurrences, under such a setting, of a given query point set, of size m, within a database point set, of size n, with running time O(mn 2 log n); partial occurrences are found in O(m 2 n 2 log n) time. The algorithms resemble the sweepline algorithm introduced in [1]. …”

Deterministic Length Reduction: Fast Convolution in Sparse Data and Applications

“…This information can be represented as points in a 2-Dimensional space where the axes are time and pitch. The problem of seeking a given melody in the archive is immediately reduced to a point set matching problem in 2-dimensional space [10].…”

“…Using the fast sparse convolution algorithm presented in this paper, this problem can be solved in time O(n log 3 n). To our knowledge, this is the first deterministic solution to the problem whose time is o(nm), where m is the number of notes in the pattern melody [10].…”