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, Clements–Georgia 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 (ExpectationMaximization) 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 <delta-pitch / Inter-onset Interval ratio> 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
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