Aggregation of information is of primary importance in the construction of knowledge based systems in various domains, ranging from medicine, economics, and engineering to decision-making processes, artificial intelligence, robotics, and machine learning. This book gives a broad introduction into the topic of aggregation functions, and provides a concise account of the properties and the main classes of such functions, including classical means, medians, ordered weighted averaging functions, Choquet and Sugeno integrals, triangular norms, conorms and copulas, uninorms, nullnorms, and symmetric sums. It also presents some state-of-the-art techniques, many graphical illustrations and new interpolatory aggregation functions. A particular attention is paid to identification and construction of aggregation functions from application specific requirements and empirical data. This book provides scientists, IT specialists and system architects with a self-contained easy-to-use guide, as well as examples of computer code and a software package. It will facilitate construction of decision support, expert, recommender, control and many other intelligent systems.

Aggregation Functions: A Guide for Practitioners

The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

The steep rise in music downloading over CD sales has created a major shift in the music industry away from physical media formats and towards online products and services. Music is one of the most popular types of online information and there are now hundreds of music streaming and download services operating on the World-Wide Web. Some of the music collections available are approaching the scale of ten million tracks and this has posed a major challenge for searching, retrieving, and organizing music content. Research efforts in music information retrieval have involved experts from music perception, cognition, musicology, engineering, and computer science engaged in truly interdisciplinary activity that has resulted in many proposed algorithmic and methodological solutions to music search using content-based methods. This paper outlines the problems of content-based music information retrieval and explores the state-of-the-art methods using audio cues (e.g., query by humming, audio fingerprinting, content-based music retrieval) and other cues (e.g., music notation and symbolic representation), and identifies some of the major challenges for the coming years.

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Content-Based Music Information Retrieval: Current Directions and Future Challenges

This doctoral dissertation proposes and evaluates a computational approach for the automatic description of tonal aspects of music from the analysis of polyphonic audio signals. These algorithms focus on the computation of pitch class distributions descriptors, the estimation of the key of a piece, the visualization of the evolution of its tonal center or the measurement of the similarity between two different musical pieces.
This dissertation substantially contributes to the field of computational tonal description: a) It provides a multidisciplinary review of tonal induction systems; b) It defines a set of requirements for low-level tonal features; c) It provides a quantitative and modular evaluation of the proposed methods; d) It contributes to bridge the gap between audio and symbolic-oriented methods without the need of a perfect transcription; e) It extents current literature dealing with classical music to other musical genres; f) It shows the usefulness of tonal descriptors for music similarity; g) It provides an optimized method which is used in a real system for music visualization and retrieval, working with over a million of musical pieces.

Tonal description of music audio signals

List of Acronyms. List of Symbols. 1. Introduction. 1.1 Audio Content Description. 1.2 MPEG-7 Audio Content Description - An Overview. 1.2.1 MPEG-7 Low-Level Descriptors. 1.2.2 MPEG-7 Description Schemes. 1.2.3 MPEG-7 Description Definition Language (DDL). 1.2.4 BiM (Binary Format for MPEG-7). 1.3 Organization of the Book. 2. Low-Level Descriptors. 2.1 Introduction. 2.2 Basic Parameters and Notations. 2.2.1 Time Domain. 2.2.2 Frequency Domain. 2.3 Scalable Series. 2.3.1 Series of Scalars. 2.3.2 Series of Vectors. 2.3.3 Binary Series. 2.4 Basic Descriptors. 2.4.1 Audio Waveform. 2.4.2 Audio Power. 2.5 Basic Spectral Descriptors. 2.5.1 Audio Spectrum Envelope. 2.5.2 Audio Spectrum Centroid. 2.5.3 Audio Spectrum Spread. 2.5.4 Audio Spectrum Flatness. 2.6 Basic Signal Parameters. 2.6.1 Audio Harmonicity. 2.6.2 Audio Fundamental Frequency. 2.7 Timbral Descriptors. 2.7.1 Temporal Timbral: Requirements. 2.7.2 Log Attack Time. 2.7.3 Temporal Centroid. 2.7.4 Spectral Timbral: Requirements. 2.7.5 Harmonic Spectral Centroid. 2.7.6 Harmonic Spectral Deviation. 2.7.7 Harmonic Spectral Spread. 2.7.8 Harmonic Spectral Variation. 2.7.9 Spectral Centroid. 2.8 Spectral Basis Representations. 2.9 Silence Segment. 2.10 Beyond the Scope of MPEG-7. 2.10.1 Other Low-Level Descriptors. 2.10.2 Mel-Frequency Cepstrum Coefficients. References. 3. Sound Classification and Similarity. 3.1 Introduction. 3.2 Dimensionality Reduction. 3.2.1 Singular Value Decomposition (SVD). 3.2.2 Principal Component Analysis (PCA). 3.2.3 Independent Component Analysis (ICA). 3.2.4 Non-Negative Factorization (NMF). 3.3 Classification Methods. 3.3.1 Gaussian Mixture Model (GMM). 3.3.2 Hidden Markov Model (HMM). 3.3.3 Neural Network (NN). 3.3.4 Support Vector Machine (SVM). 3.4 MPEG-7 Sound Classification. 3.4.1 MPEG-7 Audio Spectrum Projection (ASP) Feature Extraction. 3.4.2 Training Hidden Markov Models (HMMs). 3.4.3 Classification of Sounds. 3.5 Comparison of MPEG-7 Audio Spectrum Projection vs. MFCC Features. 3.6 Indexing and Similarity. 3.6.1 Audio Retrieval Using Histogram Sum of Squared Differences. 3.7 Simulation Results and Discussion. 3.7.1 Plots of MPEG-7 Audio Descriptors. 3.7.2 Parameter Selection. 3.7.3 Results for Distinguishing Between Speech, Music and Environmental Sound. 3.7.4 Results of Sound Classification Using Three Audio Taxonomy Methods. 3.7.5 Results for Speaker Recognition. 3.7.6 Results of Musical Instrument Classification. 3.7.7 Audio Retrieval Results. 3.8 Conclusions. References. 4. Spoken Content. 4.1 Introduction. 4.2 Automatic Speech Recognition. 4.2.1 Basic Principles. 4.2.2 Types of Speech Recognition Systems. 4.2.3 Recognition Results. 4.3 MPEG-7 SpokenContent Description. 4.3.1 General Structure. 4.3.2 SpokenContentHeader. 4.3.3 SpokenContentLattice. 4.4 Application: Spoken Document Retrieval. 4.4.1 Basic Principles of IR and SDR. 4.4.2 Vector Space Models. 4.4.3 Word-Based SDR. 4.4.4 Sub-Word-Based Vector Space Models. 4.4.5 Sub-Word String Matching. 4.4.6 Combining Word and Sub-Word Indexing. 4.5 Conclusions. 4.5.1 MPEG-7 Interoperability. 4.5.2 MPEG-7 Flexibility. 4.5.3 Perspectives. References. 5. Music Description Tools. 5.1 Timbre. 5.1.1 Introduction. 5.1.2 InstrumentTimbre. 5.1.3 HarmonicInstrumentTimbre. 5.1.4 PercussiveInstrumentTimbre. 5.1.5 Distance Measures. 5.2 Melody. 5.2.1 Melody. 5.2.2 Meter. 5.2.3 Scale. 5.2.4 Key. 5.2.5 MelodyContour. 5.2.6 MelodySequence. 5.3 Tempo. 5.3.1 AudioTempo. 5.3.2 AudioBPM. 5.4 Application Example: Query-by-Humming. 5.4.1 Monophonic Melody Transcription. 5.4.2 Polyphonic Melody Transcription. 5.4.3 Comparison of Melody Contours. References. 6. Fingerprinting and Audio Signal Quality. 6.1 Introduction. 6.2 Audio Signature. 6.2.1 Generalities on Audio Fingerprinting. 6.2.2 Fingerprint Extraction. 6.2.3 Distance and Searching Methods. 6.2.4 MPEG-7-Standardized AudioSignature. 6.3 Audio Signal Quality. 6.3.1 AudioSignalQuality Description Scheme. 6.3.2 BroadcastReady. 6.3.3 IsOriginalMono. 6.3.4 BackgroundNoiseLevel. 6.3.5 CrossChannelCorrelation. 6.3.6 RelativeDelay. 6.3.7 Balance. 6.3.8 DcOffset. 6.3.9 Bandwidth. 6.3.10 TransmissionTechnology. 6.3.11 ErrorEvent and ErrorEventList. References. 7. Application. 7.1 Introduction. 7.2 Automatic Audio Segmentation. 7.2.1 Feature Extraction. 7.2.2 Segmentation. 7.2.3 Metric-Based Segmentation. 7.2.4 Model-Selection-Based Segmentation. 7.2.5 Hybrid Segmentation. 7.2.6 Hybrid Segmentation Using MPEG-7 ASP. 7.2.7 Segmentation Results. 7.3 Sound Indexing and Browsing of Home Video Using Spoken Annotations. 7.3.1 A Simple Experimental System. 7.3.2 Retrieval Results. 7.4 Highlights Extraction for Sport Programmes Using Audio Event Detection. 7.4.1 Goal Event Segment Selection. 7.4.2 System Results. 7.5 A Spoken Document Retrieval System for Digital Photo Albums. References. Index.

MPEG-7 Audio and Beyond: Audio Content Indexing and Retrieval

Musical audio-mining technology allows users to search and retrieve music by means of content-based text and audio queries. Though these systems are promising, there is a need for a better understanding of the role of user preferences and user profiles. The development of taxonomies for different aspects of a musical audio-mining system aims at bridging the gap between system development and user interactive interfacing. In the first part of this paper, the need for user-dependent taxonomy development is addressed and an experiment in spontaneous user behavior is described, based on 72 users and 1148 vocal queries. Statistical analysis provides insight into the characteristics of vocal querying and possible useful concepts. In the second part of the paper, it is described how categories and concepts from the statistical analysis have been used for the refinement of taxonomies that address user interactive interfacing and feature extraction.

User-dependent taxonomy of musical features as a conceptual framework for musical audio-mining technology

This contribution deals with the dominance relation on the class of conjunctors, containing as particular cases the subclasses of quasi-copulas, copulas and t-norms. The main results pertain to the summand-wise nature of the dominance relation, when applied to ordinal sum conjunctors, and to the relationship between the idempotent elements of two conjunctors involved in a dominance relationship. The results are illustrated on some well-known parametric families of t-norms and copulas.

On the dominance relation between ordinal sums of conjunctors

The discrete dice model essentially amounts to comparing discrete uniform probability distributions and generates reciprocal relations that exhibit a particular type of transitivity called dice-transitivity. In this contribution, this comparison method is extended and applied to general probability distributions and the generated reciprocal relations are shown to generalize the concept of stochastic dominance. For a variety of parametrized probability distributions, we analyse the transitivity properties of these reciprocal relations within the framework of cycle-transitivity. The relationship between normal probability distributions and the different types of stochastic transitivity is emphasized.

A fuzzy approach to stochastic dominance of random variables

Content-based music information retrieval and associated data-mining opens a number of perspectives for music industry and related multimedia commercial activities. Due to the great variability of musical audio, its non-verbal basis, and its interconnected levels of description, musical audio-mining is a very complex research domain that involves efforts from musicology, signal processing, and statistical modeling. This paper gives a general critical overview of the state-of-theart followed by a discussion of musical audio-mining issues which are related to bottom-up processing (feature extraction), top-down processing (taxonomies and knowledge-driven processing), similarity matching, and user analysis and profiling. INTRODUCTION Musical audio-mining deals with the extraction and processing of patterns and knowledge from musical audio. In its proper context of music information retrieval (MIR) this knowledge allows users to search and retrieve music by means of content-based text and audio queries, such as query-byhumming/singing/playing/excerpts, or specification of a list of musical terms, such as 'happy', 'energetic', etc., or by any combination of these. The result will be a ranking of answers, based on similarity ratings, pointing to relevant audio-files. First we present the general architecture of a MIR system and an overview of the characteristics of existing MIR systems. Then we discuss issues of musical audio-mining which are related to bottom-up processing (feature extraction), top-down processing (taxonomies and knowledge-driven processing), similarity matching, and user analysis and profiling. GENERAL ARCHITECTURE OF A MIR SYSTEM Figure 1 depicts the general architecture of a MIR system. It basically consists of a database part (left), a query part (right), and a similarity matching engine with optional parts that account for a taxonomy and users profiling. The task is to retrieve the wanted music files using information provided by the query. Papers related to several aspects of MIR can be found at the ISMIR websites http://ciir.cs.umass.edu/music2000/ and http://ismir2001.indiana.edu/index.html. OVERVIEW OF EXISTING SYSTEMS Most existing MIR systems (Table 1) have limited capabilities in terms of dataand audio-mining. The music collections typically consist of sets of short fragments, mostly incipits of (monophonic) melodies which are represented as strings of pitches, pitch intervals, contours, and durations in an electronic score format such as MIDI or Humdrum. Information retrieval is based on dynamic pattern matching (string editing), that is, calculation of the cost of editing a symbolic sequence query such that it fits with a set of symbolic sequences of music. The ranking of answers is based on this cost. No taxonomies thus far have been used. Some systems, however, do allow audioinput queries. These are processed into symbolic strings (melodies) that can be used in pattern matching.

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Tendencies, perspectives, and opportunities of musical audio-mining

We introduce four families of semilinear copulas (i. e. copulas that are linear in at least one coordinate of any point of the unit square) of which the diagonal and opposite diagonal sections are given functions. For each of these families, we provide necessary and sufficient conditions under which given diagonal and opposite diagonal functions can be the diagonal and opposite diagonal sections of a semilinear copula belonging to that family. We focus particular attention on the family of orbital semilinear copulas, which are obtained by linear interpolation on segments connecting the diagonal and opposite diagonal of the unit square.

Hans De Meyer

Papers

User-dependent taxonomy of musical features as a conceptual framework for musical audio-mining technology

On the dominance relation between ordinal sums of conjunctors

A fuzzy approach to stochastic dominance of random variables

Tendencies, perspectives, and opportunities of musical audio-mining

Orbital semilinear copulas