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.

/pdf/learning-overcomplete-representations-42fsd31woo.pdf

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

We consider the problem of convolutive blind source separation (BSS). This is usually tackled through either multichannel blind deconvolution (MCBD) or using frequency-domain independent component analysis (FD-ICA). Here, instead of using a fixed time or frequency basis to solve the convolutive blind source separation problem we propose learning an adaptive spatial–temporal transform directly from the speech mixture. Most of the learnt space–time basis vectors exhibit properties suggesting that they represent the components of individual sources as they are observed at the microphones. Source separation can then be performed by projection onto the appropriate group of basis vectors.We go on to show that both MCBD and FD-ICA techniques can be considered as particular forms of this general separation method with certain constraints. While our space–time approach involves considerable additional computation it is also enlightening as to the nature of the problem and has the potential for performance benefits in terms of separation and de-noising.

Blind Source Separation using Space–Time Independent Component Analysis

In the transition from traditional to digital musicology, large scale music data are increasingly becoming available which require research methods that work on the collection level and at scale. In the Digital Music Lab (DML) project, a software system has been developed that provides large-scale analysis of music audio with an interactive interface. The DML system includes distributed processing of audio and other music data, remote analysis of copyright-restricted data, logical inference on the extracted information and metadata, and visual web-based interfaces for exploring and querying music collections. A system prototype has been set up in collaboration with the British Library and I Like Music Ltd, which has been used to analyse a diverse corpus of over 250,000 music recordings. In this paper we describe the system requirements, architecture, components, and data sources, explaining their interaction. Use cases and applications with initial evaluations of the proposed system are also reported.

Digital Music Lab - A Framework for Analysing Big Music Data (abstract only)

In this paper, we describe a knowledge management framework that addresses the needs of multimedia analysis projects and provides a basis for information retrieval systems. The framework uses Semantic Web technologies to provide a shared knowledge environment, and active Knowledge Machines, wrapping multimedia processing tools, to exploit and/or export knowledge to this environment. This framework is able to handle a wide range of use cases, from an enhanced workspace for researchers to end-user information access. As an illustration of how the proposed framework can be used, we present a case study of music analysis.

A scalable framework for multimedia knowledge management

/pdf/a-scalable-framework-for-multimedia-knowledge-management-gystz3qf4a.pdf

Samer A. Abdallah

Papers

Blind Source Separation using Space–Time Independent Component Analysis

Digital Music Lab - A Framework for Analysing Big Music Data (abstract only)

A scalable framework for multimedia knowledge management

A scalable framework for multimedia knowledge management

Model-based audio source separation