The data reduction can be established with the purpose to reduce representation of the data set in the smaller volume but still produce the same analytical results. In data mining and knowledge discovery, there are a large number of techniques for data reduction. The common methods for this task include data aggregation; attribute subset selection, dimensionality reduction and numerosity reduction. In order to make data preprocessing technique successfully, the overall information of data set is necessary. The data summarization techniques include the typical properties of data and emphasize which data values should be treated as outliers. The measures include mean, median, mode, and midrange, while measures of data scattering include quartiles, interquartile range, and variance. This statistic description provides greatest help in understanding the distribution of the source data. Real world data, such as speech signals, finance stock data usually have a high dimensionality. In order to handle effectively the real world data, its dimensionality needs to be reduced. The main task of dimensionality reduction is the transformation of high dimensional data into a meaningful representation of reduced dimensionality. In additional, the reduced representation should have a dimensionality that corresponds to the essential dimensionality of the data. The essential dimensionality of data is the minimum number of parameters needed to account for the observed properties of the data.
The Research on Time Series Analysis Techniques With the task of dimensionality reduction approach, the data transformations must be applied to get a reduced or compressed representation of the original data. In case the original data can be reconstructed from the compressed data without any loss of information, this data reduction is called lossless. The data reduction is called lossy if the reconstruction is only an approximation of the original data. The linear signal processing technique discrete wavelet transform (DWT) applies to a data vector X, transforms it to a numerically different vector Xrsquo;, of wavelet coefficients. In this case, two vectors X and Xrsquo; are of the same length. “How can this technique be useful for data reduction if the wavelet transformed data are of the same length as the original data?” The usefulness of these techniques in order to reduce dimensions lie in the actuality that the wavelet transformed data can be truncated. A compressed approximation of the data can be retained by storing only a small fraction of the strongest of the wavelet coefficients.
Principal Component Analysis (PCA) technique is used to compress the information contained in the data set. The principal goal of this technique is to be able to calculate the most relevant components from the original features. The objective is to simplify the data structure transforming the original features into others, applying linear combinations of those features. PCA attempts to reduce the dimensionality, keeping as much as possible the original variance in the high dimensional space. A time series is different from the traditionally achieved data as they have their own special characteristics, such as high dimensionality with large data size, and necessity to update continuously. Dimensionality reduction is one of the most important preprocessing procedures for analyzing a stream time series environment. Dimensionality reduction is the process of reducing the number of variables or points under specific consideration. It can be divided into two main problems as an example of feature selection and feature extraction. The technique is called feature selection implementation for selecting a subset of related features for building strong and useful learning models. The feature selection technique helps improving the performance of an analyzing model, such as moderating the effect of the course of dimensionality, enhancing generalization capability, speeding up the learning process, and improving model interpretability. In many cases, the original representation of the time series data might be redundant because of some reasons. For example, first, many of the variables will have a variation smaller than the measurement noise and thus will be irrelevant and second, many of the variables will be correlated with each other and thus a new set of in-correlated variables will be found.
There are some typical methods for time series dimensionality reduction in order to represent time series in lower dimensional spaces including the DFT, Discrete Wavelet Transform (DWT), Piecewise Linear Approximation, Piecewise Aggregate Approximation (PAA), Singular Value Decomposition (SVD) and Adaptive Piecewise Constant Approximation (APCA). Time series are highly correlated data, so that, the representation techniques use a scheme that aims at reducing the dimensionality of time series by projecting the original data onto lower dimensional spaces and processing the query in those reduced spaces. This scheme is widely used in time series data mining literature. A sequence of data point is known as a time series and the major change of the data point has different extents of influence on the shape of the time series. That is why each data point of the time series has its own importance to the data stream. Some data points may contribute to the overall shape of the time series while others may only have little influence on the time series or they may even be discarded. These points are therefore, more important than other data points in the time series. Several approaches are based on important points such as Landmark points, Extreme points and Perceptually Important Points (PIPs). Recent studies make an analysis of the movement of a stock based on a selected number of points from the time series. These problems include Important Points (IPs), Perceptually Important Points and Turning Points (TPs). In a time series data, the important points a
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The data reduction can be established with the purpose to reduce representation of the data set in the smaller volume but still produce the same analytical results. In data mining and knowledge discovery, there are a large number of techniques for data reduction. The common methods for this task include data aggregation; attribute subset selection, dimensionality reduction and numerosity reduction. In order to make data preprocessing technique successfully, the overall information of data set is necessary. The data summarization techniques include the typical properties of data and emphasize which data values should be treated as outliers. The measures include mean, median, mode, and midrange, while measures of data scattering include quartiles, interquartile range, and variance. This statistic description provides greatest help in understanding the distribution of the source data. Real world data, such as speech signals, finance stock data usually have a high dimensionality. In order to handle effectively the real world data, its dimensionality needs to be reduced. The main task of dimensionality reduction is the transformation of high dimensional data into a meaningful representation of reduced dimensionality. In additional, the reduced representation should have a dimensionality that corresponds to the essential dimensionality of the data. The essential dimensionality of data is the minimum number of parameters needed to account for the observed properties of the data.
The Research on Time Series Analysis Techniques With the task of dimensionality reduction approach, the data transformations must be applied to get a reduced or compressed representation of the original data. In case the original data can be reconstructed from the compressed data without any loss of information, this data reduction is called lossless. The data reduction is called lossy if the reconstruction is only an approximation of the original data. The linear signal processing technique discrete wavelet transform (DWT) applies to a data vector X, transforms it to a numerically different vector Xrsquo;, of wavelet coefficients. In this case, two vectors X and Xrsquo; are of the same length. “How can this technique be useful for data reduction if the wavelet transformed data are of the same length as the original data?” The usefulness of these techniques in order to reduce dimensions lie in the actuality that the wavelet transformed data can be truncated. A compressed approximation of the data can be retained by storing only a small fraction of the strongest of the wavelet coefficients.
Principal Component Analysis (PCA) technique is used to compress the information contained in the data set. The principal goal of this technique is to be able to calculate the most relevant components from the original features. The objective is to simplify the data structure transforming the original features into others, applying linear combinations of those features. PCA attempts to reduce the dimensionality, keeping as much as possible the original variance in the high dimensional space. A time series is different from the traditionally achieved data as they have their own special characteristics, such as high dimensionality with large data size, and necessity to update continuously. Dimensionality reduction is one of the most important preprocessing procedures for analyzing a stream time series environment. Dimensionality reduction is the process of reducing the number of variables or points under specific consideration. It can be divided into two main problems as an example of feature selection and feature extraction. The technique is called feature selection implementation for selecting a subset of related features for building strong and useful learning models. The feature selection technique helps improving the performance of an analyzing model, such as moderating the effect of the course of dimensionality, enhancing generalization capability, speeding up the learning process, and improving model interpretability. In many cases, the original representation of the time series data might be redundant because of some reasons. For example, first, many of the variables will have a variation smaller than the measurement noise and thus will be irrelevant and second, many of the variables will be correlated with each other and thus a new set of in-correlated variables will be found.
There are some typical methods for time series dimensionality reduction in order to represent time series in lower dimensional spaces including the DFT, Discrete Wavelet Transform (DWT), Piecewise Linear Approximation, Piecewise Aggregate Approximation (PAA), Singular Value Decomposition (SVD) and Adaptive Piecewise Constant Approximation (APCA). Time series are highly correlated data, so that, the representation techniques use a scheme that aims at reducing the dimensionality of time series by projecting the original data onto lower dimensional spaces and processing the query in those reduced spaces. This scheme is widely used in time series data mining literature. A sequence of data point is known as a time series and the major change of the data point has different extents of influence on the shape of the time series. That is why each data point of the time series has its own importance to the data stream. Some data points may contribute to the overall shape of the time series while others may only have little influence on the time series or they may even be discarded. These points are therefore, more important than other data points in the time series. Several approaches are based on important points such as Landmark points, Extreme points and Perceptually Important Points (PIPs). Recent studies make an analysis of the movement of a stock based on a selected number of points from the time series. These problems include Important Points (IPs), Perceptually Important Points and Turning Points (TPs). In a time series data, the important points a
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