text: 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.
  @cite_27: Fast retrieval of time series in terms of their contents is important in many application domains. This paper studies database techniques supporting fast searches for time series whose contents are similar to what users specify. The content types studied include shapes, trends, cyclic components, autocorrelation functions and partial autocorrelation functions. Due to the complex nature of the similarity searches involving such contents, traditional database techniques usually cannot provide a fast response when the involved data volume is high. This paper proposes to answer such content-based queries using appropriate approximation techniques. The paper then introduces two specific approximation methods, one is wavelet based and the other line-fitting based. Finally, the paper reports some experiments conducted on a stock price data set as well as a synthesized random walk data set, and shows that both approximation methods significantly reduce the query processing time without introducing intolerable errors.
  @cite_9: 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.
  @cite_3: Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions involve performing dimensionality reduction on the data, then indexing the reduced data with a multidimensional index structure. Many dimensionality reduction techniques have been proposed, including Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), and the Discrete Wavelet Transform (DWT). In this work we introduce a new dimensionality reduction technique which we call Adaptive Piecewise Constant Approximation (APCA). While previous techniques (e.g., SVD, DFT and DWT) choose a common representation for all the items in the database that minimizes the global reconstruction error, APCA approximates each time series by a set of constant value segments of varying lengths such that their individual reconstruction errors are minimal. We show how APCA can be indexed using a multidimensional index structure. We propose two distance measures in the indexed space that exploit the high fidelity of APCA for fast searching: a lower bounding Euclidean distance approximation, and a non-lower bounding, but very tight Euclidean distance approximation and show how they can support fast exact searching, and even faster approximate searching on the same index structure. We theoretically and empirically compare APCA to all the other techniques and demonstrate its superiority.
summary: 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 .