# Chord Recognition Based on Temporal Correlation Support Vector Machine
## 1 Introduction  
A musical chord can be defined as a set of notes played simultaneously. A succession of chords over time forms the harmony core in a piece of music. Hence, the compact representation of the overall harmonic content and structure of a song often requires labeling every chord in the song. Chord recognition has been applied in many applications such as the segmentation of pieces into characteristic segments, the selection of similar pieces, and the semantic analysis of music [1; 2]. With its many applications, automatic chord recognition has been one of the main fields of interest in musical information retrieval in the last few years.  
The basic chord recognition system has two main steps: feature extraction and chord classification. In the first step, the features used in chord recognition are typically variants of the pitch class profile (PCP) introduced by [PERSON] (1999) [1]. Many publications have improved PCP features for chord recognition by addressing potentially negative influences such as percussion [2], mistuning [3; 4], harmonics [5; 6; 7], or timbre dependency [5; 8]. In particular, harmonic contents are abundant in both musical instrument sounds and the human singing voice. However, harmonic patterns in instrument sounds are more regular compared with the singing voice, which often includes ornamental features such as vibrato that lead to significant deviations of the frequency of partials from perfectlyharmonic [9]. To attenuate the effect of the singing voice and consider the temporal correlations of music, we separate the singing voice from the accompaniment before obtaining the PCP.  
Chord classification is computed once the feature has been extracted. Modeling techniques typically use template-fitting methods [1; 3; 10; 11; 12; 13], the hidden Markov model (HMM) [14; 15; 16; 17; 18; 19; 20], and dynamic Bayesian networks [21; 22] for this recognition process. The template-based method has some advantages, including the fact that it does not require annotated data and has a low computational time. However, its drawbacks include the problem of creating a model of templates of chroma vectors and the selection of a distance measure. The HMM method is a statistical model and its parameter estimation requires substantial training data. The recognition rate of the HMM method is typically relatively high, but it only considers the role of positive training samples without addressing the impact of negative training samples, thereby greatly limiting its discriminative ability. The support vector machine (SVM) method can achieve a high recognition rate, but encounters challenges in the presence of cross-aliasing that cannot be accurately judged. The main difference between HMM and SVM is in the principle of risk minimization [23]. HMM uses empirical risk minimization, which is the simplest induction principle. In contrast, SVM uses structural risk minimization as its induction principle. The difference in risk minimization leads to the better generalization performance of SVM compared with HMM [24]. We present a new method for chord estimation based on a hybrid model of HMM and SVM.  
The remainder of this paper is organized as follows: Section 2 reviews related chord estimation work; Section 3 describes our PCP feature vector construction method; Section 4 explains our approach; Section 5 displays the results on the MIREX'09 (Music Information Retrieval Evaluation eXchange) dataset and a provides a comparison with other methods; and Section 6 concludes our work and suggests directions for future work.