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

In the paper an algorithm for calculating the ranking distribution and the averaged ranking probability (averaged rank) of each element of a poset that avoids the enumeration of all linear extensions and relies on the lattice of ideals representation of the poset is presented.

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A Lattice-Theoretic Approach to Computing Averaged Ranks Illustrated on Pollution Data in Baden-Württemberg

Given a random vector with components that are pairwisely coupled by means of a same commutative copula C, we analyze the transitivity of the reciprocal relation obtained from the pairwise comparison of these components The transitivity of this reciprocal relation can be elegantly described within the cycle-transitivity framework if the commutative copula C satisfies a countably infinite family of (functional) inequalities Each functional inequality uniquely characterizes the Frank family of copulas Finally, we highlight the transitivity results for a random vector whose coupling structure is captured by an extended Frank m-copula

Hans De Meyer

Papers

A Lattice-Theoretic Approach to Computing Averaged Ranks Illustrated on Pollution Data in Baden-Württemberg

Functional Inequalities Characterizing the Frank Family of Copulas

The Winning Probability Relation of Parametrized Families of Random Vectors