Harmonic Analysis with Probabilistic Graphical Models

A technique for harmonic analysis is presented that partitions a piece of music into contiguous regions and labels each with the key, mode, and functional chord, e.g. tonic, dominant, etc. The analysis is performed with a hidden Markov model and, as such, is automatically trainable from generic MIDI files and capable of finding the globally optimal harmonic labeling. Experiments are presented highlighting our current state of the art. An extension to a more complex probabilistic graphical model is outlined in which music is modeled as a collection of voices that evolve independently given the harmonic progression

Automatic Synchronization of Multi-User Photo Galleries

In this paper we address the issue of photo galleries synchronization, where pictures related to the same event are collected by different users. Existing solutions to address the problem are usually based on unrealistic assumptions, like time consistency across photo galleries, and often heavily rely on heuristics, limiting therefore the applicability to real-world scenarios. We propose a solution that achieves better generalization performance for the synchronization task compared to the available literature. The method is characterized by three stages: at first, deep convolutional neural network features are used to assess the visual similarity among the photos; then, pairs of similar photos are detected across different galleries and used to construct a graph; eventually, a probabilistic graphical model is used to estimate the temporal offset of each pair of galleries, by traversing the minimum spanning tree extracted from this graph. The experimental evaluation is conducted on four publicly available datasets covering different types of events, demonstrating the strength of our proposed method. A thorough discussion of the obtained results is provided for a critical assessment of the quality in synchronization.Comment: ACCEPTED to IEEE Transactions on Multimedi

Joint Multi-Pitch Detection Using Harmonic Envelope Estimation for Polyphonic Music Transcription

In this paper, a method for automatic transcription of music signals based on joint multiple-F0 estimation is proposed. As a time-frequency representation, the constant-Q resonator time-frequency image is employed, while a novel noise suppression technique based on pink noise assumption is applied in a preprocessing step. In the multiple-F0 estimation stage, the optimal tuning and inharmonicity parameters are computed and a salience function is proposed in order to select pitch candidates. For each pitch candidate combination, an overlapping partial treatment procedure is used, which is based on a novel spectral envelope estimation procedure for the log-frequency domain, in order to compute the harmonic envelope of candidate pitches. In order to select the optimal pitch combination for each time frame, a score function is proposed which combines spectral and temporal characteristics of the candidate pitches and also aims to suppress harmonic errors. For postprocessing, hidden Markov models (HMMs) and conditional random fields (CRFs) trained on MIDI data are employed, in order to boost transcription accuracy. The system was trained on isolated piano sounds from the MAPS database and was tested on classic and jazz recordings from the RWC database, as well as on recordings from a Disklavier piano. A comparison with several state-of-the-art systems is provided using a variety of error metrics, where encouraging results are indicated

Learning Laplacian Matrix in Smooth Graph Signal Representations

The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful graph is not always readily available from the data, nor easy to define depending on the application domain. In particular, it is often desirable in graph signal processing applications that a graph is chosen such that the data admit certain regularity or smoothness on the graph. In this paper, we address the problem of learning graph Laplacians, which is equivalent to learning graph topologies, such that the input data form graph signals with smooth variations on the resulting topology. To this end, we adopt a factor analysis model for the graph signals and impose a Gaussian probabilistic prior on the latent variables that control these signals. We show that the Gaussian prior leads to an efficient representation that favors the smoothness property of the graph signals. We then propose an algorithm for learning graphs that enforces such property and is based on minimizing the variations of the signals on the learned graph. Experiments on both synthetic and real world data demonstrate that the proposed graph learning framework can efficiently infer meaningful graph topologies from signal observations under the smoothness prior

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page