We investigate the use of the Riemannian optimization method over the flag manifold in subspace ICA problems such as independent subspace analysis (ISA) and complex ICA. In the ISA experiment, we use the Riemannian approach over the flag manifold together with an MCMC method to overcome the problem of local minima of the ISA cost function. Experiments demonstrate the effectiveness of both Riemannian methods - simple geodesic gradient descent and hybrid geodesic gradient descent, compared with the ordinary gradient method.

This paper describes a method for automatically segmenting and labelling sections in recordings of musical audio. We incorporate the user's expectations for segment duration as an explicit prior probability distribution in a Bayesian framework, and demonstrate experimentally that this method can produce accurate labelled segmentations for popular music

We investigate a data-driven approach to the analysis and transcription of polyphonic music, using a probabilistic model which is able to find sparse linear decompositions of a sequence of short-term Fourier spectra. The resulting system represents each input spectrum as a weighted sum of a small number of "atomic" spectra chosen from a larger dictionary; this dictionary is, in turn, learned from the data in such a way as to represent the given training set in an (information theoretically) efficient way. When exposed to examples of polyphonic music, most of the dictionary elements take on the spectral characteristics of individual notes in the music, so that the sparse decomposition can be used to identify the notes in a polyphonic mixture. Our approach differs from other methods of polyphonic analysis based on spectral decomposition by combining all of the following: (a) a formulation in terms of an explicitly given probabilistic model, in which the process estimating which notes are present corresponds naturally with the inference of latent variables in the model; (b) a particularly simple generative model, motivated by very general considerations about efficient coding, that makes very few assumptions about the musical origins of the signals being processed; and (c) the ability to learn a dictionary of atomic spectra (most of which converge to harmonic spectral profiles associated with specific notes) from polyphonic examples alone-no separate training on monophonic examples is required.

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.

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.