Polar Polytopes and Recovery of Sparse Representations

Suppose we have a signal y which we wish to represent using a linear combination of a number of basis atoms a_i, y=sum_i x_i a_i = Ax. The problem of finding the minimum L0 norm representation for y is a hard problem. The Basis Pursuit (BP) approach proposes to find the minimum L1 norm representation instead, which corresponds to a linear program (LP) that can be solved using modern LP techniques, and several recent authors have given conditions for the BP (minimum L1 norm) and sparse (minimum L0 solutions) representations to be identical. In this paper, we explore this sparse representation problem} using the geometry of convex polytopes, as recently introduced into the field by Donoho. By considering the dual LP we find that the so-called polar polytope P of the centrally-symmetric polytope P whose vertices are the atom pairs +-a_i is particularly helpful in providing us with geometrical insight into optimality conditions given by Fuchs and Tropp for non-unit-norm atom sets. In exploring this geometry we are able to tighten some of these earlier results, showing for example that the Fuchs condition is both necessary and sufficient for L1-unique-optimality, and that there are situations where Orthogonal Matching Pursuit (OMP) can eventually find all L1-unique-optimal solutions with m nonzeros even if ERC fails for m, if allowed to run for more than m steps

An open dataset for research on audio field recording archives: freefield1010

We introduce a free and open dataset of 7690 audio clips sampled from the field-recording tag in the Freesound audio archive. The dataset is designed for use in research related to data mining in audio archives of field recordings / soundscapes. Audio is standardised, and audio and metadata are Creative Commons licensed. We describe the data preparation process, characterise the dataset descriptively, and illustrate its use through an auto-tagging experiment

A measure of statistical complexity based on predictive information

We introduce an information theoretic measure of statistical structure, called 'binding information', for sets of random variables, and compare it with several previously proposed measures including excess entropy, Bialek et al.'s predictive information, and the multi-information. We derive some of the properties of the binding information, particularly in relation to the multi-information, and show that, for finite sets of binary random variables, the processes which maximises binding information are the 'parity' processes. Finally we discuss some of the implications this has for the use of the binding information as a measure of complexity.Comment: 4 pages, 3 figure

Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras

We explore the use of geometrical methods to tackle the non-negative independent component analysis (non-negative ICA) problem, without assuming the reader has an existing background in differential geometry. We concentrate on methods that achieve this by minimizing a cost function over the space of orthogonal matrices. We introduce the idea of the manifold and Lie group SO(n) of special orthogonal matrices that we wish to search over, and explain how this is related to the Lie algebra so(n) of skew-symmetric matrices. We describe how familiar optimization methods such as steepest-descent and conjugate gradients can be transformed into this Lie group setting, and how the Newton update step has an alternative Fourier version in SO(n). Finally we introduce the concept of a toral subgroup generated by a particular element of the Lie group or Lie algebra, and explore how this commutative subgroup might be used to simplify searches on our constraint surface. No proofs are presented in this article

Raw Multi-Channel Audio Source Separation using Multi-Resolution Convolutional Auto-Encoders

Supervised multi-channel audio source separation requires extracting useful spectral, temporal, and spatial features from the mixed signals. The success of many existing systems is therefore largely dependent on the choice of features used for training. In this work, we introduce a novel multi-channel, multi-resolution convolutional auto-encoder neural network that works on raw time-domain signals to determine appropriate multi-resolution features for separating the singing-voice from stereo music. Our experimental results show that the proposed method can achieve multi-channel audio source separation without the need for hand-crafted features or any pre- or post-processing

Audio Set classification with attention model: A probabilistic perspective

This paper investigates the classification of the Audio Set dataset. Audio Set is a large scale weakly labelled dataset of sound clips. Previous work used multiple instance learning (MIL) to classify weakly labelled data. In MIL, a bag consists of several instances, and a bag is labelled positive if at least one instances in the audio clip is positive. A bag is labelled negative if all the instances in the bag are negative. We propose an attention model to tackle the MIL problem and explain this attention model from a novel probabilistic perspective. We define a probability space on each bag, where each instance in the bag has a trainable probability measure for each class. Then the classification of a bag is the expectation of the classification output of the instances in the bag with respect to the learned probability measure. Experimental results show that our proposed attention model modeled by fully connected deep neural network obtains mAP of 0.327 on Audio Set dataset, outperforming the Google's baseline of 0.314 and recurrent neural network of 0.325.Comment: Accepted by ICASSP 201

Deep Remix: Remixing Musical Mixtures Using a Convolutional Deep Neural Network

Audio source separation is a difficult machine learning problem and performance is measured by comparing extracted signals with the component source signals. However, if separation is motivated by the ultimate goal of re-mixing then complete separation is not necessary and hence separation difficulty and separation quality are dependent on the nature of the re-mix. Here, we use a convolutional deep neural network (DNN), trained to estimate 'ideal' binary masks for separating voice from music, to perform re-mixing of the vocal balance by operating directly on the individual magnitude components of the musical mixture spectrogram. Our results demonstrate that small changes in vocal gain may be applied with very little distortion to the ultimate re-mix. Our method may be useful for re-mixing existing mixes

Surrey-cvssp system for DCASE2017 challenge task4

In this technique report, we present a bunch of methods for the task 4 of Detection and Classification of Acoustic Scenes and Events 2017 (DCASE2017) challenge. This task evaluates systems for the large-scale detection of sound events using weakly labeled training data. The data are YouTube video excerpts focusing on transportation and warnings due to their industry applications. There are two tasks, audio tagging and sound event detection from weakly labeled data. Convolutional neural network (CNN) and gated recurrent unit (GRU) based recurrent neural network (RNN) are adopted as our basic framework. We proposed a learnable gating activation function for selecting informative local features. Attention-based scheme is used for localizing the specific events in a weakly-supervised mode. A new batch-level balancing strategy is also proposed to tackle the data unbalancing problem. Fusion of posteriors from different systems are found effective to improve the performance. In a summary, we get 61% F-value for the audio tagging subtask and 0.73 error rate (ER) for the sound event detection subtask on the development set. While the official multilayer perceptron (MLP) based baseline just obtained 13.1% F-value for the audio tagging and 1.02 for the sound event detection.Comment: DCASE2017 challenge ranked 1st system, task4, tech repor