Kjell Lemström

Algorithms for discovering repeated patterns in multidimensional representations of polyphonic music

In previous approaches to repetition discovery in music, the music to be analysed has been represented using strings. However, there are certain types of interesting musical repetitions that cannot be discovered using string algorithms. We propose a geometric approach to repetition discovery in which the music is represented as a multidimensional dataset. Certain types of interesting musical repetition that cannot be found using string algorithms can efficiently be found using algorithms that process multidimensional datasets. Our approach allows polyphonic music to be analysed as efficiently as monophonic music and it can be used to discover polyphonic repeated patterns “with gaps” in the timbre, dynamic and rhythmic structure of a passage as well as its pitch structure. We present two new algorithms: SIA and SIATEC. SIA computes all the maximal repeated patterns in a multidimensional dataset and SIATEC computes all the occurrences of all the maximal repeated patterns in a dataset. For a k -dimensional dataset of size n, the worstcase running time of SIA is O (kn 2 log 2 n) and the worst-case running time of SIATEC is O (kn 3).

Perceptual Issues in Music Pattern Recognition: Complexity of Rhythm and Key Finding

We consider several perceptual issues in the context of machine recognition ofmusic patterns. It is argued that a successful implementation of a musicrecognition system must incorporate perceptual information and error criteria.We discuss several measures of rhythm complexity which are used fordetermining relative weights of pitch and rhythm errors. Then, a new methodfor determining a localized tonal context is proposed. This method is based onempirically derived key distances. The generated key assignments are then usedto construct the perceptual pitch error criterion which is based on noterelatedness ratings obtained from experiments with human listeners.

Sweepline the music

The problem of matching sets of points or sets of horizontal line segments in plane under translations is considered. For finding the exact occurrences of a point set of size m within another point set of size n we give an algorithm with running time O(mn), and for finding partial occurrences an algorithm with running time O(mnlogm). To find the largest overlap between two line segment patterns we develop an algorithm with running time O(mnlog(mn)). All algorithms are based on a simple sweepline traversal of one of the patterns in the lexicographic order. The motivation for the problems studied comes from music retrieval and analysis.

Practical algorithms for transposition-invariant string-matching

Abstract We consider the problems of (1) longest common subsequence (LCS) of two given strings in the case where the first may be shifted by some constant (that is, transposed) to match the second, and (2) transposition-invariant text searching using indel distance. These problems have applications in music comparison and retrieval. We introduce two novel techniques to solve these problems efficiently. The first is based on the branch and bound method, the second on bit-parallelism. Our branch and bound algorithm computes the longest common transposition-invariant subsequence (LCTS) in time O ( ( m 2 + log log σ ) log σ ) in the best case and O ( ( m 2 + log σ ) σ ) in the worst case, where m and σ, respectively, are the length of the strings and the size of the alphabet. On the other hand, we show that the same problem can be solved by using bit-parallelism and thus obtain a speedup of O ( w / log m ) over the classical algorithms, where the computer word has w bits. The advantage of this latter algorithm over the present bit-parallel ones is that it allows the use of more complex distances, including general integer weights. Since our branch and bound method is very flexible, it can be further improved by combining it with other efficient algorithms such as our novel bit-parallel algorithm. We experiment on several combination possibilities and discuss which are the best settings for each of those combinations. Our algorithms are easily extended to other musically relevant cases, such as δ-matching and polyphony (where there are several parallel texts to be considered). We also show how our bit-parallel algorithm is adapted to text searching and illustrate its effectiveness in complex cases where the only known competing method is the use of brute force.

On comparing edit distance and geometric frameworks in content-based retrieval of symbolically encoded polyphonic music:

This paper deals with content-based music retrieval (CBMR) of symbolically encoded polyphonic music. It is one of the key issues in the field of music information retrieval. Due to extensive research, there are already satisfactory methods for monophonic CBMR. Unfortunately, this is not the case with the polyphonic task. The problem has been approached in various ways; the majority of the methods suggested fall into two frameworks. The first framework models music as linear strings and the similarity is based on the well-known edit-distance concept. The second one models music as sets of two-dimensional geometric objects (consider the piano-roll representation), but the definition of similarity varies considerably within the framework. We scrutinise these frameworks trying to find common, relevant properties that either inhibit or boost the effectiveness of the methods. Although the edit-distance framework offers more efficient solutions, we conclude that the geometric framework is the choice for the CBMR task because of the very natural way of modelling music still preserving the features intrinsic to the task.

Filtering methods for content-based retrieval on indexed symbolic music databases

We introduce fast filtering methods for content-based music retrieval problems, where the music is modeled as sets of points in the Euclidean plane, formed by the (on-set time, pitch) pairs. The filters exploit a precomputed index for the database, and run in time dependent on the query length and intermediate output sizes of the filters, being almost independent of the database size. With a quadratic size index, the filters are provably lossless for general point sets of this kind. In the context of music, the search space can be narrowed down, which enables the use of a linear sized index for effective and efficient lossless filtering. For the checking phase, which dominates the overall running time, we exploit previously designed algorithms suitable for local checking. In our experiments on a music database, our best filter-based methods performed several orders of a magnitude faster than the previously designed solutions.

Tree Representation in Combined Polyphonic Music Comparison

Identifying copies or different versions of a same musical work is a focal problem in maintaining large music databases. In this paper we introduce novel ideas and methods that are applicable to metered, symbolically encoded polyphonic music. We show how to represent and compare polyphonic music using a tree structure. Moreover, we put for trial various comparison methods and observe whether better comparison results can be obtained by combining distinct similarity measures. Our experiments show that the proposed representation is adequate for the task with good quality results and processing times, and when combined with other methods it becomes more robust against various types of music.

Flexible and Efficient Bit-Parallel Techniques for Transposition Invariant Approximate Matching in Music Retrieval

Recent research in music retrieval has shown that a combinatorial approach to the problem could be fruitful. Three distinguishing requirements of this particular problem are (a) approximate searching permitting missing, extra, and distorted notes, (b) transposition invariance, to allow matching a sequence that appears in a different scale, and (c) handling polyphonic music. These combined requirements make up a complex combinatorial problem that is currently under research. On the other hand, bit-parallelism has proved a powerful practical tool for combinatorial pattern matching, both flexible and efficient. In this paper we use bit-parallelism to search for several transpositions at the same time, and obtain speedups of O(w/logk) over the classical algorithms, where the computer word has w bits and k is the error threshold allowed in the match. Although not the best solution for the easier approximation measures, we show that our technique can be adapted to complex cases where no competing method exists, and that are the most interesting in terms of music retrieval.

Transposition and time-warp invariant geometric music retrieval algorithms

In this paper, we study the problem of transposition and time-warp invariant (TTWI) polyphonic content-based music retrieval (CBMR) in symbolically encoded music for which, to our best knowledge, no solutions exist. Representing music by sets of points in plane, we introduce two new algorithms for this setting. Given a query point set, of size m, to be searched for in a database point set, of size n, and applying a search window of width w, our algorithms run in time O(mwn log n) for finding exact TTWI occurrences, and O(mnw2 log n) for partial occurrences. The algorithms are related to our prior transposition and time-scale invariant (TTSI) algorithms [1]. As local tempo changes and jittering are always present in real-world CBMR queries, any TTSI algorithm cannot provide a sufficient solution to the problem; the extra robustness of the new algorithms bridges this gap perfectly.

Polyphonic Music Retrieval with Classifier Ensembles

Abstract Music comparison and retrieval tasks rely on the concept of music similarity, whatever this might be. No similarity measure performs the best for all tasks, genres, or music formats. It is not even easy to formalize human perception of music similarity. A number of papers in the literature deal with the development of appropriate similarity measures. In this paper, we pose the problem under a different perspective, showing that a careful combination of different measures through an ensemble of classifiers performs in a more robust way than any of the particular measures involved, when they are applied as stand-alone measures. The task posed here is the retrieval of a music work from a repository, given a polyphonic score as a query. For the experiments, five state-of-the-art polyphonic similarity measures and three different corpora of polyphonic music scores have been tested.