Part I. Experimental Studies: 2. Experiment in psychology 3. Experiments on perceiving III Experiments on imaging 4-8. Experiments on remembering: (a) The method of description (b) The method of repeated reproduction (c) The method of picture writing (d) The method of serial reproduction (e) The method of serial reproduction picture material 9. Perceiving, recognizing, remembering 10. A theory of remembering 11. Images and their functions 12. Meaning Part II. Remembering as a Study in Social Psychology: 13. Social psychology 14. Social psychology and the matter of recall 15. Social psychology and the manner of recall 16. Conventionalism 17. The notion of a collective unconscious 18. The basis of social recall 19. A summary and some conclusions.

Remembering. A Study in Experimental and Social Psychology, Cambridge (University Press) 1964.

In an overcomplete basis, the number of basis vectors is greater than the dimensionality of the input, and the representation of an input is not a unique combination of basis vectors. Overcomplete representations have been advocated because they have greater robustness in the presence of noise, can be sparser, and can have greater flexibility in matching structure in the data. Overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex. Previous work has focused on finding the best representation of a signal using a fixed overcomplete basis (or dictionary). We present an algorithm for learning an overcomplete basis by viewing it as probabilistic model of the observed data. We show that overcomplete bases can yield a better approximation of the underlying statistical distribution of the data and can thus lead to greater coding efficiency. This can be viewed as a generalization of the technique of independent component analysis and provides a method for Bayesian reconstruction of signals in the presence of noise and for blind source separation when there are more sources than mixtures.

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Learning Overcomplete Representations

This letter presents theoretical, algorithmic, and experimental results about nonnegative matrix factorization (NMF) with the Itakura-Saito (IS) divergence. We describe how IS-NMF is underlaid by a well-defined statistical model of superimposed gaussian components and is equivalent to maximum likelihood estimation of variance parameters. This setting can accommodate regularization constraints on the factors through Bayesian priors. In particular, inverse-gamma and gamma Markov chain priors are considered in this work. Estimation can be carried out using a space-alternating generalized expectation-maximization (SAGE) algorithm; this leads to a novel type of NMF algorithm, whose convergence to a stationary point of the IS cost function is guaranteed.

We also discuss the links between the IS divergence and other cost functions used in NMF, in particular, the Euclidean distance and the generalized Kullback-Leibler (KL) divergence. As such, we describe how IS-NMF can also be performed using a gradient multiplicative algorithm (a standard algorithm structure in NMF) whose convergence is observed in practice, though not proven.

Finally, we report a furnished experimental comparative study of Euclidean-NMF, KL-NMF, and IS-NMF algorithms applied to the power spectrogram of a short piano sequence recorded in real conditions, with various initializations and model orders. Then we show how IS-NMF can successfully be employed for denoising and upmix (mono to stereo conversion) of an original piece of early jazz music. These experiments indicate that IS-NMF correctly captures the semantics of audio and is better suited to the representation of music signals than NMF with the usual Euclidean and KL costs.

Nonnegative matrix factorization with the itakura-saito divergence: With application to music analysis

An unsupervised learning algorithm for the separation of sound sources in one-channel music signals is presented. The algorithm is based on factorizing the magnitude spectrogram of an input signal into a sum of components, each of which has a fixed magnitude spectrum and a time-varying gain. Each sound source, in turn, is modeled as a sum of one or more components. The parameters of the components are estimated by minimizing the reconstruction error between the input spectrogram and the model, while restricting the component spectrograms to be nonnegative and favoring components whose gains are slowly varying and sparse. Temporal continuity is favored by using a cost term which is the sum of squared differences between the gains in adjacent frames, and sparseness is favored by penalizing nonzero gains. The proposed iterative estimation algorithm is initialized with random values, and the gains and the spectra are then alternatively updated using multiplicative update rules until the values converge. Simulation experiments were carried out using generated mixtures of pitched musical instrument samples and drum sounds. The performance of the proposed method was compared with independent subspace analysis and basic nonnegative matrix factorization, which are based on the same linear model. According to these simulations, the proposed method enables a better separation quality than the previous algorithms. Especially, the temporal continuity criterion improved the detection of pitched musical sounds. The sparseness criterion did not produce significant improvements

Monaural Sound Source Separation by Nonnegative Matrix Factorization With Temporal Continuity and Sparseness Criteria

We present a methodology for analyzing polyphonic musical passages comprised of notes that exhibit a harmonically fixed spectral profile (such as piano notes). Taking advantage of this unique note structure, we can model the audio content of the musical passage by a linear basis transform and use non-negative matrix decomposition methods to estimate the spectral profile and the temporal information of every note. This approach results in a very simple and compact system that is not knowledge-based, but rather learns notes by observation.

/pdf/non-negative-matrix-factorization-for-polyphonic-music-4nqml6shbr.pdf

Non-negative matrix factorization for polyphonic music transcription

Note onset detection and localization is useful in a number of analysis and indexing techniques for musical signals. The usual way to detect onsets is to look for "transient" regions in the signal, a notion that leads to many definitions: a sudden burst of energy, a change in the short-time spectrum of the signal or in the statistical properties, etc. The goal of this paper is to review, categorize, and compare some of the most commonly used techniques for onset detection, and to present possible enhancements. We discuss methods based on the use of explicitly predefined signal features: the signal's amplitude envelope, spectral magnitudes and phases, time-frequency representations; and methods based on probabilistic signal models: model-based change point detection, surprise signals, etc. Using a choice of test cases, we provide some guidelines for choosing the appropriate method for a given application.

/pdf/a-tutorial-on-onset-detection-in-music-signals-14ctpy0rf7.pdf

A tutorial on onset detection in music signals

In this paper, we overview some Semantic Web technologies and describe the Music Ontology: a formal framework for dealing with music-related information on the Semantic Web, including editorial, cultural and acoustic information. We detail how this ontology can act as a grounding for more domain-specific knowledge representation. In addition, we describe current projects involving the Music Ontology and interlinked repositories of musicrelated knowledge.

The Music Ontology.

In this paper we propose a text represention for musical chord symbols that is simple and intuitive for musically trained individuals to write and understand, yet highly structured and unambiguous to parse with computer programs. When designing feature extraction algorithms, it is important to have a hand annotated test set providing a ground truth to compare results against. Hand labelling of chords in music files is a long and arduous task and there is no standard annotation methodology, which causes difficulties sharing with existing annotations. In this paper we address this problem by defining a rigid, contextindependent syntax for representing chord symbols in text, supported with a new database of annotations using this system.

/pdf/symbolic-representation-of-musical-chords-a-proposed-syntax-23nf777sgw.pdf

Symbolic Representation of Musical Chords: A Proposed Syntax for Text Annotations.

We present a system for adaptive spectral basis decomposition that learns to identify independent spectral features given a sequence of short-term Fourier spectra When applied to recordings of polyphonic piano music, the individual notes are identified as salient features, and hence each short-term spectrum is decomposed into a sum of note spectra; the resulting encoding can be used as a basis for polyphonic transcription The system is based on a probabilistic model equivalent to a form of noisy independent component analysis (ICA) or sparse coding with non-negativity constraints We introduce a novel modification to this model that recognises that a short-term Fourier spectrum can be thought of as a noisy realisation of the power spectral density of an underlying Gaussian process, where the noise is essentially multiplicative and non-Gaussian Results are presented for an analysis of a live recording of polyphonic piano music

/pdf/polyphonic-music-transcription-by-non-negative-sparse-coding-1m35txmfkg.pdf

Polyphonic music transcription by non-negative sparse coding of power spectra

Most sound scenes result from the superposition of several sources, which can be separately perceived and analyzed by human listeners Source separation aims to provide machine listeners with similar skills by extracting the sounds of individual sources from a given scene Existing separation systems operate either by emulating the human auditory system or by inferring the parameters of probabilistic sound models In this chapter, the authors focus on the latter approach and provide a joint overview of established and recent models, including independent component analysis, local time-frequency models and spectral template-based models They show that most models are instances of one of the following two general paradigms: linear modeling or variance modeling They compare the merits of either paradigm and report objective performance figures They also,conclude by discussing promising combinations of probabilistic priors and inference algorithms that could form the basis of future state-of-the-art systems

/pdf/probabilistic-modeling-paradigms-for-audio-source-separation-26g3zqv5ok.pdf

Samer A. Abdallah

Papers

A tutorial on onset detection in music signals

The Music Ontology.

Symbolic Representation of Musical Chords: A Proposed Syntax for Text Annotations.

Polyphonic music transcription by non-negative sparse coding of power spectra

Probabilistic Modeling Paradigms for Audio Source Separation