Musical Instrument Classification Using NonNegative Matrix Factorization Algorithms

1
Musical Instrument Classification Using
Non-Negative Matrix Factorization Algorithms

• Artificial Intelligence Information Analysis
• Laboratory
• Department of Informatics
• Aristotle University of Thessaloniki, Greece

2
1. Introduction

• Automatic musical instrument classification is
  the first step in developing content-based music
  retrieval systems.
• Experiments carried out so far are separated into
  two categories classification of isolated
  instrument tones and classification of sound
  segments.
• In our work, six instrument classes are
  classified by extracting timbral and MPEG-7 Audio
  features using non-negative matrix factorization
  (NMF) algorithms, thus introducing a novel
  application for NMF.

3
2. Feature Extraction

• Timbral texture features

4
2. Feature Extraction

• MPEG-7 Features

5
3. Non-negative Matrix Factorization

• Non-negative matrix factorization (NMF) is a
  subspace analysis method which is able to obtain
  a parts-based representation of objects.
• The NMF problem Given a non-negative n ? m
  matrix V, find non-negative matrix factors W and
  H such as
• where the n ? r matrix W contains the basis
  vectors and the r ? m matrix H contains the
  weights needed to approximate the corresponding
  column of matrix V.
• To find a factorization, an objective function
  has to be defined, such as the KL divergence
  between V and WH.

6
3. Non-negative Matrix Factorization

• Standard NMF The first proposed algorithm
  enforces the non-negativity constraints on
  matrices W and H, by using the generalized KL
  divergence as a cost function
• where WH Y yij. The problem of minimizing
  the divergence can be solved by using iterative
  update rules.
• Local NMF Aiming to impose constraints on
  spatial locality, LNMF attempts to
• Minimize the number of basis components
  representing V.
• Minimize redundancy among different bases
  (orthogonal bases).
• Retain components giving most important
  information.

7
3. Non-negative Matrix Factorization

• Sparse NMF Imposes constraints that can reveal
  local sparse features on data matrix V
• where is a positive constant and hjl the
  l-norm of the j-th column of H.
• Discriminant NMF Keeps the local constraints
  imposed by LNMF and incorporates information
  about class discrimination in the cost function
• where and are constants, and Sw and Sb are
  the within and between-class scatter matrices,
  respectively.

8
4. Experimental Procedure

• Classification in the NMF subspace is performed
• The data matrix V is created (each column vj
  contains a training feature vector).
• Training is performed by applying an NMF
  algorithm into matrix V, yielding the basis
  matrix W and the encoding matrix H.
• In the test phase, for each test vector vtest a
  new test encoding vector is formed
  ,where is the Moore-Penrose
  generalized inverse of W.
• Having formed during training 6 encoding vectors
  hl for each class, the test samples are
  classified using the Cosine Similarity Measure.
  The class label for the test file is defined
  as

9
4. Experimental Procedure

• 300 audio files from the UIOWA MIS database (each
  about 20sec long) were used, consisting of 6
  classes piano, violin, cello, flute, bassoon and
  saxophone. 210 files were used for training and
  90 for testing.
• Two feature matrices were created, the first
  containing MPEG-7 statistical spectrum
  descriptors (ASC, ASS and ASF) and timbral
  features. The second contains the MPEG-7 ASP
  coefficients along with the timbral features.

10
5. Results Future Work

• Classification Results
• In the future
• NMF techniques can be used in broader instrument
  classification experiments and in general sound
  classification applications.
• Other proposed NMF algorithms could also be used
  for classification.
• Finally, advanced MPEG-7 timbral descriptors
  could be utilized for feature extraction.

11
6. MATLAB Implementation
12
7. References