Melody recognition with learned edit distances

In a music recognition task, the classification of a new melody is often achieved by looking for the closest piece in a set of already known prototypes. The definition of a relevant similarity measure becomes then a crucial point. So far, the edit distance approach with a-priori fixed operation costs has been one of the most used to accomplish the task. In this paper, the application of a probabilistic learning model to both string and tree edit distances is proposed and is compared to a genetic algorithm cost fitting approach. The results show that both learning models outperform fixed-costs systems, and that the probabilistic approach is able to describe consistently the underlying melodic similarity model.This work was funded by the French ANR Marmota project, the Spanish PROSEMUS project (TIN2006-14932-C02), the research programme Consolider Ingenio 2010 (MIPRCV, CSD2007-00018), and the Pascal Network of Excellence

Learning Constrained Edit State Machines

International audienceLearning the parameters of the edit distance has been increasingly studied during the past few years to improve the assessment of similarities between structured data, such as strings, trees or graphs. Often based on the optimization of the likelihood of pairs of data, the learned models usually take the form of probabilistic state machines, such as pair-Hidden Markov Models (pair-HMM), stochastic transducers, or probabilistic deterministic automata. Although the use of such models has lead to significant improvements of edit distance-based classification tasks, a new challenge has appeared on the horizon: How integrating background knowledge during the learning process? This is the subject matter of this paper in the case of (input,output) pairs of strings. We present a generalization of the pair-HMM in the form of a constrained state machine, where a transition between two states is driven by constraints fulfilled on the input string. Experimental results are provided on a task in molecular biology, aiming to detect transcription factor binding sites

Space-efficient Feature Maps for String Alignment Kernels

String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly due to their quadratic computation complexity in the number of input strings, which limits large-scale applications in practice. We address this need by presenting the first approximation for string alignment kernels, which we call space-efficient feature maps for edit distance with moves (SFMEDM), by leveraging a metric embedding named edit sensitive parsing (ESP) and feature maps (FMs) of random Fourier features (RFFs) for large-scale string analyses. The original FMs for RFFs consume a huge amount of memory proportional to the dimension d of input vectors and the dimension D of output vectors, which prohibits its large-scale applications. We present novel space-efficient feature maps (SFMs) of RFFs for a space reduction from O(dD) of the original FMs to O(d) of SFMs with a theoretical guarantee with respect to concentration bounds. We experimentally test SFMEDM on its ability to learn SVM for large-scale string classifications with various massive string data, and we demonstrate the superior performance of SFMEDM with respect to prediction accuracy, scalability and computation efficiency.Comment: Full version for ICDM'19 pape

Tree Edit Distance Learning via Adaptive Symbol Embeddings

Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as molecular structures, abstract syntax trees of computer programs, or syntax trees of natural language, by learning the cost function of an edit distance, i.e. the costs of replacing, deleting, or inserting nodes in a tree. However, learning such costs directly may yield an edit distance which violates metric axioms, is challenging to interpret, and may not generalize well. In this contribution, we propose a novel metric learning approach for trees which we call embedding edit distance learning (BEDL) and which learns an edit distance indirectly by embedding the tree nodes as vectors, such that the Euclidean distance between those vectors supports class discrimination. We learn such embeddings by reducing the distance to prototypical trees from the same class and increasing the distance to prototypical trees from different classes. In our experiments, we show that BEDL improves upon the state-of-the-art in metric learning for trees on six benchmark data sets, ranging from computer science over biomedical data to a natural-language processing data set containing over 300,000 nodes.Comment: Paper at the International Conference of Machine Learning (2018), 2018-07-10 to 2018-07-15 in Stockholm, Swede

Learning discriminative tree edit similarities for linear classification — Application to melody recognition

Similarity functions are a fundamental component of many learning algorithms. When dealing with string or tree-structured data, measures based on the edit distance are widely used, and there exist a few methods for learning them from data. In this context, we recently proposed GESL (Bellet et al., 2012 [3]), an approach to string edit similarity learning based on loss minimization which offers theoretical guarantees as to the generalization ability and discriminative power of the learned similarities. In this paper, we argue that GESL, which has been originally dedicated to deal with strings, can be extended to trees and lead to powerful and competitive similarities. We illustrate this claim on a music recognition task, namely melody classification, where each piece is represented as a tree modeling its structure as well as rhythm and pitch information. The results show that GESL outperforms standard as well as probabilistically-learned edit distances and that it is able to describe consistently the underlying melodic similarity model.This work was supported by a grant from CPER Nord-Pas de Calais/FEDER DATA Advanced data science and technologies 2015-2020 and the Spanish Ministerio de Economía y Competitividad project TIMuL (No. TIN2013--48152--C2--1--R supported by UE FEDER funds)

Graph edit distance from spectral seriation

This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graph-matching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems