## A Distance Model for Rhythms

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Citations: | 2 - 2 self |

### BibTeX

@MISC{Paiement_adistance,

author = {Jean-françois Paiement and Yves Grandvalet and Samy Bengio and Douglas Eck},

title = {A Distance Model for Rhythms},

year = {}

}

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### Abstract

Modeling long-term dependencies in time series has proved very difficult to achieve with traditional machine learning methods. This problem occurs when considering music data. In this paper, we introduce a model for rhythms based on the distributions of distances between subsequences. A specific implementation of the model when considering Hamming distances over a simple rhythm representation is described. The proposed model consistently outperforms a standard Hidden Markov Model in terms of conditional prediction accuracy on two different music databases. 1.

### Citations

8094 | Maximum likelihood from incomplete data via the em algorithm
- Dempster, Laird, et al.
- 1977
(Show Context)
Citation Context ...d j, and Si,j defined similarly as in Eq. (2). Parameters θi,j = {w (1) i,j , . . . , w(c−1) i,j } ∪ {p (1) i,j , . . . , p(c) i,j }A Distance Model for Rhythms can be learned with the EM algorithm (=-=Dempster et al., 1977-=-) on rhythm data for a specific music style. In words, we model the difference between the observed distance dl i,j between two subsequences and the minimum possible value βi,j for such a difference b... |

4275 | A tutorial on hidden Markov models and selected applications in speech recognition
- Rabiner
- 1989
(Show Context)
Citation Context ...distribution of d(yi, yj) for each specific choice of i and j may be more important when modeling rhythms (and music in general) than the actual choice of subsequences yi. Hidden Markov Models (HMM) (=-=Rabiner, 1989-=-) are commonly used to model temporal data. In principle, an HMM is able to capture complex regularities in patterns between subsequences of data, provided its number of hidden states is large enough.... |

625 |
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- Titterington, S, et al.
- 1995
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Citation Context ...ixture. Estimation procedures may not be well-defined and asymptotic theory may not hold if a model is not identifiable. However, the model defined in Eq. (6) is identifiable if αi,j − βi,j > 2c − 1 (=-=Titterington et al., 1985-=-, p.40). While this is the case for most di,j, we observed that this condition is sometimes violated. Whatever happens, there is no impact on the estimation because we only care about what happens at ... |

471 | A gentle tutorial of the EM algorithm and its application to parameter estimation for gaussian mixture and hidden markov models
- Bilmes
- 1998
(Show Context)
Citation Context ...ements in troids and {n (1) i,j , . . . , n(c) i,j each of these clusters. We initialize the parameters θi,j with w (k) n(k) i,j i,j = and p n (k) i,j = µ(k) i,j . We then follow a standard approach (=-=Bilmes, 1997-=-) to apply the EM algorithm to the binomial mixture in Eq. (6). Let zl i,j ∈ {1, . . . , c} be a hidden variable telling which component density generated dl i,j . For every iteration of the EM algori... |

349 |
The Alignment Template Approach to Statistical Machine Translation
- Och
- 2004
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Citation Context ...erize and constrain the relative distances between various parts of a sequence of bags-of-concepts could be an efficient means to improve performance of automatic systems such as machine translation (=-=Och & Ney, 2004-=-). On a more general level, learning constraints related to distances between subsequences can boost the performance of ”short memory” models such as the HMM.A Distance Model for Rhythms Acknowledgme... |

299 |
Tempo and beat analysis of acoustic musical signals
- Scheirer
- 1998
(Show Context)
Citation Context ...act, even random music can sound structured and melodic if it is built by repeating random subsequences with slight variation. Many algorithms have been proposed for audio beat tracking (Dixon, 2007; =-=Scheirer, 1998-=-). Probabilistic models have also been proposed for tempo tracking and inference of rhythmic structure in musical audio (Whiteley et al., 2007; Cemgil & Kappen, 2002). The goal of these models is to a... |

253 | Learning longterm dependencies with gradient descent is difficult
- Bengio, Simard, et al.
- 1994
(Show Context)
Citation Context ...s, which has proved very difficult to achieve with traditional statistical methods. Note that the problem of long-term dependencies is not limited to music, nor to one particular probabilistic model (=-=Bengio et al., 1994-=-). Music is characterized by strong hierarchical dependencies determined in large part by meter, the sense of strong and weak beats that arises from the interaction among hierarchical levels of sequen... |

143 |
Listening: An introduction to the perception of auditory events
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- 1993
(Show Context)
Citation Context ...etrical hierarchy (e.g. sequences of 4, 8 or 16 measures). It is well know in music theory that distance patterns are more important than the actual choice of notes in order to create coherent music (=-=Handel, 1993-=-). In this work, distance patterns refer to distances between subsequences of equal length in particular positions. For instance, measure 1 may be always similar to measure 5 in a particular musical g... |

127 |
Pattern Classification, Second edition
- Stork, Duda, et al.
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Citation Context ...on, one may get better models and speed up the learning process by choosing sensible values for the initial parameters. In the experiments reported in Section 3, the k-means algorithm for clustering (=-=Duda et al., 2000-=-) was used. More precisely, k-means was used to partition the values (dl i,j − βl i,j )/(αl i,j − βl i,j ) into c clusters corresponding to each component of the mixture in Eq. (6). Let {µ (1) i,j , .... |

71 | The continuator: Musical interaction with style
- Pachet
- 2003
(Show Context)
Citation Context ...used to model the transitions between rhythms themselves. Hence, these models do not take into account long-term dependencies. A few generative models have already been proposed for music in general (=-=Pachet, 2003-=-; Dubnov et al., 2003). While these models generate impressive musical results, we are not aware of quantitative comparisons between models of music with machine learning standards, as it is done in S... |

34 |
Evaluation of the Audio Beat Tracking System BeatRoot
- Dixon
- 2007
(Show Context)
Citation Context ...l genre. In fact, even random music can sound structured and melodic if it is built by repeating random subsequences with slight variation. Many algorithms have been proposed for audio beat tracking (=-=Dixon, 2007-=-; Scheirer, 1998). Probabilistic models have also been proposed for tempo tracking and inference of rhythmic structure in musical audio (Whiteley et al., 2007; Cemgil & Kappen, 2002). The goal of thes... |

30 |
Using Machine-Learning Methods for Musical Style Modeling
- Dubnov, Assayag, et al.
- 2003
(Show Context)
Citation Context ...the transitions between rhythms themselves. Hence, these models do not take into account long-term dependencies. A few generative models have already been proposed for music in general (Pachet, 2003; =-=Dubnov et al., 2003-=-). While these models generate impressive musical results, we are not aware of quantitative comparisons between models of music with machine learning standards, as it is done in Section 3 in terms of ... |

29 | Finding temporal structure in music: Blues improvisation with LSTM recurrent networks
- Eck, Schmidhuber
- 2002
(Show Context)
Citation Context ...dio transcription algorithm, it should help improve the poor performance of state-of-the-art transcription systems; it could as well be included in genre classifiers or automatic composition systems (=-=Eck & Schmidhuber, 2002-=-); used to generate rhythms, the model could act as a drum machine or automatic accompaniment system which learns by example. Our main contribution is to propose a generative model for distance patter... |

11 | Methods for binary multidimensional scaling
- Rohde
(Show Context)
Citation Context ...Naively trying all possible subsequences to maximize (8) leads to O(|A| (m−s+1)) computations. Instead, we propose to search the space of sequences using a variant of the Greedy Max Cut (GMC) method (=-=Rohde, 2002-=-) that has proven to be optimal in terms of running time and performance for binary MDS optimization. The subsequence ˆxs, . . . , ˆxm can be simply initialized with (ˆxs, . . . , ˆxm) = max pHMM(˜xs,... |

4 |
Rhythm quantization and tempo tracking by sequential Monte Carlo
- Cemgil, Kappen
- 2002
(Show Context)
Citation Context ...sed for audio beat tracking (Dixon, 2007; Scheirer, 1998). Probabilistic models have also been proposed for tempo tracking and inference of rhythmic structure in musical audio (Whiteley et al., 2007; =-=Cemgil & Kappen, 2002-=-). The goal of these models is to align rhythm events with the metrical structure. However, simple Markovian assumptions are used to model the transitions between rhythms themselves. Hence, these mode... |

2 | Sequential inference of rhythmic structure in musical audio
- Whiteley, Cemgil, et al.
- 2007
(Show Context)
Citation Context ...orithms have been proposed for audio beat tracking (Dixon, 2007; Scheirer, 1998). Probabilistic models have also been proposed for tempo tracking and inference of rhythmic structure in musical audio (=-=Whiteley et al., 2007-=-; Cemgil & Kappen, 2002). The goal of these models is to align rhythm events with the metrical structure. However, simple Markovian assumptions are used to model the transitions between rhythms themse... |