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feature_mining.py
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#!/usr/bin/python3
"""Module for simulating ipfixprobe for adding new TimeSeries plugin.
author: Josef Koumar
e-mail: [email protected], [email protected]
Copyright (C) 2022 CESNET
LICENSE TERMS
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
3. Neither the name of the Company nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
ALTERNATIVELY, provided that this notice is retained in full, this product may be distributed under the terms of the GNU General Public License (GPL) version 2 or later, in which case the provisions of the GPL apply INSTEAD OF those given above.
This software is provided as is'', and any express or implied warranties, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose are disclaimed. In no event shall the company or contributors be liable for any direct, indirect, incidental, special, exemplary, or consequential damages (including, but not limited to, procurement of substitute goods or services; loss of use, data, or profits; or business interruption) however caused and on any theory of liability, whether in contract, strict liability, or tort (including negligence or otherwise) arising in any way out of the use of this software, even if advised of the possibility of such damage.
"""
# Standard libraries imports
import sys
import csv
csv.field_size_limit(sys.maxsize)
import time
import argparse
from argparse import RawTextHelpFormatter
import statistics
import math
import numpy as np
import json
from scipy.stats import norm
from statsmodels.stats.diagnostic import lilliefors
from scipy.special import gamma
from astropy.timeseries import LombScargle
from collections import Counter
import warnings
warnings.filterwarnings("ignore")
# 4x speeder than scapy
from pypacker import ppcap
from pypacker.layer12 import ethernet
from pypacker.layer3 import ip
from pypacker.layer4 import tcp
DEFAULT_VALUE = "" # 0
DEFAULT_VALUE_DIR = -1
class TimeSeriesPlugin(object):
def __init__(self,src_ip, dst_ip, src_port, dst_port):
# Basic plugin features
self.DST_IP = dst_ip
self.SRC_IP = src_ip
self.BYTES = 0
self.BYTES_REV = 0
self.TIME_FIRST = 0
self.TIME_LAST = 0
self.PACKETS = 0
self.PACKETS_REV = 0
self.DST_PORT = dst_port
self.SRC_PORT = src_port
# statistics-based features
self.MEAN = DEFAULT_VALUE
self.MEDIAN = DEFAULT_VALUE
self.STDEV = DEFAULT_VALUE
self.VAR = DEFAULT_VALUE
self.BURSTINESS = DEFAULT_VALUE
self.Q1 = DEFAULT_VALUE
self.Q3 = DEFAULT_VALUE
self.MIN = DEFAULT_VALUE
self.MAX = DEFAULT_VALUE
self.MIN_MINUS_MAX = DEFAULT_VALUE
self.MODE = DEFAULT_VALUE
self.COEFFICIENT_OF_VARIATION = DEFAULT_VALUE
self.AVERAGE_DISPERSION = DEFAULT_VALUE
self.PERCENT_DEVIATION = DEFAULT_VALUE
self.ROOT_MEAN_SQUARE = DEFAULT_VALUE
self.PERCENT_BELOW_MEAN = DEFAULT_VALUE
self.PERCENT_ABOVE_MEAN = DEFAULT_VALUE
self.PEARSON_SK1_SKEWNESS = DEFAULT_VALUE
self.PEARSON_SK2_SKEWNESS = DEFAULT_VALUE
self.FISHER_MI_3_SKEWNESS = DEFAULT_VALUE
self.FISHER_PEARSON_g1_SKEWNESS = DEFAULT_VALUE
self.FISHER_PEARSON_G1_SKEWNESS = DEFAULT_VALUE
self.GALTON_SKEWNESS = DEFAULT_VALUE
self.KURTOSIS = DEFAULT_VALUE
self.ENTROPY = DEFAULT_VALUE
self.SCALED_ENTROPY = DEFAULT_VALUE
# distribution-based features
self.HURST_EXPONENT = DEFAULT_VALUE
self.BENFORD_LAW_PRESENTED = False
self.P_BENFORD = DEFAULT_VALUE
self.NORMAL_DISTRIBUTION = DEFAULT_VALUE
self.CNT_DISTRIBUTION = DEFAULT_VALUE
self.TIME_DISTRIBUTION = DEFAULT_VALUE
self.AREA_VALUES_DISTRIBUTION = DEFAULT_VALUE
# time-based features
self.MEAN_SCALED_TIME = DEFAULT_VALUE
self.MEDIAN_SCALED_TIME = DEFAULT_VALUE
self.Q1_SCALED_TIME = DEFAULT_VALUE
self.Q3_SCALED_TIME = DEFAULT_VALUE
self.DURATION = DEFAULT_VALUE
self.MEAN_DIFFTIMES = DEFAULT_VALUE
self.MEDIAN_DIFFTIMES = DEFAULT_VALUE
self.MIN_DIFFTIMES = DEFAULT_VALUE
self.MAX_DIFFTIMES = DEFAULT_VALUE
self.MEAN_SCALED_DIFFTIMES = DEFAULT_VALUE
# beahavior-based features
self.SIG_SPACES = False
self.SWITCHING_METRIC = DEFAULT_VALUE
self.TRANSIENTS = False
self.CNT_ZEROS = DEFAULT_VALUE
self.CNT_NZ_DISTRIBUTION = DEFAULT_VALUE
self.BIGGEST_CNT_1_SEC = DEFAULT_VALUE
self.DIRECTIONS = DEFAULT_VALUE
self.PERIODICITY = False
self.VAL = 0
self.TIME = 0
# frequency-based features
self.MIN_POWER = DEFAULT_VALUE
self.MAX_POWER = DEFAULT_VALUE
self.MIN_POWER_FREQ = DEFAULT_VALUE
self.MAX_POWER_FREQ = DEFAULT_VALUE
self.POWER_MEAN = DEFAULT_VALUE
self.POWER_STD = DEFAULT_VALUE
self.POWER_MODE = DEFAULT_VALUE
self.SPECTRAL_ENERGY = DEFAULT_VALUE
self.SPECTRAL_ENTROPY = DEFAULT_VALUE
self.SPECTRAL_KURTOSIS = DEFAULT_VALUE
self.SPECTRAL_SKEWNESS = DEFAULT_VALUE
self.SPECTRAL_ROLLOFF = DEFAULT_VALUE
self.SPECTRAL_CENTROID = DEFAULT_VALUE
self.SPECTRAL_SPREAD = DEFAULT_VALUE
self.SPECTRAL_SLOPE = DEFAULT_VALUE
self.SPECTRAL_CREST = DEFAULT_VALUE
self.SPECTRAL_FLUX = DEFAULT_VALUE
self.SPECTRAL_BANDWIDTH = DEFAULT_VALUE
self.PERIODICITY_SCDF = False
#extension based on direction
self.MEAN_0 = DEFAULT_VALUE_DIR
self.MEDIAN_0 = DEFAULT_VALUE_DIR
self.STDEV_0 = DEFAULT_VALUE_DIR
self.VAR_0 = DEFAULT_VALUE_DIR
self.BURSTINESS_0 = DEFAULT_VALUE_DIR
self.Q1_0 = DEFAULT_VALUE_DIR
self.Q3_0 = DEFAULT_VALUE_DIR
self.MIN_0 = DEFAULT_VALUE_DIR
self.MAX_0 = DEFAULT_VALUE_DIR
self.MIN_MINUS_MAX_0 = DEFAULT_VALUE_DIR
self.MODE_0 = DEFAULT_VALUE_DIR
self.COEFFICIENT_OF_VARIATION_0 = DEFAULT_VALUE_DIR
self.AVERAGE_DISPERSION_0 = DEFAULT_VALUE_DIR
self.PERCENT_DEVIATION_0 = DEFAULT_VALUE_DIR
self.ROOT_MEAN_SQUARE_0 = DEFAULT_VALUE_DIR
self.PERCENT_BELOW_MEAN_0 = DEFAULT_VALUE_DIR
self.PERCENT_ABOVE_MEAN_0 = DEFAULT_VALUE_DIR
self.PEARSON_SK1_SKEWNESS_0 = DEFAULT_VALUE_DIR
self.PEARSON_SK2_SKEWNESS_0 = DEFAULT_VALUE_DIR
self.FISHER_MI_3_SKEWNESS_0 = DEFAULT_VALUE_DIR
self.FISHER_PEARSON_g1_SKEWNESS_0 = DEFAULT_VALUE_DIR
self.FISHER_PEARSON_G1_SKEWNESS_0 = DEFAULT_VALUE_DIR
self.GALTON_SKEWNESS_0 = DEFAULT_VALUE_DIR
self.KURTOSIS_0 = DEFAULT_VALUE_DIR
self.ENTROPY_0 = DEFAULT_VALUE_DIR
self.SCALED_ENTROPY_0 = DEFAULT_VALUE_DIR
self.HURST_EXPONENT_0 = DEFAULT_VALUE_DIR
self.BENFORD_LAW_PRESENTED_0 = False
self.P_BENFORD_0 = DEFAULT_VALUE_DIR
self.NORMAL_DISTRIBUTION_0 = DEFAULT_VALUE_DIR
self.CNT_DISTRIBUTION_0 = DEFAULT_VALUE_DIR
self.TIME_DISTRIBUTION_0 = DEFAULT_VALUE_DIR
self.AREA_VALUES_DISTRIBUTION_0 = DEFAULT_VALUE_DIR
self.MEAN_SCALED_TIME_0 = DEFAULT_VALUE_DIR
self.MEDIAN_SCALED_TIME_0 = DEFAULT_VALUE_DIR
self.Q1_SCALED_TIME_0 = DEFAULT_VALUE_DIR
self.Q3_SCALED_TIME_0 = DEFAULT_VALUE_DIR
self.DURATION_0 = DEFAULT_VALUE_DIR
self.MEAN_DIFFTIMES_0 = DEFAULT_VALUE_DIR
self.MEDIAN_DIFFTIMES_0 = DEFAULT_VALUE_DIR
self.MIN_DIFFTIMES_0 = DEFAULT_VALUE_DIR
self.MAX_DIFFTIMES_0 = DEFAULT_VALUE_DIR
self.MEAN_SCALED_DIFFTIMES_0 = DEFAULT_VALUE_DIR
self.SIG_SPACES_0 = False
self.SWITCHING_METRIC_0 = DEFAULT_VALUE_DIR
self.TRANSIENTS_0 = False
self.CNT_ZEROS_0 = DEFAULT_VALUE_DIR
self.CNT_NZ_DISTRIBUTION_0 = DEFAULT_VALUE_DIR
self.BIGGEST_CNT_1_SEC_0 = DEFAULT_VALUE_DIR
self.PERIODICITY_0 = False
self.VAL_0 = 0
self.TIME_0 = 0
self.MEAN_1 = DEFAULT_VALUE_DIR
self.MEDIAN_1 = DEFAULT_VALUE_DIR
self.STDEV_1 = DEFAULT_VALUE_DIR
self.VAR_1 = DEFAULT_VALUE_DIR
self.BURSTINESS_1 = DEFAULT_VALUE_DIR
self.Q1_1 = DEFAULT_VALUE_DIR
self.Q3_1 = DEFAULT_VALUE_DIR
self.MIN_1 = DEFAULT_VALUE_DIR
self.MAX_1 = DEFAULT_VALUE_DIR
self.MIN_MINUS_MAX_1 = DEFAULT_VALUE_DIR
self.MODE_1 = DEFAULT_VALUE_DIR
self.COEFFICIENT_OF_VARIATION_1 = DEFAULT_VALUE_DIR
self.AVERAGE_DISPERSION_1 = DEFAULT_VALUE_DIR
self.PERCENT_DEVIATION_1 = DEFAULT_VALUE_DIR
self.ROOT_MEAN_SQUARE_1 = DEFAULT_VALUE_DIR
self.PERCENT_BELOW_MEAN_1 = DEFAULT_VALUE_DIR
self.PERCENT_ABOVE_MEAN_1 = DEFAULT_VALUE_DIR
self.PEARSON_SK1_SKEWNESS_1 = DEFAULT_VALUE_DIR
self.PEARSON_SK2_SKEWNESS_1 = DEFAULT_VALUE_DIR
self.FISHER_MI_3_SKEWNESS_1 = DEFAULT_VALUE_DIR
self.FISHER_PEARSON_g1_SKEWNESS_1 = DEFAULT_VALUE_DIR
self.FISHER_PEARSON_G1_SKEWNESS_1 = DEFAULT_VALUE_DIR
self.GALTON_SKEWNESS_1 = DEFAULT_VALUE_DIR
self.KURTOSIS_1 = DEFAULT_VALUE_DIR
self.ENTROPY_1 = DEFAULT_VALUE_DIR
self.SCALED_ENTROPY_1 = DEFAULT_VALUE_DIR
self.HURST_EXPONENT_1 = DEFAULT_VALUE_DIR
self.BENFORD_LAW_PRESENTED_1 = False
self.P_BENFORD_1 = DEFAULT_VALUE_DIR
self.NORMAL_DISTRIBUTION_1 = DEFAULT_VALUE_DIR
self.CNT_DISTRIBUTION_1 = DEFAULT_VALUE_DIR
self.TIME_DISTRIBUTION_1 = DEFAULT_VALUE_DIR
self.AREA_VALUES_DISTRIBUTION_1 = DEFAULT_VALUE_DIR
self.MEAN_SCALED_TIME_1 = DEFAULT_VALUE_DIR
self.MEDIAN_SCALED_TIME_1 = DEFAULT_VALUE_DIR
self.Q1_SCALED_TIME_1 = DEFAULT_VALUE_DIR
self.Q3_SCALED_TIME_1 = DEFAULT_VALUE_DIR
self.DURATION_1 = DEFAULT_VALUE_DIR
self.MEAN_DIFFTIMES_1 = DEFAULT_VALUE_DIR
self.MEDIAN_DIFFTIMES_1 = DEFAULT_VALUE_DIR
self.MIN_DIFFTIMES_1 = DEFAULT_VALUE_DIR
self.MAX_DIFFTIMES_1 = DEFAULT_VALUE_DIR
self.MEAN_SCALED_DIFFTIMES_1 = DEFAULT_VALUE_DIR
self.SIG_SPACES_1 = False
self.SWITCHING_METRIC_1 = DEFAULT_VALUE_DIR
self.TRANSIENTS_1 = False
self.CNT_ZEROS_1 = DEFAULT_VALUE_DIR
self.CNT_NZ_DISTRIBUTION_1 = DEFAULT_VALUE_DIR
self.BIGGEST_CNT_1_SEC_1 = DEFAULT_VALUE_DIR
self.PERIODICITY_1 = False
self.VAL_1 = 0
self.TIME_1 = 0
def extend_with_0_direction(self, ts_plugin_0):
self.MEDIAN_0 = ts_plugin_0.MEDIAN_0
self.STDEV_0 = ts_plugin_0.STDEV_0
self.VAR_0 = ts_plugin_0.VAR_0
self.BURSTINESS_0 = ts_plugin_0.BURSTINESS_0
self.Q1_0 = ts_plugin_0.Q1_0
self.Q3_0 = ts_plugin_0.Q3_0
self.MIN_0 = ts_plugin_0.MIN_0
self.MAX_0 = ts_plugin_0.MAX_0
self.MIN_MINUS_MAX_0 = ts_plugin_0.MIN_MINUS_MAX_0
self.MODE_0 = ts_plugin_0.MODE_0
self.COEFFICIENT_OF_VARIATION_0 = ts_plugin_0.COEFFICIENT_OF_VARIATION_0
self.AVERAGE_DISPERSION_0 = ts_plugin_0.AVERAGE_DISPERSION_0
self.PERCENT_DEVIATION_0 = ts_plugin_0.PERCENT_DEVIATION_0
self.ROOT_MEAN_SQUARE_0 = ts_plugin_0.ROOT_MEAN_SQUARE_0
self.PERCENT_BELOW_MEAN_0 = ts_plugin_0.PERCENT_BELOW_MEAN_0
self.PERCENT_ABOVE_MEAN_0 = ts_plugin_0.PERCENT_ABOVE_MEAN_0
self.PEARSON_SK1_SKEWNESS_0 = ts_plugin_0.PEARSON_SK1_SKEWNESS_0
self.PEARSON_SK2_SKEWNESS_0 = ts_plugin_0.PEARSON_SK2_SKEWNESS_0
self.FISHER_MI_3_SKEWNESS_0 = ts_plugin_0.FISHER_MI_3_SKEWNESS_0
self.FISHER_PEARSON_g1_SKEWNESS_0 = ts_plugin_0.FISHER_PEARSON_g1_SKEWNESS_0
self.FISHER_PEARSON_G1_SKEWNESS_0 = ts_plugin_0.FISHER_PEARSON_G1_SKEWNESS_0
self.GALTON_SKEWNESS_0 = ts_plugin_0.GALTON_SKEWNESS_0
self.KURTOSIS_0 = ts_plugin_0.KURTOSIS_0
self.ENTROPY_0 = ts_plugin_0.ENTROPY_0
self.SCALED_ENTROPY_0 = ts_plugin_0.SCALED_ENTROPY_0
self.HURST_EXPONENT_0 = ts_plugin_0.HURST_EXPONENT_0
self.BENFORD_LAW_PRESENTED_0 = ts_plugin_0.BENFORD_LAW_PRESENTED_0
self.P_BENFORD_0 = ts_plugin_0.P_BENFORD_0
self.NORMAL_DISTRIBUTION_0 = ts_plugin_0.NORMAL_DISTRIBUTION_0
self.CNT_DISTRIBUTION_0 = ts_plugin_0.CNT_DISTRIBUTION_0
self.TIME_DISTRIBUTION_0 = ts_plugin_0.TIME_DISTRIBUTION_0
self.AREA_VALUES_DISTRIBUTION_0 = ts_plugin_0.AREA_VALUES_DISTRIBUTION_0
self.MEAN_SCALED_TIME_0 = ts_plugin_0.MEAN_SCALED_TIME_0
self.MEDIAN_SCALED_TIME_0 = ts_plugin_0.MEDIAN_SCALED_TIME_0
self.Q1_SCALED_TIME_0 = ts_plugin_0.Q1_SCALED_TIME_0
self.Q3_SCALED_TIME_0 = ts_plugin_0.Q3_SCALED_TIME_0
self.DURATION_0 = ts_plugin_0.DURATION_0
self.MEAN_DIFFTIMES_0 = ts_plugin_0.MEAN_DIFFTIMES_0
self.MEDIAN_DIFFTIMES_0 = ts_plugin_0.MEDIAN_DIFFTIMES_0
self.MIN_DIFFTIMES_0 = ts_plugin_0.MIN_DIFFTIMES_0
self.MAX_DIFFTIMES_0 = ts_plugin_0.MAX_DIFFTIMES_0
self.MEAN_SCALED_DIFFTIMES_0 = ts_plugin_0.MEAN_SCALED_DIFFTIMES_0
self.SIG_SPACES_0 = ts_plugin_0.SIG_SPACES_0
self.SWITCHING_METRIC_0 = ts_plugin_0.SWITCHING_METRIC_0
self.TRANSIENTS_0 = ts_plugin_0.TRANSIENTS_0
self.CNT_ZEROS_0 = ts_plugin_0.CNT_ZEROS_0
self.CNT_NZ_DISTRIBUTION_0 = ts_plugin_0.CNT_NZ_DISTRIBUTION_0
self.BIGGEST_CNT_1_SEC_0 = ts_plugin_0.BIGGEST_CNT_1_SEC_0
self.PERIODICITY_0 = ts_plugin_0.PERIODICITY_0
self.VAL_0 = ts_plugin_0.VAL_0
self.TIME_0 = ts_plugin_0.TIME_0
def extend_with_1_direction(self, ts_plugin_1):
self.MEDIAN_1 = ts_plugin_1.MEDIAN
self.STDEV_1 = ts_plugin_1.STDEV
self.VAR_1 = ts_plugin_1.VAR
self.BURSTINESS_1 = ts_plugin_1.BURSTINESS
self.Q1_1 = ts_plugin_1.Q1
self.Q3_1 = ts_plugin_1.Q3
self.MIN_1 = ts_plugin_1.MIN
self.MAX_1 = ts_plugin_1.MAX
self.MIN_MINUS_MAX_1 = ts_plugin_1.MIN_MINUS_MAX
self.MODE_1 = ts_plugin_1.MODE
self.COEFFICIENT_OF_VARIATION_1 = ts_plugin_1.COEFFICIENT_OF_VARIATION
self.AVERAGE_DISPERSION_1 = ts_plugin_1.AVERAGE_DISPERSION
self.PERCENT_DEVIATION_1 = ts_plugin_1.PERCENT_DEVIATION
self.ROOT_MEAN_SQUARE_1 = ts_plugin_1.ROOT_MEAN_SQUARE
self.PERCENT_BELOW_MEAN_1 = ts_plugin_1.PERCENT_BELOW_MEAN
self.PERCENT_ABOVE_MEAN_1 = ts_plugin_1.PERCENT_ABOVE_MEAN
self.PEARSON_SK1_SKEWNESS_1 = ts_plugin_1.PEARSON_SK1_SKEWNESS
self.PEARSON_SK2_SKEWNESS_1 = ts_plugin_1.PEARSON_SK2_SKEWNESS
self.FISHER_MI_3_SKEWNESS_1 = ts_plugin_1.FISHER_MI_3_SKEWNESS
self.FISHER_PEARSON_g1_SKEWNESS_1 = ts_plugin_1.FISHER_PEARSON_g1_SKEWNESS
self.FISHER_PEARSON_G1_SKEWNESS_1 = ts_plugin_1.FISHER_PEARSON_G1_SKEWNESS
self.GALTON_SKEWNESS_1 = ts_plugin_1.GALTON_SKEWNESS
self.KURTOSIS_1 = ts_plugin_1.KURTOSIS
self.ENTROPY_1 = ts_plugin_1.ENTROPY
self.SCALED_ENTROPY_1 = ts_plugin_1.SCALED_ENTROPY
self.HURST_EXPONENT_1 = ts_plugin_1.HURST_EXPONENT
self.BENFORD_LAW_PRESENTED_1 = ts_plugin_1.BENFORD_LAW_PRESENTED
self.P_BENFORD_1 = ts_plugin_1.P_BENFORD
self.NORMAL_DISTRIBUTION_1 = ts_plugin_1.NORMAL_DISTRIBUTION
self.CNT_DISTRIBUTION_1 = ts_plugin_1.CNT_DISTRIBUTION
self.TIME_DISTRIBUTION_1 = ts_plugin_1.TIME_DISTRIBUTION
self.AREA_VALUES_DISTRIBUTION_1 = ts_plugin_1.AREA_VALUES_DISTRIBUTION
self.MEAN_SCALED_TIME_1 = ts_plugin_1.MEAN_SCALED_TIME
self.MEDIAN_SCALED_TIME_1 = ts_plugin_1.MEDIAN_SCALED_TIME
self.Q1_SCALED_TIME_1 = ts_plugin_1.Q1_SCALED_TIME
self.Q3_SCALED_TIME_1 = ts_plugin_1.Q3_SCALED_TIME
self.DURATION_1 = ts_plugin_1.DURATION
self.MEAN_DIFFTIMES_1 = ts_plugin_1.MEAN_DIFFTIMES
self.MEDIAN_DIFFTIMES_1 = ts_plugin_1.MEDIAN_DIFFTIMES
self.MIN_DIFFTIMES_1 = ts_plugin_1.MIN_DIFFTIMES
self.MAX_DIFFTIMES_1 = ts_plugin_1.MAX_DIFFTIMES
self.MEAN_SCALED_DIFFTIMES_1 = ts_plugin_1.MEAN_SCALED_DIFFTIMES
self.SIG_SPACES_1 = ts_plugin_1.SIG_SPACES
self.SWITCHING_METRIC_1 = ts_plugin_1.SWITCHING_METRIC
self.TRANSIENTS_1 = ts_plugin_1.TRANSIENTS
self.CNT_ZEROS_1 = ts_plugin_1.CNT_ZEROS
self.CNT_NZ_DISTRIBUTION_1 = ts_plugin_1.CNT_NZ_DISTRIBUTION
self.BIGGEST_CNT_1_SEC_1 = ts_plugin_1.BIGGEST_CNT_1_SEC
self.PERIODICITY_1 = ts_plugin_1.PERIODICITY
self.VAL_1 = ts_plugin_1.VAL
self.TIME_1 = ts_plugin_1.TIME
def export(self):
return [
self.DST_IP,
self.SRC_IP,
self.PACKETS,
self.PACKETS_REV,
self.BYTES,
self.BYTES_REV,
self.TIME_FIRST,
self.TIME_LAST,
self.DST_PORT,
self.SRC_PORT,
self.MEAN,
self.MEDIAN,
self.STDEV,
self.VAR,
self.BURSTINESS,
self.Q1,
self.Q3,
self.MIN,
self.MAX,
self.MIN_MINUS_MAX,
self.MODE,
self.COEFFICIENT_OF_VARIATION,
self.AVERAGE_DISPERSION,
self.PERCENT_DEVIATION,
self.ROOT_MEAN_SQUARE,
self.PERCENT_BELOW_MEAN,
self.PERCENT_ABOVE_MEAN,
self.PEARSON_SK1_SKEWNESS,
self.PEARSON_SK2_SKEWNESS,
self.FISHER_MI_3_SKEWNESS,
self.FISHER_PEARSON_g1_SKEWNESS,
self.FISHER_PEARSON_G1_SKEWNESS,
self.GALTON_SKEWNESS,
self.KURTOSIS,
self.ENTROPY,
self.SCALED_ENTROPY,
self.HURST_EXPONENT,
self.BENFORD_LAW_PRESENTED,
self.P_BENFORD,
self.NORMAL_DISTRIBUTION,
self.CNT_DISTRIBUTION,
self.TIME_DISTRIBUTION,
self.AREA_VALUES_DISTRIBUTION,
self.MEAN_SCALED_TIME,
self.MEDIAN_SCALED_TIME,
self.Q1_SCALED_TIME,
self.Q3_SCALED_TIME,
self.DURATION,
self.MEAN_DIFFTIMES,
self.MEDIAN_DIFFTIMES,
self.MIN_DIFFTIMES,
self.MAX_DIFFTIMES,
self.MEAN_SCALED_DIFFTIMES,
self.SIG_SPACES,
self.SWITCHING_METRIC,
self.TRANSIENTS,
self.CNT_ZEROS,
self.CNT_NZ_DISTRIBUTION,
self.BIGGEST_CNT_1_SEC,
self.DIRECTIONS,
self.PERIODICITY,
self.VAL,
self.TIME,
self.MIN_POWER,
self.MAX_POWER,
self.MIN_POWER_FREQ,
self.MAX_POWER_FREQ,
self.POWER_MEAN,
self.POWER_STD,
self.POWER_MODE,
self.SPECTRAL_ENERGY,
self.SPECTRAL_ENTROPY,
self.SPECTRAL_KURTOSIS,
self.SPECTRAL_SKEWNESS,
self.SPECTRAL_ROLLOFF,
self.SPECTRAL_CENTROID,
self.SPECTRAL_SPREAD,
self.SPECTRAL_SLOPE,
self.SPECTRAL_CREST,
self.SPECTRAL_FLUX,
self.SPECTRAL_BANDWIDTH,
self.PERIODICITY_SCDF,
# self.MEAN_0,
# self.MEDIAN_0,
# self.STDEV_0,
# self.VAR_0,
# self.BURSTINESS_0,
# self.Q1_0,
# self.Q3_0,
# self.MIN_0,
# self.MAX_0,
# self.MIN_MINUS_MAX_0,
# self.MODE_0,
# self.COEFFICIENT_OF_VARIATION_0,
# self.AVERAGE_DISPERSION_0,
# self.PERCENT_DEVIATION_0,
# self.ROOT_MEAN_SQUARE_0,
# self.PERCENT_BELOW_MEAN_0,
# self.PERCENT_ABOVE_MEAN_0,
# self.PEARSON_SK1_SKEWNESS_0,
# self.PEARSON_SK2_SKEWNESS_0,
# self.FISHER_MI_3_SKEWNESS_0,
# self.FISHER_PEARSON_g1_SKEWNESS_0,
# self.FISHER_PEARSON_G1_SKEWNESS_0,
# self.GALTON_SKEWNESS_0,
# self.KURTOSIS_0,
# self.ENTROPY_0,
# self.SCALED_ENTROPY_0,
# self.HURST_EXPONENT_0,
# self.BENFORD_LAW_PRESENTED_0,
# self.P_BENFORD_0,
# self.NORMAL_DISTRIBUTION_0,
# self.CNT_DISTRIBUTION_0,
# self.TIME_DISTRIBUTION_0,
# self.AREA_VALUES_DISTRIBUTION_0,
# self.MEAN_SCALED_TIME_0,
# self.MEDIAN_SCALED_TIME_0,
# self.Q1_SCALED_TIME_0,
# self.Q3_SCALED_TIME_0,
# self.DURATION_0,
# self.MEAN_DIFFTIMES_0,
# self.MEDIAN_DIFFTIMES_0,
# self.MIN_DIFFTIMES_0,
# self.MAX_DIFFTIMES_0,
# self.MEAN_SCALED_DIFFTIMES_0,
# self.SIG_SPACES_0,
# self.SWITCHING_METRIC_0,
# self.TRANSIENTS_0,
# self.CNT_ZEROS_0,
# self.CNT_NZ_DISTRIBUTION_0,
# self.BIGGEST_CNT_1_SEC_0,
# self.PERIODICITY_0,
# self.VAL_0,
# self.TIME_0,
# self.MEAN_1,
# self.MEDIAN_1,
# self.STDEV_1,
# self.VAR_1,
# self.BURSTINESS_1,
# self.Q1_1,
# self.Q3_1,
# self.MIN_1,
# self.MAX_1,
# self.MIN_MINUS_MAX_1,
# self.MODE_1,
# self.COEFFICIENT_OF_VARIATION_1,
# self.AVERAGE_DISPERSION_1,
# self.PERCENT_DEVIATION_1,
# self.ROOT_MEAN_SQUARE_1,
# self.PERCENT_BELOW_MEAN_1,
# self.PERCENT_ABOVE_MEAN_1,
# self.PEARSON_SK1_SKEWNESS_1,
# self.PEARSON_SK2_SKEWNESS_1,
# self.FISHER_MI_3_SKEWNESS_1,
# self.FISHER_PEARSON_g1_SKEWNESS_1,
# self.FISHER_PEARSON_G1_SKEWNESS_1,
# self.GALTON_SKEWNESS_1,
# self.KURTOSIS_1,
# self.ENTROPY_1,
# self.SCALED_ENTROPY_1,
# self.HURST_EXPONENT_1,
# self.BENFORD_LAW_PRESENTED_1,
# self.P_BENFORD_1,
# self.NORMAL_DISTRIBUTION_1,
# self.CNT_DISTRIBUTION_1,
# self.TIME_DISTRIBUTION_1,
# self.AREA_VALUES_DISTRIBUTION_1,
# self.MEAN_SCALED_TIME_1,
# self.MEDIAN_SCALED_TIME_1,
# self.Q1_SCALED_TIME_1,
# self.Q3_SCALED_TIME_1,
# self.DURATION_1,
# self.MEAN_DIFFTIMES_1,
# self.MEDIAN_DIFFTIMES_1,
# self.MIN_DIFFTIMES_1,
# self.MAX_DIFFTIMES_1,
# self.MEAN_SCALED_DIFFTIMES_1,
# self.SIG_SPACES_1,
# self.SWITCHING_METRIC_1,
# self.TRANSIENTS_1,
# self.CNT_ZEROS_1,
# self.CNT_NZ_DISTRIBUTION_1,
# self.BIGGEST_CNT_1_SEC_1,
# self.PERIODICITY_1,
# self.VAL_1,
# self.TIME_1,
]
HEADER = [
"DST_IP",
"SRC_IP",
"PACKETS",
"PACKETS_REV",
"BYTES",
"BYTES_REV",
"TIME_FIRST",
"TIME_LAST",
"DST_PORT",
"SRC_PORT",
"MEAN",
"MEDIAN",
"STDEV",
"VAR",
"BURSTINESS",
"Q1",
"Q3",
"MIN",
"MAX",
"MIN_MINUS_MAX",
"MODE",
"COEFFICIENT_OF_VARIATION",
"AVERAGE_DISPERSION",
"PERCENT_DEVIATION",
"ROOT_MEAN_SQUARE",
"PERCENT_BELOW_MEAN",
"PERCENT_ABOVE_MEAN",
"PEARSON_SK1_SKEWNESS",
"PEARSON_SK2_SKEWNESS",
"FISHER_MI_3_SKEWNESS",
"FISHER_PEARSON_g1_SKEWNESS",
"FISHER_PEARSON_G1_SKEWNESS",
"GALTON_SKEWNESS",
"KURTOSIS",
"ENTROPY",
"SCALED_ENTROPY",
"HURST_EXPONENT",
"BENFORD_LAW_PRESENTED",
"P_BENFORD",
"NORMAL_DISTRIBUTION",
"CNT_DISTRIBUTION",
"TIME_DISTRIBUTION",
"AREA_VALUES_DISTRIBUTION",
"MEAN_SCALED_TIME",
"MEDIAN_SCALED_TIME",
"Q1_SCALED_TIME",
"Q3_SCALED_TIME",
"DURATION",
"MEAN_DIFFTIMES",
"MEDIAN_DIFFTIMES",
"MIN_DIFFTIMES",
"MAX_DIFFTIMES",
"MEAN_SCALED_DIFFTIMES",
"SIG_SPACES",
"SWITCHING_METRIC",
"TRANSIENTS",
"CNT_ZEROS",
"CNT_NZ_DISTRIBUTION",
"BIGGEST_CNT_1_SEC",
"DIRECTIONS",
"PERIODICITY",
"VAL",
"TIME",
"MIN_POWER",
"MAX_POWER",
"MIN_POWER_FREQ",
"MAX_POWER_FREQ",
"POWER_MEAN",
"POWER_STD",
"POWER_MODE",
"SPECTRAL_ENERGY",
"SPECTRAL_ENTROPY",
"SPECTRAL_KURTOSIS",
"SPECTRAL_SKEWNESS",
"SPECTRAL_ROLLOFF",
"SPECTRAL_CENTROID",
"SPECTRAL_SPREAD",
"SPECTRAL_SLOPE",
"SPECTRAL_CREST",
"SPECTRAL_FLUX",
"SPECTRAL_BANDWIDTH",
"PERIODICITY_SCDF",
# "MEAN_0",
# "MEDIAN_0",
# "STDEV_0",
# "VAR_0",
# "BURSTINESS_0",
# "Q1_0",
# "Q3_0",
# "MIN_0",
# "MAX_0",
# "MIN_MINUS_MAX_0",
# "MODE_0",
# "COEFFICIENT_OF_VARIATION_0",
# "AVERAGE_DISPERSION_0",
# "PERCENT_DEVIATION_0",
# "ROOT_MEAN_SQUARE_0",
# "PERCENT_BELOW_MEAN_0",
# "PERCENT_ABOVE_MEAN_0",
# "PEARSON_SK1_SKEWNESS_0",
# "PEARSON_SK2_SKEWNESS_0",
# "FISHER_MI_3_SKEWNESS_0",
# "FISHER_PEARSON_g1_SKEWNESS_0",
# "FISHER_PEARSON_G1_SKEWNESS_0",
# "GALTON_SKEWNESS_0",
# "KURTOSIS_0",
# "ENTROPY_0",
# "SCALED_ENTROPY_0",
# "HURST_EXPONENT_0",
# "BENFORD_LAW_PRESENTED_0",
# "P_BENFORD_0",
# "NORMAL_DISTRIBUTION_0",
# "CNT_DISTRIBUTION_0",
# "TIME_DISTRIBUTION_0",
# "AREA_VALUES_DISTRIBUTION_0",
# "MEAN_SCALED_TIME_0",
# "MEDIAN_SCALED_TIME_0",
# "Q1_SCALED_TIME_0",
# "Q3_SCALED_TIME_0",
# "DURATION_0",
# "MEAN_DIFFTIMES_0",
# "MEDIAN_DIFFTIMES_0",
# "MIN_DIFFTIMES_0",
# "MAX_DIFFTIMES_0",
# "MEAN_SCALED_DIFFTIMES_0",
# "SIG_SPACES_0",
# "SWITCHING_METRIC_0",
# "TRANSIENTS_0",
# "CNT_ZEROS_0",
# "CNT_NZ_DISTRIBUTION_0",
# "BIGGEST_CNT_1_SEC_0",
# "PERIODICITY_0",
# "VAL_0",
# "TIME_0",
# "MEAN_1",
# "MEDIAN_1",
# "STDEV_1",
# "VAR_1",
# "BURSTINESS_1",
# "Q1_1",
# "Q3_1",
# "MIN_1",
# "MAX_1",
# "MIN_MINUS_MAX_1",
# "MODE_1",
# "COEFFICIENT_OF_VARIATION_1",
# "AVERAGE_DISPERSION_1",
# "PERCENT_DEVIATION_1",
# "ROOT_MEAN_SQUARE_1",
# "PERCENT_BELOW_MEAN_1",
# "PERCENT_ABOVE_MEAN_1",
# "PEARSON_SK1_SKEWNESS_1",
# "PEARSON_SK2_SKEWNESS_1",
# "FISHER_MI_3_SKEWNESS_1",
# "FISHER_PEARSON_g1_SKEWNESS_1",
# "FISHER_PEARSON_G1_SKEWNESS_1",
# "GALTON_SKEWNESS_1",
# "KURTOSIS_1",
# "ENTROPY_1",
# "SCALED_ENTROPY_1",
# "HURST_EXPONENT_1",
# "BENFORD_LAW_PRESENTED_1",
# "P_BENFORD_1",
# "NORMAL_DISTRIBUTION_1",
# "CNT_DISTRIBUTION_1",
# "TIME_DISTRIBUTION_1",
# "AREA_VALUES_DISTRIBUTION_1",
# "MEAN_SCALED_TIME_1",
# "MEDIAN_SCALED_TIME_1",
# "Q1_SCALED_TIME_1",
# "Q3_SCALED_TIME_1",
# "DURATION_1",
# "MEAN_DIFFTIMES_1",
# "MEDIAN_DIFFTIMES_1",
# "MIN_DIFFTIMES_1",
# "MAX_DIFFTIMES_1",
# "MEAN_SCALED_DIFFTIMES_1",
# "SIG_SPACES_1",
# "SWITCHING_METRIC_1",
# "TRANSIENTS_1",
# "CNT_ZEROS_1",
# "CNT_NZ_DISTRIBUTION_1",
# "BIGGEST_CNT_1_SEC_1",
# "PERIODICITY_1",
# "VAL_1",
# "TIME_1",
]
INACTIVE_TIMEOUT = 65
ACTIVE_TIMEOUT = 300
T = 300 # duration of time series in seconds
Pmin = 1 # minimum period in seconds
Pmax = T/2 # maximum period in seconds
fmin = 1/Pmax # minimum frequency in Hz
fmax = 1/Pmin # maximum frequency in Hz
N = 5000 # frequency resolution -- This will depend on the desired precision of the periodogram and the amount of computational resources you have available.
# fmin = 0 # minimum frequency in Hz
# fmax = 1 # maximum frequency in Hz
df = (fmax - fmin)/N # frequency resolution
FREQUENCY = np.arange(fmin, fmax, df)
# statistics features
def get_basic_stats(data: np.ndarray, plugin: TimeSeriesPlugin):
"""Compute basic statistical features.
Args:
data (np.array): Time series data.
plugin (TimeSeriesPlugin): Class TimeSeriesPlugin that contains records for save plugin export items.
"""
plugin.MEAN = statistics.mean(data)
plugin.MEDIAN = statistics.median(data)
if len(data) == 1:
plugin.STDEV = data[0]
elif len(data) == 0:
plugin.STDEV = 0 # type: ignore
else:
try:
plugin.STDEV = statistics.stdev(data)
except:
plugin.STDEV = statistics.stdev(data[:1000])
if len(data) < 2:
plugin.VAR = 0
else:
plugin.VAR = statistics.variance(data, xbar=plugin.MEAN)
plugin.BURSTINESS = (plugin.STDEV - plugin.MEAN) / (plugin.STDEV + plugin.MEAN)
plugin.MODE = np.bincount(data).argmax() # type: ignore
# mode is most frequent value of data
plugin.Q1 = np.percentile(data, 25) # type: ignore
plugin.Q3 = np.percentile(data, 75) # type: ignore
if plugin.MEAN == 0:
plugin.COEFFICIENT_OF_VARIATION = 0
else:
plugin.COEFFICIENT_OF_VARIATION = (plugin.STDEV / plugin.MEAN) * 100
plugin.MIN = data.min()
plugin.MAX = data.max()
plugin.MIN_MINUS_MAX = plugin.MAX - plugin.MIN
new_data = []
for d in data:
new_data.append(abs(d - plugin.MEAN))
plugin.AVERAGE_DISPERSION = statistics.mean(new_data)
if plugin.MEAN == 0:
plugin.PERCENT_DEVIATION = 0
else:
plugin.PERCENT_DEVIATION = (plugin.AVERAGE_DISPERSION / plugin.MEAN) * 100
if len(data) == 0:
plugin.ROOT_MEAN_SQUARE = 0
else:
plugin.ROOT_MEAN_SQUARE = 0 # type: ignore
for d in data:
plugin.ROOT_MEAN_SQUARE += math.pow(d, 2) # type: ignore
plugin.ROOT_MEAN_SQUARE *= 1 / len(data) # type: ignore
plugin.ROOT_MEAN_SQUARE = math.sqrt(plugin.ROOT_MEAN_SQUARE) # type: ignore
plugin.PERCENT_BELOW_MEAN = (data < plugin.MEAN).sum() / len(data)
plugin.PERCENT_ABOVE_MEAN = (data > plugin.MEAN).sum() / len(data)
def get_entropy(data: np.ndarray, plugin: TimeSeriesPlugin):
"""Compute statistical feature called Entropy that is a scientific concept as well as
a measurable physical property that is most commonly associated with a state of disorder,
randomness, or uncertainty. And than scaled entropy, that is scaled by maximum entropy
to be comparable with another results.
Args:
data (np.array): Time series data.
plugin (TimeSeriesPlugin): Class TimeSeriesPlugin that contains records for save plugin export items.
"""
N = len(data)
if N == 0:
return
p = {}
for d in data:
if d not in p:
p[d] = 0
p[d] += 1
plugin.ENTROPY = 0 # type: ignore
for d in p:
prob = p[d] / N
plugin.ENTROPY += prob * math.log2(prob)
if plugin.ENTROPY != 0:
plugin.ENTROPY = -plugin.ENTROPY
if N == 1:
plugin.SCALED_ENTROPY = 0 # type: ignore
else:
plugin.SCALED_ENTROPY = plugin.ENTROPY / (-math.log2(1 / N)) # type: ignore
def get_skewness(data: np.ndarray, hist_data: dict, plugin: TimeSeriesPlugin):
"""Compute statistic feature called Skewness that is a measure of the asymmetry of
the probability distribution of a real-valued random variable about its mean. The
skewness value can be positive, zero, negative, or undefined.
Args:
data (np.array): Time series data.
plugin (TimeSeriesPlugin): Class TimeSeriesPlugin that contains records for save plugin export items.
"""
# Pearson's Skewness formula:
# sk1 = (X_ - Mo) / s, where X_ is mean, Mo is mode and s is standard deviation
# sk2 = (3*X_ - Md) / s, where X_ is mean, Md is median and s is standard deviation
if plugin.STDEV == 0:
plugin.PEARSON_SK1_SKEWNESS = 0
plugin.PEARSON_SK2_SKEWNESS = 0
plugin.FISHER_MI_3_SKEWNESS = 0
plugin.FISHER_PEARSON_g1_SKEWNESS = 0
plugin.FISHER_PEARSON_G1_SKEWNESS = 0
plugin.GALTON_SKEWNESS = 0
return
plugin.PEARSON_SK1_SKEWNESS = (plugin.MEAN - plugin.MODE) / plugin.STDEV # type: ignore
plugin.PEARSON_SK2_SKEWNESS = (3 * plugin.MEAN - plugin.MEDIAN) / plugin.STDEV # type: ignore
# Fisher's moment coefficient of skewness:
# mi_3 = E[ ((X - X_)/ s)^3 ], where X is random variable, X_ is mean, s is standard deviation and E is expectation operator
# mi_3 = E[ ((X - X_)/ s)^3 ] = (E[X^3] - 3*X_*s^2 - X_^3)/(s^3) = (((x1^3)*p1 + (x2^3)*p2 + ... + (xk^3)*pk) - 3*X_*s^2 - X_^3)/(s^3)
EX = 0
N = len(data)
for d in hist_data:
EX += math.pow(d, 3) * hist_data[d] / N
plugin.FISHER_MI_3_SKEWNESS = (
EX - 3 * plugin.MEAN * math.pow(plugin.STDEV, 2) - math.pow(plugin.MEAN, 3) # type: ignore
) / (
math.pow(plugin.STDEV, 3) # type: ignore
)
# Fisher-Pearson skewness coeficient:
# g1 = (SUM_i_n[(x_i - X_)^3/n]) / s^3
sum_g1 = 0
for d in data:
sum_g1 += math.pow((d - plugin.MEAN), 3) / N
plugin.FISHER_PEARSON_g1_SKEWNESS = sum_g1 / math.pow(plugin.STDEV, 3) # type: ignore
# Adjusted Fisher-Pearson skewness coeficient:
# G1 = \frac{5}{n\sigma^3} \sum_{i=1}^{n}\frac{(x_i - \mu)^3}{(n-1)(n-2)} - \frac{3(n-1)}{(n-2)}\left(\frac{\sum_{i=1}^{n}(x_i - \mu)^2}{n\sigma^2}\right)^{\frac{3}{2}} \)
if N - 2 == 0:
plugin.FISHER_PEARSON_G1_SKEWNESS = 0
else:
sum_G1_1 = 0
for d in data:
sum_G1_1 += math.pow((d - plugin.MEAN), 3) / ((N-1)*(N-2))
sum_G1_2 = 0
for d in data:
sum_G1_2 += math.pow((d - plugin.MEAN), 2)
plugin.FISHER_PEARSON_G1_SKEWNESS = 5 / (N*plugin.STDEV) * sum_G1_1 - ((3*(N-1)) / (N-2)) * math.pow((N*math.pow(plugin.STDEV, 2)), 3/2)
# ((math.sqrt(N * (N - 1))) / (N - 2)) * plugin.FISHER_PEARSON_g1_SKEWNESS # type: ignore
# Galton skewness:
# gq = (Q1 + Q3 - 2*Q2) / (Q3 - Q1), where Q1 is the lower quartile, Q3 is the upper quartile, and Q2 is the median.
if plugin.Q3 - plugin.Q1 == 0: # type: ignore
plugin.GALTON_SKEWNESS = 0
else:
plugin.GALTON_SKEWNESS = (plugin.Q1 + plugin.Q3 - 2 * plugin.MEAN) / ( # type: ignore
plugin.Q3 - plugin.Q1 # type: ignore
)
def get_kurtosis(data: np.ndarray, plugin: TimeSeriesPlugin):
"""Compute statistic feature called Kurtosis that is a measure of the "tailedness"
of the probability distribution of a real-valued random variable. Like skewness,
kurtosis describes the shape of a probability distribution and there are different
ways of quantifying it for a theoretical distribution and corresponding ways of
estimating it from a sample from a population. Different measures of kurtosis may
have different interpretations.
Args:
data (np.array): Time series data.
plugin (TimeSeriesPlugin): Class TimeSeriesPlugin that contains records for save plugin export items.
"""
# kurtosis = ( SUM_i_n (x_i - x_)^4 ) / ( n * s^4 ), where x_ is mean, s is standard deviation
numerator = 0
for d in data:
numerator += math.pow(d - plugin.MEAN, 4)
denominator = len(data) * math.pow(plugin.STDEV, 4) # type: ignore
if denominator == 0:
plugin.KURTOSIS = 0
else:
plugin.KURTOSIS = numerator / denominator # type: ignore
# hurst exponent
def get_partial_ts(ts: np.ndarray, length=5):
partial_ts = {}
for i in range(1, length):
n = int(len(ts) / i)
if n == 0:
break
partial_ts[n] = []
for k in range(int(len(ts) / n)):
partial_ts[n].append(np.array(ts[k * n : (k + 1) * n]))
return partial_ts
def get_R_S(data: np.ndarray):
mean = data.mean()
Y = data - mean
Z = np.cumsum(Y)
R = Z.max() - Z.min()
S = np.std(data)
if R == 0 or S == 0:
return 0
return R / S
def get_avarage_R_S(partial_ts: dict):
sums_bytes = 0
n = len(partial_ts)
for ts in partial_ts:
sums_bytes += get_R_S(ts)
return sums_bytes / n
def get_hurst_exponents(partial_ts: dict):
"""Create Anis-Lloyd correlated R/S Hurst exponent."""
log_ns = []
log_R_Ss_bytes = []
for n in partial_ts:
avarage_R_S_bytes = get_avarage_R_S(partial_ts[n])
if avarage_R_S_bytes == 0:
continue
E_R_S = 0
for i in range(1, n):
E_R_S += (n - i) / i
if n > 340:
E_R_S *= 1 / math.sqrt(n * math.pi / 2)
else:
E_R_S *= (gamma((n - 1) / 2)) / (math.sqrt(n) * gamma(n / 2))
log_ns.append(n)
log_R_Ss_bytes.append(abs(avarage_R_S_bytes - E_R_S))
if len(log_ns) == 0:
return 1
slope_bytes, intercept = np.polyfit(log_ns, log_R_Ss_bytes, 1)
return 0.5 + slope_bytes
def perform_getting_hurst_exponent(bytes: np.ndarray, plugin: TimeSeriesPlugin):
partial_ts = get_partial_ts(bytes)
plugin.HURST_EXPONENT = get_hurst_exponents(partial_ts)
# distribution of number of data points values in time series
def is_benford_law_present(
data: np.ndarray, hist_data: dict, plugin: TimeSeriesPlugin, THRESHOLD: float = 0.05
):
"""Benford's law says that in sets that obey the law, the number 1 appears as the leading significant
digit about 30 percent of the time, while 9 appears as the leading significant digit less than 5 percent
of the time. Benford's law also makes predictions about the distribution of second digits, third digits,
digit combinations, and so on.
In this function we try check if Benford's law is present in our data.
Args: