This paper presents a new method for a quick similarity-based search through long unlabeled audio streams to detect and locate audio clips provided by users. The method involves feature-dimension reduction based on a piecewise linear representation of a sequential feature trajectory extracted from a long audio stream. Two techniques enable us to obtain a piecewise linear representation: the dynamic segmentation of feature trajectories and the segment-based Karhunen-Loeve (KL) transform. The proposed search method guarantees the same search results as the search method without the proposed feature-dimension reduction method in principle. Experimental results indicate significant improvements in search speed. For example, the proposed method reduced the total search time to approximately 1 12 that of previous methods and detected queries in approximately 0.3 s from a 200-h audio database.
Dimensionality reduction methods for time-series signals are categorized into two types: temporal dimensionality reduction , namely dimensionality reduction along the temporal axis (e.g. feature sampling), and spatial dimensionality reduction , namely the dimensionality reduction of each multi-dimensional feature sample. Keogh @cite_3 @cite_9 and Wang @cite_27 have introduced temporal dimensionality reduction into waveform signal retrieval. Their framework considers the waveform itself as a feature for detecting similar signal segments. That is why they mainly focused on temporal dimensionality reduction. When considering audio fingerprinting, however, we handle sequences of high-dimensional features that are necessary to identify various kinds of audio segments. Thus, both spatial and temporal dimensionality reduction are required. To this end, our method mainly focuses on spatial dimensionality reduction. We also incorporate a temporal dimensionality reduction technique inspired by the method of @cite_9 , which is described in Section .
@cite_27 @cite_9 @cite_3
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Dimensionality reduction in multivariate time series analysis has broad applications, ranging from financial data analysis to biomedical research. However, high levels of ambient noise and various interferences result in nonstationary signals, which may lead to inefficient performance of conventional methods. In this paper, we propose a nonlinear dimensionality reduction framework using diffusion maps on a learned statistical manifold, which gives rise to the construction of a low-dimensional representation of the high-dimensional nonstationary time series. We show that diffusion maps, with affinity kernels based on the Kullback-Leibler divergence between the local statistics of samples, allow for efficient approximation of pairwise geodesic distances. To construct the statistical manifold, we estimate time-evolving parametric distributions by designing a family of Bayesian generative models. The proposed framework can be applied to problems in which the time-evolving distributions (of temporally localized data), rather than the samples themselves, are driven by a low-dimensional underlying process. We provide efficient parameter estimation and dimensionality reduction methodologies, and apply them to two applications: music analysis and epileptic-seizure prediction. Author-HighlightsWe build a class of Bayesian models to learn the evolving statistics of time series.We construct diffusion maps based on the time-evolving distributional information.The proposed method recovers the underlying process controlling the time series.The proposed framework is applied to the analysis of music and icEEG recordings. The problem of similarity search in large time series databases has attracted much attention recently. It is a non-trivial problem because of the inherent high dimensionality of the data. The most promising solutions involve first performing dimensionality reduction on the data, and then indexing the reduced data with a spatial access method. Three major dimensionality reduction techniques have been proposed: Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), and more recently the Discrete Wavelet Transform (DWT). In this work we introduce a new dimensionality reduction technique which we call Piecewise Aggregate Approximation (PAA). We theoretically and empirically compare it to the other techniques and demonstrate its superiority. In addition to being competitive with or faster than the other methods, our approach has numerous other advantages. It is simple to understand and to implement, it allows more flexible distance measures, including weighted Euclidean queries, and the index can be built in linear time. Time series stored as feature vectors can be indexed by multidimensional index trees like R-Trees for fast retrieval. Due to the dimensionality curse problem, transformations are applied to time series to reduce the number of dimensions of the feature vectors. Different transformations like Discrete Fourier Transform (DFT) Discrete Wavelet Transform (DWT), Karhunen-Loeve (KL) transform or Singular Value Decomposition (SVD) can be applied. While the use of DFT and K-L transform or SVD have been studied on the literature, to our knowledge, there is no in-depth study on the application of DWT. In this paper we propose to use Haar Wavelet Transform for time series indexing. The major contributions are: (1) we show that Euclidean distance is preserved in the Haar transformed domain and no false dismissal will occur, (2) we show that Haar transform can outperform DFT through experiments, (3) a new similarity model is suggested to accommodate vertical shift of time series, and (4) a two-phase method is proposed for efficient n-nearest neighbor query in time series databases. While approaches based on bags of features excel at low-level action classification, they are ill-suited for recognizing complex events in video, where concept-based temporal representations currently dominate. This paper proposes a novel representation that captures the temporal dynamics of windowed mid-level concept detectors in order to improve complex event recognition. We first express each video as an ordered vector time series, where each time step consists of the vector formed from the concatenated confidences of the pre-trained concept detectors. We hypothesize that the dynamics of time series for different instances from the same event class, as captured by simple linear dynamical system (LDS) models, are likely to be similar even if the instances differ in terms of low-level visual features. We propose a two-part representation composed of fusing: (1) a singular value decomposition of block Hankel matrices (SSID-S) and (2) a harmonic signature (HS) computed from the corresponding eigen-dynamics matrix. The proposed method offers several benefits over alternate approaches: our approach is straightforward to implement, directly employs existing concept detectors and can be plugged into linear classification frameworks. Results on standard datasets such as NIST's TRECVID Multimedia Event Detection task demonstrate the improved accuracy of the proposed method.