ECMusic 2012 @GECCO 2012 Presentation

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ECMusic 2012 @GECCO 2012 Presentation

  1. 1. OutlineEvolutionary Algorithms and the Automatic Transcription of MusicGustavo Reis1 Francisco Fernandez2 Anibal Ferreira3 1 Schoolof Technology and Management Polytechnic Institute of Leiria, Portugal 2 University of Extremadura,Spain 3 University of Porto, Portugal Sunday, 8th July 2012, Philadelphia, USA Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  2. 2. OutlineOutline 1 Introduction 2 Evolutionary Approach First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Automatic Music Transcription using Synthesized Instruments First approach on Real Audio Recordings Reducing the Harmonic Overfitting Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results 3 Conclusion 4 References Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  3. 3. OutlineOutline 1 Introduction 2 Evolutionary Approach First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Automatic Music Transcription using Synthesized Instruments First approach on Real Audio Recordings Reducing the Harmonic Overfitting Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results 3 Conclusion 4 References Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  4. 4. OutlineOutline 1 Introduction 2 Evolutionary Approach First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Automatic Music Transcription using Synthesized Instruments First approach on Real Audio Recordings Reducing the Harmonic Overfitting Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results 3 Conclusion 4 References Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  5. 5. OutlineOutline 1 Introduction 2 Evolutionary Approach First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Automatic Music Transcription using Synthesized Instruments First approach on Real Audio Recordings Reducing the Harmonic Overfitting Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results 3 Conclusion 4 References Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  6. 6. OutlineOutline 1 Introduction 2 Evolutionary Approach First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Automatic Music Transcription using Synthesized Instruments First approach on Real Audio Recordings Reducing the Harmonic Overfitting Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results 3 Conclusion 4 References Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  7. 7. OutlineOutline 1 Introduction 2 Evolutionary Approach First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Automatic Music Transcription using Synthesized Instruments First approach on Real Audio Recordings Reducing the Harmonic Overfitting Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results 3 Conclusion 4 References Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  8. 8. OutlineOutline 1 Introduction 2 Evolutionary Approach First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Automatic Music Transcription using Synthesized Instruments First approach on Real Audio Recordings Reducing the Harmonic Overfitting Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results 3 Conclusion 4 References Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  9. 9. Introduction Evolutionary Approach Conclusion ReferencesOutline 1 Introduction 2 Evolutionary Approach First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Automatic Music Transcription using Synthesized Instruments First approach on Real Audio Recordings Reducing the Harmonic Overfitting Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results 3 Conclusion 4 References Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  10. 10. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription Monophonic Music Transcription Polyphonic Music Transcription Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  11. 11. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription It is a very difficult problem: computational point of view musical view it can only be addressed by the most skilled musicians. Traditional approaches to Automatic Music Transcription try to extract the information directly from audio source signal. Related Work Since the first works by Moorer [12] and Piszczalski & Galler [14], polyphonic music transcription systems almost always rely on the analysis of information in the frequency domain. Klapuri [6], for instance, uses iterative calculation of predominant F0s in separate frequency bands. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  12. 12. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription It is a very difficult problem: computational point of view musical view it can only be addressed by the most skilled musicians. Traditional approaches to Automatic Music Transcription try to extract the information directly from audio source signal. Related Work Since the first works by Moorer [12] and Piszczalski & Galler [14], polyphonic music transcription systems almost always rely on the analysis of information in the frequency domain. Klapuri [6], for instance, uses iterative calculation of predominant F0s in separate frequency bands. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  13. 13. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription It is a very difficult problem: computational point of view musical view it can only be addressed by the most skilled musicians. Traditional approaches to Automatic Music Transcription try to extract the information directly from audio source signal. Related Work Since the first works by Moorer [12] and Piszczalski & Galler [14], polyphonic music transcription systems almost always rely on the analysis of information in the frequency domain. Klapuri [6], for instance, uses iterative calculation of predominant F0s in separate frequency bands. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  14. 14. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription It is a very difficult problem: computational point of view musical view it can only be addressed by the most skilled musicians. Traditional approaches to Automatic Music Transcription try to extract the information directly from audio source signal. Related Work Since the first works by Moorer [12] and Piszczalski & Galler [14], polyphonic music transcription systems almost always rely on the analysis of information in the frequency domain. Klapuri [6], for instance, uses iterative calculation of predominant F0s in separate frequency bands. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  15. 15. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription It is a very difficult problem: computational point of view musical view it can only be addressed by the most skilled musicians. Traditional approaches to Automatic Music Transcription try to extract the information directly from audio source signal. Related Work Since the first works by Moorer [12] and Piszczalski & Galler [14], polyphonic music transcription systems almost always rely on the analysis of information in the frequency domain. Klapuri [6], for instance, uses iterative calculation of predominant F0s in separate frequency bands. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  16. 16. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription It is a very difficult problem: computational point of view musical view it can only be addressed by the most skilled musicians. Traditional approaches to Automatic Music Transcription try to extract the information directly from audio source signal. Related Work Since the first works by Moorer [12] and Piszczalski & Galler [14], polyphonic music transcription systems almost always rely on the analysis of information in the frequency domain. Klapuri [6], for instance, uses iterative calculation of predominant F0s in separate frequency bands. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  17. 17. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription It is a very difficult problem: computational point of view musical view it can only be addressed by the most skilled musicians. Traditional approaches to Automatic Music Transcription try to extract the information directly from audio source signal. Related Work Since the first works by Moorer [12] and Piszczalski & Galler [14], polyphonic music transcription systems almost always rely on the analysis of information in the frequency domain. Klapuri [6], for instance, uses iterative calculation of predominant F0s in separate frequency bands. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  18. 18. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription Related Work Martin [9] uses blackboard systems. Bayesian Probabilistic Networks [5, 21, 22]. Hidden Markov Model and Spectral Feature Vectors were proposed by Raphael [15]. Neural Networks were used by Carreras et al. [1]. Marolt [8] uses networks of adaptive oscillators to track partials over time. Physical Modeling. [13]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  19. 19. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription Related Work Martin [9] uses blackboard systems. Bayesian Probabilistic Networks [5, 21, 22]. Hidden Markov Model and Spectral Feature Vectors were proposed by Raphael [15]. Neural Networks were used by Carreras et al. [1]. Marolt [8] uses networks of adaptive oscillators to track partials over time. Physical Modeling. [13]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  20. 20. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription Related Work Martin [9] uses blackboard systems. Bayesian Probabilistic Networks [5, 21, 22]. Hidden Markov Model and Spectral Feature Vectors were proposed by Raphael [15]. Neural Networks were used by Carreras et al. [1]. Marolt [8] uses networks of adaptive oscillators to track partials over time. Physical Modeling. [13]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  21. 21. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription Related Work Martin [9] uses blackboard systems. Bayesian Probabilistic Networks [5, 21, 22]. Hidden Markov Model and Spectral Feature Vectors were proposed by Raphael [15]. Neural Networks were used by Carreras et al. [1]. Marolt [8] uses networks of adaptive oscillators to track partials over time. Physical Modeling. [13]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  22. 22. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription Related Work Martin [9] uses blackboard systems. Bayesian Probabilistic Networks [5, 21, 22]. Hidden Markov Model and Spectral Feature Vectors were proposed by Raphael [15]. Neural Networks were used by Carreras et al. [1]. Marolt [8] uses networks of adaptive oscillators to track partials over time. Physical Modeling. [13]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  23. 23. Introduction Evolutionary Approach Conclusion ReferencesAutomatic Music Transcription Related Work Martin [9] uses blackboard systems. Bayesian Probabilistic Networks [5, 21, 22]. Hidden Markov Model and Spectral Feature Vectors were proposed by Raphael [15]. Neural Networks were used by Carreras et al. [1]. Marolt [8] uses networks of adaptive oscillators to track partials over time. Physical Modeling. [13]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  24. 24. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsOutline 1 Introduction 2 Evolutionary Approach First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Automatic Music Transcription using Synthesized Instruments First approach on Real Audio Recordings Reducing the Harmonic Overfitting Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results 3 Conclusion 4 References Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  25. 25. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsEvolutionary Approach It is important to emphasize that the main idea behind a Genetic Algorithm [4] is to have a set of candidate solutions (individuals) to a problem evolving towards the desired solution. In each generation those individuals are evaluated according to their quality (fitness). The worst individuals are then discarded and the best will generate new individuals resulting from the combination of their parent’s characteristics (genes) and minor variations (mutation). This way, individuals with better quality tend to live longer and to generate better and fitter offspring, thus improving the robustness of the algorithm. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  26. 26. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsEvolutionary Approach It is important to emphasize that the main idea behind a Genetic Algorithm [4] is to have a set of candidate solutions (individuals) to a problem evolving towards the desired solution. In each generation those individuals are evaluated according to their quality (fitness). The worst individuals are then discarded and the best will generate new individuals resulting from the combination of their parent’s characteristics (genes) and minor variations (mutation). This way, individuals with better quality tend to live longer and to generate better and fitter offspring, thus improving the robustness of the algorithm. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  27. 27. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsEvolutionary Approach It is important to emphasize that the main idea behind a Genetic Algorithm [4] is to have a set of candidate solutions (individuals) to a problem evolving towards the desired solution. In each generation those individuals are evaluated according to their quality (fitness). The worst individuals are then discarded and the best will generate new individuals resulting from the combination of their parent’s characteristics (genes) and minor variations (mutation). This way, individuals with better quality tend to live longer and to generate better and fitter offspring, thus improving the robustness of the algorithm. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  28. 28. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsEvolutionary Approach It is important to emphasize that the main idea behind a Genetic Algorithm [4] is to have a set of candidate solutions (individuals) to a problem evolving towards the desired solution. In each generation those individuals are evaluated according to their quality (fitness). The worst individuals are then discarded and the best will generate new individuals resulting from the combination of their parent’s characteristics (genes) and minor variations (mutation). This way, individuals with better quality tend to live longer and to generate better and fitter offspring, thus improving the robustness of the algorithm. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  29. 29. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsMoreover, when addressing a genetic algorithm to a problem thereare several aspects that must be taken into account: Genotype How to encode each individual or candidate solution to the problem?Fitness Function How to evaluate the quality of each candidate solution? Selection How individuals are selected from the population to breed? Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  30. 30. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsMoreover, when addressing a genetic algorithm to a problem thereare several aspects that must be taken into account: Genotype How to encode each individual or candidate solution to the problem?Fitness Function How to evaluate the quality of each candidate solution? Selection How individuals are selected from the population to breed? Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  31. 31. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsMoreover, when addressing a genetic algorithm to a problem thereare several aspects that must be taken into account: Genotype How to encode each individual or candidate solution to the problem?Fitness Function How to evaluate the quality of each candidate solution? Selection How individuals are selected from the population to breed? Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  32. 32. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results Recombination How to employ recombination: given two individuals, how to exchange genetic material between them to breed two new individuals (offspring)? Mutation What kind of mutations we should take into account, according to the problem being solved? Initialization How the first population is generated?Survivor Selection How survivors are selected from one generation to the next? Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  33. 33. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results Recombination How to employ recombination: given two individuals, how to exchange genetic material between them to breed two new individuals (offspring)? Mutation What kind of mutations we should take into account, according to the problem being solved? Initialization How the first population is generated?Survivor Selection How survivors are selected from one generation to the next? Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  34. 34. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results Recombination How to employ recombination: given two individuals, how to exchange genetic material between them to breed two new individuals (offspring)? Mutation What kind of mutations we should take into account, according to the problem being solved? Initialization How the first population is generated?Survivor Selection How survivors are selected from one generation to the next? Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  35. 35. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results Recombination How to employ recombination: given two individuals, how to exchange genetic material between them to breed two new individuals (offspring)? Mutation What kind of mutations we should take into account, according to the problem being solved? Initialization How the first population is generated?Survivor Selection How survivors are selected from one generation to the next? Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  36. 36. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsOutline 1 Introduction 2 Evolutionary Approach First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Automatic Music Transcription using Synthesized Instruments First approach on Real Audio Recordings Reducing the Harmonic Overfitting Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art Results 3 Conclusion 4 References Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  37. 37. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFirst Genetic Algorithm approach to Polyphonic PitchDetection The first work in the literature using Genetic Algorithms for polyphonic pitch detection appears in 2001 by Garcia [2]. Garcia claims that polyphonic pitch detection can be considered as a search space problem where the goal is to find the pitches that compose a polyphonic acoustic signal. This way, it makes sense to use genetic algorithms since they perform very well in search problems [3]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  38. 38. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFirst Genetic Algorithm approach to Polyphonic PitchDetection The first work in the literature using Genetic Algorithms for polyphonic pitch detection appears in 2001 by Garcia [2]. Garcia claims that polyphonic pitch detection can be considered as a search space problem where the goal is to find the pitches that compose a polyphonic acoustic signal. This way, it makes sense to use genetic algorithms since they perform very well in search problems [3]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  39. 39. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFirst Genetic Algorithm approach to Polyphonic PitchDetection The first work in the literature using Genetic Algorithms for polyphonic pitch detection appears in 2001 by Garcia [2]. Garcia claims that polyphonic pitch detection can be considered as a search space problem where the goal is to find the pitches that compose a polyphonic acoustic signal. This way, it makes sense to use genetic algorithms since they perform very well in search problems [3]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  40. 40. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsGenotype L L L Figure: Garcia’s approach chromosome structure with L = 4 bits. Garcia’s approach encodes each chromosome as a binary string with variable length. The chromosome’s structure is a concatenation of N substrings of L bits each. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  41. 41. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsGenotype L L L Figure: Garcia’s approach chromosome structure with L = 4 bits. Garcia’s approach encodes each chromosome as a binary string with variable length. The chromosome’s structure is a concatenation of N substrings of L bits each. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  42. 42. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsGenotype Although the length of the L substrings is fixed since F0 range and resolution is specified as an input parameter, the length of the chromosome is variable because no assumption is made about the number of F0s in the signal. The length of the substrings is defined according to the frequency range, ∆F 0, and frequency resolution, dF 0, as the minimum integer L, where: Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  43. 43. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsGenotype Although the length of the L substrings is fixed since F0 range and resolution is specified as an input parameter, the length of the chromosome is variable because no assumption is made about the number of F0s in the signal. The length of the substrings is defined according to the frequency range, ∆F 0, and frequency resolution, dF 0, as the minimum integer L, where: Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  44. 44. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsGenotype Although the length of the L substrings is fixed since F0 range and resolution is specified as an input parameter, the length of the chromosome is variable because no assumption is made about the number of F0s in the signal. The length of the substrings is defined according to the frequency range, ∆F 0, and frequency resolution, dF 0, as the minimum integer L, where: ∆F 0 2L ≥ (1) dF 0 Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  45. 45. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function The fitness measure of Garcia’s approach [2], f (s), for a given string or chromosome, s, is based upon a correlation between the input spectrum and a comb spectrum defined in [10]. The partial fitness value fp (s, j) is computed for each fundamental frequency value, F 0j , coded by substring j in string s, as the correlation between the input magnitude spectrum |X (ω)| and a reference comb spectrum with exponentially decreasing amplitudes e −αh , where h is the harmonic index and α a specified input parameter: Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  46. 46. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function The fitness measure of Garcia’s approach [2], f (s), for a given string or chromosome, s, is based upon a correlation between the input spectrum and a comb spectrum defined in [10]. The partial fitness value fp (s, j) is computed for each fundamental frequency value, F 0j , coded by substring j in string s, as the correlation between the input magnitude spectrum |X (ω)| and a reference comb spectrum with exponentially decreasing amplitudes e −αh , where h is the harmonic index and α a specified input parameter: Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  47. 47. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function The fitness measure of Garcia’s approach [2], f (s), for a given string or chromosome, s, is based upon a correlation between the input spectrum and a comb spectrum defined in [10]. The partial fitness value fp (s, j) is computed for each fundamental frequency value, F 0j , coded by substring j in string s, as the correlation between the input magnitude spectrum |X (ω)| and a reference comb spectrum with exponentially decreasing amplitudes e −αh , where h is the harmonic index and α a specified input parameter: fp (s, j) = X (2πhF 0j ) .e −αh (2) h Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  48. 48. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function After the partial fitness fp (s, j) is computed for a substring j, the input DFT bins used in the correlation sum are zeroed for the remaining partial fitness evaluations of the string. This way, each spectral bin is constrained to belong to only one harmonic series. This strategy penalizes strings or chromosomes that harmonic related notes. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  49. 49. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function After the partial fitness fp (s, j) is computed for a substring j, the input DFT bins used in the correlation sum are zeroed for the remaining partial fitness evaluations of the string. This way, each spectral bin is constrained to belong to only one harmonic series. This strategy penalizes strings or chromosomes that harmonic related notes. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  50. 50. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function After the partial fitness fp (s, j) is computed for a substring j, the input DFT bins used in the correlation sum are zeroed for the remaining partial fitness evaluations of the string. This way, each spectral bin is constrained to belong to only one harmonic series. This strategy penalizes strings or chromosomes that harmonic related notes. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  51. 51. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function For each chromosome a raw fitness value, fraw , is then calculated as the sum of partial fitnesses over all its j substrings: The chromosome fitness, f (s), is then computed from the raw fitness as: Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  52. 52. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function For each chromosome a raw fitness value, fraw , is then calculated as the sum of partial fitnesses over all its j substrings: NS fraw (s) = fp (s, j) (3) j=1 The chromosome fitness, f (s), is then computed from the raw fitness as: Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  53. 53. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function For each chromosome a raw fitness value, fraw , is then calculated as the sum of partial fitnesses over all its j substrings: NS fraw (s) = fp (s, j) (3) j=1 The chromosome fitness, f (s), is then computed from the raw fitness as: Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  54. 54. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function For each chromosome a raw fitness value, fraw , is then calculated as the sum of partial fitnesses over all its j substrings: NS fraw (s) = fp (s, j) (3) j=1 The chromosome fitness, f (s), is then computed from the raw fitness as: f (s) = fraw (s) − Ns f p (4) Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  55. 55. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function where f p is the mean partial fitness over the whole population: and where Ns is the number of F0s or substrings in the chromosome. The subtraction by Ns f p in Equation 4 is a way to penalize strings with too many F0 codes (it is equivalent to subtracting the average partial fitness from each partial fitness) since substrings with partial fitness values smaller than average will become negative and then will penalize the global fitness of the chromosome. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  56. 56. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function where f p is the mean partial fitness over the whole population: s,j fp (s, j) fp = (5) s Ns and where Ns is the number of F0s or substrings in the chromosome. The subtraction by Ns f p in Equation 4 is a way to penalize strings with too many F0 codes (it is equivalent to subtracting the average partial fitness from each partial fitness) since substrings with partial fitness values smaller than average will become negative and then will penalize the global fitness of the chromosome. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  57. 57. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function where f p is the mean partial fitness over the whole population: s,j fp (s, j) fp = (5) s Ns and where Ns is the number of F0s or substrings in the chromosome. The subtraction by Ns f p in Equation 4 is a way to penalize strings with too many F0 codes (it is equivalent to subtracting the average partial fitness from each partial fitness) since substrings with partial fitness values smaller than average will become negative and then will penalize the global fitness of the chromosome. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  58. 58. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function where f p is the mean partial fitness over the whole population: s,j fp (s, j) fp = (5) s Ns and where Ns is the number of F0s or substrings in the chromosome. The subtraction by Ns f p in Equation 4 is a way to penalize strings with too many F0 codes (it is equivalent to subtracting the average partial fitness from each partial fitness) since substrings with partial fitness values smaller than average will become negative and then will penalize the global fitness of the chromosome. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  59. 59. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function Strings with any F0 value outside the allowed range are assigned null fitness. A final fitness correction step is applied to prevent the premature convergence of the genetic algorithm. This is employed by imposing a fitness floor value Fmin , such as: where Fmax is the maximum fitness in the current generation, and β is an input positive constant. Individuals whose f (s) < Fmin have their fitness reset at f (s) = Fmin . Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  60. 60. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function Strings with any F0 value outside the allowed range are assigned null fitness. A final fitness correction step is applied to prevent the premature convergence of the genetic algorithm. This is employed by imposing a fitness floor value Fmin , such as: where Fmax is the maximum fitness in the current generation, and β is an input positive constant. Individuals whose f (s) < Fmin have their fitness reset at f (s) = Fmin . Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  61. 61. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function Strings with any F0 value outside the allowed range are assigned null fitness. A final fitness correction step is applied to prevent the premature convergence of the genetic algorithm. This is employed by imposing a fitness floor value Fmin , such as: Fmax Fmin = (6) β where Fmax is the maximum fitness in the current generation, and β is an input positive constant. Individuals whose f (s) < Fmin have their fitness reset at f (s) = Fmin . Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  62. 62. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function Strings with any F0 value outside the allowed range are assigned null fitness. A final fitness correction step is applied to prevent the premature convergence of the genetic algorithm. This is employed by imposing a fitness floor value Fmin , such as: Fmax Fmin = (6) β where Fmax is the maximum fitness in the current generation, and β is an input positive constant. Individuals whose f (s) < Fmin have their fitness reset at f (s) = Fmin . Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  63. 63. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsFitness Function Strings with any F0 value outside the allowed range are assigned null fitness. A final fitness correction step is applied to prevent the premature convergence of the genetic algorithm. This is employed by imposing a fitness floor value Fmin , such as: Fmax Fmin = (6) β where Fmax is the maximum fitness in the current generation, and β is an input positive constant. Individuals whose f (s) < Fmin have their fitness reset at f (s) = Fmin . Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  64. 64. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsSelection Each individual is selected for breeding according to the roulette wheel [3] selection operator: for each individual, a roulette wheel slot is assigned, with size proportional to its fitness f (s): where an uniformly distributed random number r between 0 and the total cumulative fitness fc (M) is drawn. The minimum string index s that satisfies the fc (s) > r condition is chosen. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  65. 65. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsSelection Each individual is selected for breeding according to the roulette wheel [3] selection operator: for each individual, a roulette wheel slot is assigned, with size proportional to its fitness f (s): s fc = f (j) (7) j=1 where an uniformly distributed random number r between 0 and the total cumulative fitness fc (M) is drawn. The minimum string index s that satisfies the fc (s) > r condition is chosen. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  66. 66. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsSelection Each individual is selected for breeding according to the roulette wheel [3] selection operator: for each individual, a roulette wheel slot is assigned, with size proportional to its fitness f (s): s fc = f (j) (7) j=1 where an uniformly distributed random number r between 0 and the total cumulative fitness fc (M) is drawn. The minimum string index s that satisfies the fc (s) > r condition is chosen. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  67. 67. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsSelection Each individual is selected for breeding according to the roulette wheel [3] selection operator: for each individual, a roulette wheel slot is assigned, with size proportional to its fitness f (s): s fc = f (j) (7) j=1 where an uniformly distributed random number r between 0 and the total cumulative fitness fc (M) is drawn. The minimum string index s that satisfies the fc (s) > r condition is chosen. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  68. 68. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsRecombination As recombination operator, Garcia uses the single-point crossover. This operator is designed as follows: two different points of cut are selected - one per individual - since the number of encoded F0s can differ from individuals. This way, two individuals with different chromosome sizes can breed and generate two offspring also, with different chromosome sizes. This operator also ensures that the chromosomes length of the offspring are always multiples of L. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  69. 69. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsRecombination As recombination operator, Garcia uses the single-point crossover. This operator is designed as follows: two different points of cut are selected - one per individual - since the number of encoded F0s can differ from individuals. This way, two individuals with different chromosome sizes can breed and generate two offspring also, with different chromosome sizes. This operator also ensures that the chromosomes length of the offspring are always multiples of L. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  70. 70. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsRecombination As recombination operator, Garcia uses the single-point crossover. This operator is designed as follows: two different points of cut are selected - one per individual - since the number of encoded F0s can differ from individuals. This way, two individuals with different chromosome sizes can breed and generate two offspring also, with different chromosome sizes. This operator also ensures that the chromosomes length of the offspring are always multiples of L. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  71. 71. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsRecombination As recombination operator, Garcia uses the single-point crossover. This operator is designed as follows: two different points of cut are selected - one per individual - since the number of encoded F0s can differ from individuals. This way, two individuals with different chromosome sizes can breed and generate two offspring also, with different chromosome sizes. This operator also ensures that the chromosomes length of the offspring are always multiples of L. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  72. 72. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsMutation The mutation operator consists on flipping single bit in the whole genome of an individual. The probability of mutation (Pn )is given by: where Pm is the probability of mutation per bit and (N.L) is the chromosome length. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  73. 73. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsMutation The mutation operator consists on flipping single bit in the whole genome of an individual. The probability of mutation (Pn )is given by: where Pm is the probability of mutation per bit and (N.L) is the chromosome length. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  74. 74. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsMutation The mutation operator consists on flipping single bit in the whole genome of an individual. The probability of mutation (Pn )is given by: Pn = (1 − Pm )(N.L) (8) where Pm is the probability of mutation per bit and (N.L) is the chromosome length. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  75. 75. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsMutation The mutation operator consists on flipping single bit in the whole genome of an individual. The probability of mutation (Pn )is given by: Pn = (1 − Pm )(N.L) (8) where Pm is the probability of mutation per bit and (N.L) is the chromosome length. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  76. 76. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsInitialization The initial population is composed by randomly generated individuals: random number of F0s, each with a random F0 value. Both maximum number of F0s and F0 frequency range are specified inputs.Survivor Selection If the current best individual is not as fit as the best individual of the previous generation, the current worst individual is replaced by the best from the previous generation. This strategy is called elitism [3]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  77. 77. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsInitialization The initial population is composed by randomly generated individuals: random number of F0s, each with a random F0 value. Both maximum number of F0s and F0 frequency range are specified inputs.Survivor Selection If the current best individual is not as fit as the best individual of the previous generation, the current worst individual is replaced by the best from the previous generation. This strategy is called elitism [3]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music
  78. 78. First Genetic Algorithm approach to Polyphonic Pitch Detection Moving from Polyphonic Pitch Detection to AMT Introduction Automatic Music Transcription using Synthesized Instruments Evolutionary Approach First approach on Real Audio Recordings Conclusion Reducing the Harmonic Overfitting References Automatic Music Transcription of Multi-Timbral Music Genetic Algorithm achieves State-of-the-Art ResultsInitialization The initial population is composed by randomly generated individuals: random number of F0s, each with a random F0 value. Both maximum number of F0s and F0 frequency range are specified inputs.Survivor Selection If the current best individual is not as fit as the best individual of the previous generation, the current worst individual is replaced by the best from the previous generation. This strategy is called elitism [3]. Reis, Fernandez, Ferreira EAs and the Automatic Transcription of Music

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