Introduction and Motivation It is becoming increasingly common for organizations to collect very large amounts of data over time, and to need to For example, Yahoo has banks of mail servers that are monitored over time. Many measurements on servers/IoT device performances are collected every hour for each of thousands of servers in order to identify servers/devices that are behaving unusually. detect unusual or anomalous time series. Python library helps to compute , measuring different characteristic-features of the series. The features may include etc. tsfeature a vector of features on each time series lag correlation, the strength of seasonality, spectral entropy, In this blog, we discuss about different feature extraction techniques from a time-series and demonstrate with two different time-series. Popular Feature Extraction Metrics One of the most commonly used mechanisms of Feature Extraction mechanisms in Data Science – is also used in the context of time-series. After applying on the can be applied to the first two principal components. This enables the most unusual series, based on their feature vectors, to be identified. The methods used are based on the highest density regions. Principal Component Analysis (PCA) Principal Component Analysis(Decomposition) features, various bivariate outlier detection methods bivariate outlier detection A change in the over time can cause problems when modeling time series with classical methods like . variance or volatility ARIMA The method plays a vital role in like a change in that is , such as . ARCH or Autoregressive Conditional Heteroskedasticity time-series highly volatile models stock prediction to measure the variance time-dependent increasing or decreasing volatility Below, we state some of the time-series features, functionality, and their description. The following code snippet shows how we can for each feature. extract relevant features with one line of code Source Code tsf_hp = tf.holt_parameters(df2[ ].values) print(tsf_hp) tsf_centrpy = tf.count_entropy(df2[ ].values) print(tsf_centrpy) tsf_crossing_points =tf.crossing_points(df2[ ].values) print(tsf_centrpy) tsf_entropy =tf.entropy(df2[ ].values) print(tsf_entropy) tsf_flat_spots =tf.flat_spots(df2[ ].values) print(tsf_flat_spots) tsf_frequency =tf.frequency(df2[ ].values) print(tsf_frequency) tsf_heterogeneity = tf.heterogeneity(df2[ ].values) print(tsf_heterogeneity) tsf_guerrero =tf.guerrero(df2[ ].values) print(tsf_guerrero) tsf_hurst = tf.hurst(df2[ ].values) print(tsf_hurst) tsf_hw_parameters = tf.hw_parameters(df2[ ].values) print(tsf_hw_parameters) tsf_intv = tf.intervals(df2[ ].values) print(tsf_intv) tsf_lmp = tf.lumpiness(df2[ ].values) print(tsf_lmp) tsf_acf = tf.acf_features(df2[ ].values) print(tsf_acf) tsf_arch_stat = tf.arch_stat(df2[ ].values) print(tsf_arch_stat) tsf_pacf = tf.pacf_features(df2[ ].values) print(tsf_pacf) tsf_sparsity = tf.sparsity(df2[ ].values) print(tsf_sparsity) tsf_stability = tf.stability(df2[ ].values) print(tsf_stability) tsf_stl_features = tf.stl_features(df2[ ].values) print(tsf_stl_features) tsf_unitroot_kpss = tf.unitroot_kpss(df2[ ].values) print(tsf_unitroot_kpss) tsf_unitroot_pp = tf.unitroot_pp(df2[ ].values) print(tsf_unitroot_pp) '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' '# Direct_1' The results section illustrates from the values of extracted features Fetal ECG. Results Time Series -1 (Data from Fetal ECG) The below figure illustrates a time series of data collected . from Fetal ECG from where features have been extracted { : , : } { : } { : } { : } { : } { : } { : , : , : , : } { : } { : nan, : nan, : nan} { : , : nan} { : nan} { : } { : , : , : , : , : , : } { : } { : , : , : } { : } { : } { : , : , : nan, : nan, : nan, : nan, : nan, : nan} { : } { : } 'alpha' 0.9998016430979507 'beta' 0.5262228301908355 'count_entropy' 1.783469256071135 'crossing_points' 436 'entropy' 0.6493414196542769 'flat_spots' 131 'frequency' 1 'arch_acf' 0.3347171050143251 'garch_acf' 0.3347171050143251 'arch_r2' 0.14089508110660665 'garch_r2' 0.14089508110660665 'hurst' 0.4931972012451876 'hw_alpha' 'hw_beta' 'hw_gamma' 'intervals_mean' 2516.801557547009 'intervals_sd' 'guerrero' 'lumpiness' 0.01205944072461473 'x_acf1' 0.8262122472240574 'x_acf10' 3.079891123506255 'diff1_acf1' -0.27648384824011435 'diff1_acf10' 0.08236265771293629 'diff2_acf1' -0.5980110240921641 'diff2_acf10' 0.3724461872893135 'arch_lm' 0.7064704126082555 'x_pacf5' 0.7303549429779813 'diff1x_pacf5' 0.09311680507880443 'diff2x_pacf5' 0.7105000333917864 'sparsity' 0.0 'stability' 0.16986190432765097 'nperiods' 0 'seasonal_period' 1 'trend' 'spike' 'linearity' 'curvature' 'e_acf1' 'e_acf10' 'unitroot_kpss' 0.06485903737928193 'unitroot_pp' -908.3309773009415 The results section illustrates for date wise temperature variation. the values of extracted features Result Time-Series 2 (Data from Daily Temperature) { : , : } { : } { : } { : } { : } { : } { : , : , : , : } { : } { : nan, : nan, : nan} { : , : } { : nan} { : } { : , : , : , : , : , : } { : } { : } { : , : , : } { : } { : } { : , : , : nan, : nan, : nan, : nan, : nan, : nan} { : } { : } 'alpha' 0.4387345064923509 'beta' 0.0 'count_entropy' -101348.71338310161 'crossing_points' 706 'entropy' 0.5089893350876903 'flat_spots' 10 'frequency' 1 'arch_acf' 0.016273743642920828 'garch_acf' 0.016273743642920828 'arch_r2' 0.015091960217949008 'garch_r2' 0.015091960217949008 'hurst' 0.5716257806690483 'hw_alpha' 'hw_beta' 'hw_gamma' 'intervals_mean' 1216.0 'intervals_sd' 1299.2740280633643 'guerrero' 'lumpiness' 5.464398615083545e-05 'x_acf1' -0.0005483958183129098 'x_acf10' 3.0147995912148108e-06 'diff1_acf1' -0.5 'diff1_acf10' 0.25 'diff2_acf1' -0.6666666666666666 'diff2_acf10' 0.4722222222222222 'arch_lm' 3.6528279285796827e-06 'nonlinearity' 0.0 'x_pacf5' 1.5086491342316237e-06 'diff1x_pacf5' 0.49138888888888893 'diff2x_pacf5' 1.04718820861678 'sparsity' 0.0 'stability' 5.464398615083545e-05 'nperiods' 0 'seasonal_period' 1 'trend' 'spike' 'linearity' 'curvature' 'e_acf1' 'e_acf10' 'unitroot_kpss' 0.29884876591708787 'unitroot_pp' -3643.7791982866393 Conclusion In this blog, we discuss easy steps to extract features from time series (both time-series have seasonality =1), that can help us in discovering anomalies. It is evident from the computed metrics that the first series is more stable (higher value as given by the ) as the time-stamped data is for a longer period with relatively few fluctuations compared to its entire period. stability and entropy factor The second time series exhibits as demonstrated by a high number of crossing points. higher fluctuations Consequently, we also observe that the second time-series also has a lower and , signifying a lower variance of variance. unirooot_kpss and uniroot_pp reveal, the existence of a unit root in the vector which in both the time-series is less than 1 and negative respectively. lumpiness intervals mean also supports evaluation of custom functions that come as a NumPy array as input and returns a dictionary with the feature name as a key and its value tsfeature References https://github.com/FedericoGarza/tsfeatures https://htmlpreview.github.io/? https://github.com/robjhyndman/M4metalearning/blob/master/docs/M4_methodology.html#features https://cran.r- project.org/web/packages/tsfeatures/tsfeatures.pdf https://robjhyndman.com/papers/icdm2015.pdf https://math.berkeley.edu/~btw/thesis4.pdf https://machinelearningmastery.com/develop-arch-and-garch-models-for-time-series-forecasting-in-python/ https://ir.nctu.edu.tw/bitstream/11536/14555/1/A1997YD78100005.pdf Principal Component Analysis for Time Series and Other Non-Independent Data – https://link.springer.com/chapter/10.1007%2F0-387-22440-8_12
