Hidden%20Markov%20Model:%20Overview%20and%20Applications%20in%20MIR

1
Hidden Markov Model Overview and Applications in
MIR

• MUMT 611, March 2005
• Paul Kolesnik

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Contents

• Introduction to HMM
• Overview of Publications
• Conclusion

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Introduction

• Definition
• A structure that is used to statistically
  characterize the behavior of sequences of event
  observations
• Extension of a model known as Markov chains
• A double stochastic process with an underlying
  stochastic process which is not observable, but
  can only be observed through another set of
  stochastic process that produces the sequence of
  observed symbols (Rabiner and Huang 1986)
• Concepts
• Any observable sequence can be represented as a
  succession of states, with each state
  representing a grouped portion of the observation
  values and containing its features in a
  statistical form

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Introduction

• Concepts (ctd.)
• HMM keeps track of
• What state will the sequence start in
• What state-to-state transitions are likely to
  take place
• What values are likely to occur in each state
• Corresponding parameters
• Array of initial state probabilities
• Matrix of state-to-state transitional
  probabilities
• Matrix of state output probabilities
• ? (?, A, B)

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Introduction
Markov Model Example. - x States of the
Markov model - a Transition probabilities - b
Output probabilities - y Observable outputs
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Introduction

• Three Main HMM Problems
• Recognition
• given an observation sequence and a Hidden Markov
  Model, calculate the probability that the model
  would produce this observation sequence.
• Uncovering (Viterbi)
• given an observation sequence and a Hidden Markov
  Model, calculate the optimal sequence of states
  that would maximize the likelihood of the HMM
  producing the observation.
• Learning / Training
• given an observation sequence (or a set of
  observation sequences and a Hidden Markov Model,
  adjust the model parameters, so that probability
  of the model is maximized.

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Introduction

• HMM History
• Basic concept developed by Markov
• Theory for practical implementation summarized by
  Rabiner and Huang (1986)
• Applied in different fields to data stream
  observation problems
• Common in speech recognition
• Has become increasingly popular in music
  information retrieval applications

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Overview of Works

• Automatic Segmentation for Music Classification
  using Competitive Hidden Markov Models
• (2000) Battle, Cano University Pompeu Fabra
• System classifies audio segments (automatic
  segmentation into abstract acoustic events)
• can be applied to classify a database of audio
  sounds
• allows fast indexing and retrieval of audio
  fragments
• similar segment events are given the same label

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Overview of Works

• (2000) Battle, Cano (ctd.)
• First stage parametrization, features obtained
  from audio signals
• Mel-cepstrum analysis used to obtain feature
  vectors
• Main classification engine HMM-based
• Traditional HMMs are not suited for blind
  learning
• Competitive HMMs used instead
• CoHMMs differ from HMMs only in training stage
  recognition is exactly the same

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Overview of Works

• Melody Spotting Using Hidden Markov Models
• (2001) Durey, ClementsGeorgia Institute of
  Technology
• A melody-based database song retrieval system
• Uses melody spotting procedure adopted from word
  spotting techniques in automatic speech
  recognition
• Humming, whistling, keyboard as input
• Main goal develop a practical system for
  non-symbolic music representation (audio)
• Word/melody-spotting searching for a data
  segment in a data stream

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Overview of Works

• (2001) Durey, Clements (ctd.)
• Uses monophonic melodies, both audio and MIDI
  data
• Left-to-right, 5-state HMM to represent each
  available note and a rest
• Frequency and time-domain features for feature
  vectors
• Constructs an HMM model from the input query
• Runs all of the feature vectors from the songs in
  the database using Viterbi process
• A ranked list of melody occurances in database
  songs is created
• System presented as a proof-of-concept

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Overview of Works

• Indexing Hidden Markov Models for Music Retrieval
• (2002) Jin, Jagadish University of Michigan
• Music retrieval system
• Paper describes traditional MIR HMM techniques as
  effective but not efficient
• Efficient mechanism is suggested to index the
  HMMs
• Each state is represented by an interval / inter
  onset interval ratio
• Each transition is transformed into a
  4-dimensional box

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Overview of Works

• (2002) Jin, Jagadish (ctd.)
• All boxes are inserted into R-tree, an indexing
  structure for multidimensional data
• HMMs are ranked by the number of boxes
• Most likely candidates are selected for
  evaluation
• The evaluation uses the traditional forward
  algorithm

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Overview of Works

• Chord Segmentation and Recognition using
• EM-Trained Hidden Markov Models
• (2003) Sheh, Ellis Columbia University
• Uses HMM for chord recognition, EM
  (Expectation-Maximization) Algorithm to train
  them
• PCP (Pitch Class Profile) vectors used as
  features to train HMMs
• HMM model for each chord type (ex. A Minor,
  etc.)
• System able to successfully recognize chords in
  unstructured, polyphonic, multi-timbre audio

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Overview of Works

• Effectiveness of HMM-Based Retrieval on Large
  Databases
• (2003) Shifrin, Burmingham University of
  Michigan
• Investigates performance of an HMM-based QBH
  system on a large musical database
• VocalSearch system, part of MusArt project
• 50000-theme database (roughly 22000 songs)
• Uses ltdelta-pitch / Inter-onset Interval ratiogt
  pair as feature vectors

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Overview of Works

• (2003) Shifrin, Burmingham (ctd)
• Compared perfect and imperfect queries, simulated
  insertions and deletions
• Discovered Trends
• Longer queries have a positive effect on
  evaluation performance
• All experiments show an early saturation point
• Performed well with imperfect queries on a large
  database

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Overview of Works

• A HMM-Based Pitch Tracker for Audio Queries
• (2003) Orio, Sette University of Padova
• HMM-based approach to transcription of musical
  queries
• HMM used to model features related to singing
  voice
• A sung query is considered as an observation of
  an unknown process the melody the user has in
  mind
• Two-level HMM event-level (using pitches as
  labels), audio-level (attack-sustain-relst
  events)
• A simple model is presented, low recognition
  percentages

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Conclusion

• HTML Bibliography
• http//www.music.mcgill.ca/pkoles
• Questions