Model-free Music Similarity Measure
نویسندگان
چکیده
This thesis first takes a broad look at various music similarity measures in the literature, and then focuses on two different model-free music similarity measures and evaluates them. The term model-free in this context indicates that these music similarity measures use few or no background knowledge about music whatsoever, they are more general compared with other approaches and can, with little or no change, be used in different other or areas as well. The first approach is based on Mel-frequency cepstral coefficient features (MFCCs) and Gaussian Mixture Models (GMMs), which, technically speaking is not utterly model-free in the sense that you at least need to know that you are dealing with some audio-related problems, as the features drawn from pieces of music require this awareness. The second is based on an ideal theory of the information content in individual objects (Kolmogorov complexity), information distance, and a universal similarity metric. The latter approach performs the comparison on Musical Instrument Digital Interface (MIDI) files, which dramatically contrasts with the former one, where a wave format is used. Furthermore, we present a new method based on Neural Network (NN), known, together with fuzzy logic and evolutionary computing, as some biological-inspired methods. Our method is based on the first approach, but uses NN as classifier instead of measuring the distance between two sets of GMMs directly. Finally, we present the experimental results. The first two methods don’t work quite well on the dataset we used in the experiment, and we analyzed the possible reasons. Experiments show that the third method measures reasonably well the degree of music similarity. 1 This concept coincides with entropy in information theory, which can be regarded as the expectation version of Kolmogorov complexity in some sense. MODEL-‐FREE MUSIC SIMILARITY MEASURE Wen Shao(u4717714) List of Abbreviations NN Neural Networks GMM Gaussian Mixture Model MFCCs Mel-Frequency Cepstrum Coefficients TM Turing Machine EM Expectation Maximization MODEL-‐FREE MUSIC SIMILARITY MEASURE Wen Shao(u4717714) Table of Contents ABSTRACT ................................................................................................................................................... 1-‐1 LIST OF ABBREVIATIONS ............................................................................................................................. 1-‐2 TABLE OF FIGURES ...................................................................................................................................... 1-‐5 1. INTRODUCTION ................................................................................................................................... 1-‐6 1.1 PURPOSE ................................................................................................................................................... 1-‐6 1.2 CONTRIBUTION ........................................................................................................................................... 1-‐7 1.3 ORGANIZATION .......................................................................................................................................... 1-‐7 2. RELEVANT TECHNIQUES AND CONCEPTS .............................................................................................. 2-‐8 2.1 METRIC ..................................................................................................................................................... 2-‐8 2.2 KOLMOGOROV COMPLEXITY ......................................................................................................................... 2-‐8 2.2.1 Universal Turing machine and Kolmogorov complexity ................................................................... 2-‐8 2.2.2 Conditional Kolmogorov complexity .............................................................................................. 2-‐10 2.2.3 Incomputability of Kolmogorov complexity ................................................................................... 2-‐10 2.3 GAUSSIAN MIXTURE MODEL ....................................................................................................................... 2-‐11 2.3.1 The Gaussian distribution .............................................................................................................. 2-‐11 2.3.2 Mixtures of Gaussians .................................................................................................................... 2-‐11 2.3.3 Learning mixtures of Gaussians ..................................................................................................... 2-‐12 2.4 MEL FREQUENCY CEPSTRUM COEFFICIENTS (MFCCS) ..................................................................................... 2-‐13 2.4.1 Mel Scale ........................................................................................................................................ 2-‐13 2.4.2 Decibels .......................................................................................................................................... 2-‐14 3. LITERATURE REVIEW ........................................................................................................................... 3-‐15 3.1 MIR AND MIREX ..................................................................................................................................... 3-‐15 3.2 SYMBOLIC REPRESENTATION APPROACHES AND STRING MATCHING TECHNIQUES .................................................. 3-‐15 3.3 ACOUSTIC REPRESENTATION AND MACHINE LEARNING TECHNIQUES ................................................................... 3-‐16 4. EVALUATION OF KOLMOGOROV COMPLEXITY-‐BASED METHOD ......................................................... 4-‐17 4.1 KOLMOGOROV COMPLEXITY-‐BASED METHOD ................................................................................................. 4-‐17 4.2 DATASET AND EXPERIMENT SETUP ............................................................................................................... 4-‐17 4.3 EXPERIMENTAL RESULTS ............................................................................................................................. 4-‐18 5. EVALUATION OF MFCCS AND GMM-‐BASED METHOD .......................................................................... 5-‐20 5.1 FEATURE EXTRACTION ................................................................................................................................ 5-‐20 5.1.1 Power Spectrum ............................................................................................................................. 5-‐20 5.1.2 Mel Frequence ............................................................................................................................... 5-‐22 5.1.3 Decibel ........................................................................................................................................... 5-‐23 5.1.4 DCT ................................................................................................................................................. 5-‐23 5.2 GMM SIGNATURE .................................................................................................................................... 5-‐24 5.3 SIMILARITY MEASURE ................................................................................................................................ 5-‐26 5.4 EXPERIMENT SETUP ................................................................................................................................... 5-‐26 MODEL-‐FREE MUSIC SIMILARITY MEASURE Wen Shao(u4717714) 5.5 EXPERIMENTAL RESULTS ............................................................................................................................. 5-‐27 6. A NOVEL APPROACH: NN-‐BASED SIMILARITY MEASURE ...................................................................... 6-‐29 6.1 NEURAL NETWORKS (NN) .......................................................................................................................... 6-‐29 6.1.1 Neural Networks from biological perspective and mathematical perspective .............................. 6-‐29 6.1.2 Cross-‐entropy error function for binary classification .................................................................... 6-‐31 6.1.3 Error backpropagation ................................................................................................................... 6-‐32 6.1.4 Neural Network structures ............................................................................................................. 6-‐33 6.2 NN-‐GMMS-‐BASED MUSIC SIMILARITY MEASURE ........................................................................................... 6-‐33 6.3 EXPERIMENT RESULTS ................................................................................................................................ 6-‐35 7. FUTURE WORK .................................................................................................................................... 7-‐37 BIBLIOGRAPHY ........................................................................................................................................... 7-‐38 MODEL-‐FREE MUSIC SIMILARITY MEASURE Wen Shao(u4717714)
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