scholarly journals Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 1013 ◽  
Author(s):  
David Cuesta-Frau ◽  
Antonio Molina-Picó ◽  
Borja Vargas ◽  
Paula González
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Classification Accuracy ◽  
Markov Models ◽  
Hidden Markov ◽  
Permutation Entropy ◽  
Time Series Classification ◽  
Discriminating Power ◽  
Ordinal Patterns ◽  
Temperature Records

Many measures to quantify the nonlinear dynamics of a time series are based on estimating the probability of certain features from their relative frequencies. Once a normalised histogram of events is computed, a single result is usually derived. This process can be broadly viewed as a nonlinear I R n mapping into I R , where n is the number of bins in the histogram. However, this mapping might entail a loss of information that could be critical for time series classification purposes. In this respect, the present study assessed such impact using permutation entropy (PE) and a diverse set of time series. We first devised a method of generating synthetic sequences of ordinal patterns using hidden Markov models. This way, it was possible to control the histogram distribution and quantify its influence on classification results. Next, real body temperature records are also used to illustrate the same phenomenon. The experiments results confirmed the improved classification accuracy achieved using raw histogram data instead of the PE final values. Thus, this study can provide a very valuable guidance for the improvement of the discriminating capability not only of PE, but of many similar histogram-based measures.

scholarly journals Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series Discrimination Capabilities

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 494
Author(s):  
David Cuesta-Frau
Keyword(s):  
Time Series ◽  
Classification Accuracy ◽  
Input Parameter ◽  
Classification Performance ◽  
Permutation Entropy ◽  
Data Series ◽  
Additional Information ◽  
New Methods ◽  
Discriminating Power ◽  
Ordinal Patterns

Despite its widely tested and proven usefulness, there is still room for improvement in the basic permutation entropy (PE) algorithm, as several subsequent studies have demonstrated in recent years. Some of these new methods try to address the well-known PE weaknesses, such as its focus only on ordinal and not on amplitude information, and the possible detrimental impact of equal values found in subsequences. Other new methods address less specific weaknesses, such as the PE results’ dependence on input parameter values, a common problem found in many entropy calculation methods. The lack of discriminating power among classes in some cases is also a generic problem when entropy measures are used for data series classification. This last problem is the one specifically addressed in the present study. Toward that purpose, the classification performance of the standard PE method was first assessed by conducting several time series classification tests over a varied and diverse set of data. Then, this performance was reassessed using a new Shannon Entropy normalisation scheme proposed in this paper: divide the relative frequencies in PE by the number of different ordinal patterns actually found in the time series, instead of by the theoretically expected number. According to the classification accuracy obtained, this last approach exhibited a higher class discriminating power. It was capable of finding significant differences in six out of seven experimental datasets—whereas the standard PE method only did in four—and it also had better classification accuracy. It can be concluded that using the additional information provided by the number of forbidden/found patterns, it is possible to achieve a higher discriminating power than using the classical PE normalisation method. The resulting algorithm is also very similar to that of PE and very easy to implement.

scholarly journals Slope Entropy: A New Time Series Complexity Estimator Based on Both Symbolic Patterns and Amplitude Information

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1167 ◽  
Author(s):  
David Cuesta-Frau
Keyword(s):  
Time Series ◽  
Classification Performance ◽  
Permutation Entropy ◽  
Data Series ◽  
Time Series Classification ◽  
New Methods ◽  
Discriminating Power ◽  
Desirable Feature ◽  
Encoding Method ◽  
Robust To Noise

The development of new measures and algorithms to quantify the entropy or related concepts of a data series is a continuous effort that has brought many innovations in this regard in recent years. The ultimate goal is usually to find new methods with a higher discriminating power, more efficient, more robust to noise and artifacts, less dependent on parameters or configurations, or any other possibly desirable feature. Among all these methods, Permutation Entropy (PE) is a complexity estimator for a time series that stands out due to its many strengths, with very few weaknesses. One of these weaknesses is the PE’s disregarding of time series amplitude information. Some PE algorithm modifications have been proposed in order to introduce such information into the calculations. We propose in this paper a new method, Slope Entropy (SlopEn), that also addresses this flaw but in a different way, keeping the symbolic representation of subsequences using a novel encoding method based on the slope generated by two consecutive data samples. By means of a thorough and extensive set of comparative experiments with PE and Sample Entropy (SampEn), we demonstrate that SlopEn is a very promising method with clearly a better time series classification performance than those previous methods.

scholarly journals Edge4TSC: Binary Distribution Tree-Enabled Time Series Classification in Edge Environment

Sensors ◽  
2020 ◽  
Vol 20 (7) ◽  
pp. 1908
Author(s):  
Chao Ma ◽  
Xiaochuan Shi ◽  
Wei Li ◽  
Weiping Zhu
Keyword(s):  
Time Series ◽  
Deep Learning ◽  
Classification Accuracy ◽  
Time Series Data ◽  
Series Representation ◽  
Series Data ◽  
Feature Engineering ◽  
Time Series Classification ◽  
Binary Distribution ◽  
New Time

In the past decade, time series data have been generated from various fields at a rapid speed, which offers a huge opportunity for mining valuable knowledge. As a typical task of time series mining, Time Series Classification (TSC) has attracted lots of attention from both researchers and domain experts due to its broad applications ranging from human activity recognition to smart city governance. Specifically, there is an increasing requirement for performing classification tasks on diverse types of time series data in a timely manner without costly hand-crafting feature engineering. Therefore, in this paper, we propose a framework named Edge4TSC that allows time series to be processed in the edge environment, so that the classification results can be instantly returned to the end-users. Meanwhile, to get rid of the costly hand-crafting feature engineering process, deep learning techniques are applied for automatic feature extraction, which shows competitive or even superior performance compared to state-of-the-art TSC solutions. However, because time series presents complex patterns, even deep learning models are not capable of achieving satisfactory classification accuracy, which motivated us to explore new time series representation methods to help classifiers further improve the classification accuracy. In the proposed framework Edge4TSC, by building the binary distribution tree, a new time series representation method was designed for addressing the classification accuracy concern in TSC tasks. By conducting comprehensive experiments on six challenging time series datasets in the edge environment, the potential of the proposed framework for its generalization ability and classification accuracy improvement is firmly validated with a number of helpful insights.

scholarly journals A Hidden Markov Model for the Linguistic Analysis of the Voynich Manuscript

2019 ◽  
Vol 24 (1) ◽  
pp. 14 ◽  
Author(s):  
Luis Acedo
Keyword(s):  
Time Series ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Mathematical Linguistics ◽  
Underlying Structure ◽  
Internal States ◽  
Consonant Sounds

Hidden Markov models are a very useful tool in the modeling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden Markov model to analyze the underlying structure of an ancient and complex manuscript, known as the Voynich manuscript, which remains undeciphered. By assuming a certain number of internal states representations for the symbols of the manuscripts, we train the network by means of the α and β -pass algorithms to optimize the model. By this procedure, we are able to obtain the so-called transition and observation matrices to compare with known languages concerning the frequency of consonant andvowel sounds. From this analysis, we conclude that transitions occur between the two states with similar frequencies to other languages. Moreover, the identification of the vowel and consonant sounds matches some previous tentative bottom-up approaches to decode the manuscript.

A Fast Shapelet Discovery Algorithm Based on Important Data Points

2017 ◽  
Vol 14 (2) ◽  
pp. 67-80 ◽  
Author(s):  
Cun Ji ◽  
Chao Zhao ◽  
Li Pan ◽  
Shijun Liu ◽  
Chenglei Yang ◽  
...  
Keyword(s):  
Time Series ◽  
Classification Accuracy ◽  
Time Series Classification ◽  
Important Data ◽  
The Past ◽  
Significant Interest ◽  
Data Points ◽  
Discovery Time ◽  
Accuracy Rates

Time series classification (TSC) has attracted significant interest over the past decade. A shapelet is one fragment of a time series that can represent class characteristics of the time series. A classifier based on shapelets is interpretable, more accurate, and faster. However, the time it takes to find shapelets is enormous. This article will propose a fast shapelet (FS) discovery algorithm based on important data points (IDPs). First, the algorithm will identify IDPs. Next, the subsequence containing one or more IDPs will be selected as a candidate shapelet. Finally, the best shapelets will be selected. Results will show that the proposed algorithm reduces the shapelet discovery time by approximately 14.0% while maintaining the same level of classification accuracy rates.

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