Mark D. Plumbley

Algorithms for nonnegative independent component analysis

We consider the task of solving the independent component analysis (ICA) problem x=As given observations x, with a constraint of nonnegativity of the source random vector s. We refer to this as nonnegative independent component analysis and we consider methods for solving this task. For independent sources with nonzero probability density function (pdf) p(s) down to s=0 it is sufficient to find the orthonormal rotation y=Wz of prewhitened sources z=Vx, which minimizes the mean squared error of the reconstruction of z from the rectified version y/sup +/ of y. We suggest some algorithms which perform this, both based on a nonlinear principal component analysis (PCA) approach and on a geodesic search method driven by differential geometry considerations. We demonstrate the operation of these algorithms on an image separation problem, which shows in particular the fast convergence of the rotation and geodesic methods and apply the approach to a musical audio analysis task.

Sparse Representations in Audio and Music: From Coding to Source Separation

Sparse representations have proved a powerful tool in the analysis and processing of audio signals and already lie at the heart of popular coding standards such as MP3 and Dolby AAC. In this paper we give an overview of a number of current and emerging applications of sparse representations in areas from audio coding, audio enhancement and music transcription to blind source separation solutions that can solve the ¿cocktail party problem.¿ In each case we will show how the prior assumption that the audio signals are approximately sparse in some time-frequency representation allows us to address the associated signal processing task.

Context-Dependent Beat Tracking of Musical Audio

We present a simple and efficient method for beat tracking of musical audio. With the aim of replicating the human ability of tapping in time to music, we formulate our approach using a two state model. The first state performs tempo induction and tracks tempo changes, while the second maintains contextual continuity within a single tempo hypothesis. Beat times are recovered by passing the output of an onset detection function through adaptively weighted comb filterbank matrices to separately identify the beat period and alignment. We evaluate our beat tracker both in terms of the accuracy of estimated beat locations and computational complexity. In a direct comparison with existing algorithms, we demonstrate equivalent performance at significantly reduced computational cost

Detection and Classification of Acoustic Scenes and Events

For intelligent systems to make best use of the audio modality, it is important that they can recognize not just speech and music, which have been researched as specific tasks, but also general sounds in everyday environments. To stimulate research in this field we conducted a public research challenge: the IEEE Audio and Acoustic Signal Processing Technical Committee challenge on Detection and Classification of Acoustic Scenes and Events (DCASE). In this paper, we report on the state of the art in automatically classifying audio scenes, and automatically detecting and classifying audio events. We survey prior work as well as the state of the art represented by the submissions to the challenge from various research groups. We also provide detail on the organization of the challenge, so that our experience as challenge hosts may be useful to those organizing challenges in similar domains. We created new audio datasets and baseline systems for the challenge; these, as well as some submitted systems, are publicly available under open licenses, to serve as benchmarks for further research in general-purpose machine listening.

Audio Inpainting

We propose the audio inpainting framework that recovers portions of audio data distorted due to impairments such as impulsive noise, clipping, and packet loss. In this framework, the distorted data are treated as missing and their location is assumed to be known. The signal is decomposed into overlapping time-domain frames and the restoration problem is then formulated as an inverse problem per audio frame. Sparse representation modeling is employed per frame, and each inverse problem is solved using the Orthogonal Matching Pursuit algorithm together with a discrete cosine or a Gabor dictionary. The Signal-to-Noise Ratio performance of this algorithm is shown to be comparable or better than state-of-the-art methods when blocks of samples of variable durations are missing. We also demonstrate that the size of the block of missing samples, rather than the overall number of missing samples, is a crucial parameter for high quality signal restoration. We further introduce a constrained Matching Pursuit approach for the special case of audio declipping that exploits the sign pattern of clipped audio samples and their maximal absolute value, as well as allowing the user to specify the maximum amplitude of the signal. This approach is shown to outperform state-of-the-art and commercially available methods for audio declipping in terms of Signal-to-Noise Ratio.

Theorems on Positive Data: On the Uniqueness of NMF

We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.

Conditions for nonnegative independent component analysis

We consider the noiseless linear independent component analysis problem, in the case where the hidden sources s are nonnegative. We assume that the random variables si are well grounded in that they have a nonvanishing probability density function (PDF) in the (positive) neighborhood of zero. For an orthonormal rotation y=Wx of prewhitened observations x=QAs, under certain reasonable conditions we show that y is a permutation of the s (apart from a scaling factor) if and only if y is nonnegative with probability 1. We suggest that this may enable the construction of practical learning algorithms, particularly for sparse nonnegative sources.

Automatic music transcription and audio source separation

In this article, we give an overview of a range of approaches to the analysis and separation of musical audio. In particular, we consider the problems of automatic music transcription and audio source separation, which are of particular interest to our group. Monophonic music transcription, where a single note is present at one time, can be tackled using an autocorrelation-based method. For polyphonic music transcription, with several notes at any time, other approaches can be used, such as a blackboard model or a multiple-cause/sparse coding method. The latter is based on ideas and methods related to independent component analysis (ICA), a method for sound source separation.

Automatic large-scale classification of bird sounds is strongly improved by unsupervised feature learning.

Automatic species classification of birds from their sound is a computational tool of increasing importance in ecology, conservation monitoring and vocal communication studies. To make classification useful in practice, it is crucial to improve its accuracy while ensuring that it can run at big data scales. Many approaches use acoustic measures based on spectrogram-type data, such as the Mel-frequency cepstral coefficient (MFCC) features which represent a manually-designed summary of spectral information. However, recent work in machine learning has demonstrated that features learnt automatically from data can often outperform manually-designed feature transforms. Feature learning can be performed at large scale and “unsupervised”, meaning it requires no manual data labelling, yet it can improve performance on “supervised” tasks such as classification. In this work we introduce a technique for feature learning from large volumes of bird sound recordings, inspired by techniques that have proven useful in other domains. We experimentally compare twelve different feature representations derived from the Mel spectrum (of which six use this technique), using four large and diverse databases of bird vocalisations, classified using a random forest classifier. We demonstrate that in our classification tasks, MFCCs can often lead to worse performance than the raw Mel spectral data from which they are derived. Conversely, we demonstrate that unsupervised feature learning provides a substantial boost over MFCCs and Mel spectra without adding computational complexity after the model has been trained. The boost is particularly notable for single-label classification tasks at large scale. The spectro-temporal activations learned through our procedure resemble spectro-temporal receptive fields calculated from avian primary auditory forebrain. However, for one of our datasets, which contains substantial audio data but few annotations, increased performance is not discernible. We study the interaction between dataset characteristics and choice of feature representation through further empirical analysis.

Fast Dictionary Learning for Sparse Representations of Speech Signals

For dictionary-based decompositions of certain types, it has been observed that there might be a link between sparsity in the dictionary and sparsity in the decomposition. Sparsity in the dictionary has also been associated with the derivation of fast and efficient dictionary learning algorithms. Therefore, in this paper we present a greedy adaptive dictionary learning algorithm that sets out to find sparse atoms for speech signals. The algorithm learns the dictionary atoms on data frames taken from a speech signal. It iteratively extracts the data frame with minimum sparsity index, and adds this to the dictionary matrix. The contribution of this atom to the data frames is then removed, and the process is repeated. The algorithm is found to yield a sparse signal decomposition, supporting the hypothesis of a link between sparsity in the decomposition and dictionary. The algorithm is applied to the problem of speech representation and speech denoising, and its performance is compared to other existing methods. The method is shown to find dictionary atoms that are sparser than their time-domain waveform, and also to result in a sparser speech representation. In the presence of noise, the algorithm is found to have similar performance to the well established principal component analysis.