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_10: The problem of efficiently and accurately locating patterns of interest in massive time series data sets is an important and non-trivial problem in a wide variety of applications, including diagnosis and monitoring of complex systems, biomedical data analysis, and exploratory data analysis in scientific and business time series. In this paper a probabilistic approach is taken to this problem. Using piecewise linear segmentations as the underlying representation, local features (such as peaks, troughs, and plateaus) are defined using a prior distribution on expected deformations from a basic template. Global shape information is represented using another prior on the relative locations of the individual features. An appropriately defined probabilistic model integrates the local and global information and directly leads to an overall distance measure between sequence patterns based on prior knowledge. A search algorithm using this distance measure is shown to efficiently and accurately find matches for a variety of patterns on a number of data sets, including engineering sensor data from space Shuttle mission archives. The proposed approach provides a natural framework to support user-customizable "query by content" on time series data, taking prior domain information into account in a principled manner.
  @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: Dynamic segmentation can improve dimension reduction performance. However, finding the optimal boundaries still requires a substantial calculation. With this in mind, several studies have adopted suboptimal approaches, such as longest line fitting @cite_27 , wavelet decomposition @cite_27 @cite_3 and the bottom-up merging of segments @cite_10 . The first two approaches still incur a substantial calculation cost for long time-series signals. The last approach is promising as regards obtaining a rough global approximation at a practical calculation cost. This method is compatible with ours, however, we mainly focus on a more precise local optimization.