使用 Swift 对增长的时间序列进行峰值检测 [英] peak detection for growing time series using Swift

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本文介绍了使用 Swift 对增长的时间序列进行峰值检测的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！

问题描述

有没有人有一个好的算法来使用 Swift (v3) 测量增长的时间序列数据中的峰值?因此，在数据流入时检测峰值.

例如

样本数据集(上一个系列的总结):

让样本 = [0.01, -0.02, -0.02, 0.01, -0.01, -0.01, 0.00, 0.10, 0.31,-0.10, -0.73, -0.68, 0.21, 1.22, 0.67, -0.59, -1.04, 0.06, 0.42, 0.07,0.03, -0.18, 0.11, -0.06, -0.02, 0.16, 0.21, 0.03, -0.68, -0.89, 0.18,1.31、0.66、0.07、-1.62、-0.16、0.67、0.19、-0.42、0.23、-0.05、-0.01、0.03、0.06、0.27、0.15、-0.50、-1.18、0.11、1.30、0.93、0.16、-1.32、-0.10, 0.55, 0.23, -0.03, -0.23, 0.16, -0.04, 0.01, 0.12, 0.35, -0.38,-1.11, 0.07, 1.46, 0.61, -0.68, -1.16, 0.29, 0.54, -0.05, 0.02, -0.01,0.12、0.23、0.29、-0.75、-0.95、0.11、1.51、0.70、-0.30、-1.48、0.13、0.50, 0.18, -0.06, -0.01, -0.02, 0.03, -0.02, 0.06, 0.03, 0.03, 0.02,-0.01, 0.01, 0.02, 0.01]

更新:感谢 Jean-Paul 提供

完整数据集(应产生 25 个峰值):

让样本 = [-1.38, -0.97, -1.20, -2.06, -2.26, -0.99, 0.11, -0.47, -0.95, -2.61, -0.88, -0.74, -1.12, -1.19, -1.12, -1.04, -0.72, -1.21, -2.61, -1.41, -0.23, -0.27, -0.43, -1.77, -2.75, -0.61, -0.73, -1.53​​, -1.02, -1.14, -1.12，-1.06，-0.78，-0.72，-2.41，-1.55，-0.01，-0.44，-0.47，-2.02，-1.66，-0.43，-0.93，-1.51，-0.86，-1.06，-1.10，-0.88, -0.84, -1.26, -2.59, -0.92, 0.29, -0.50, -1.31, -2.40, -0.88, -0.56, -1.09, -1.14, -1.09, -0.90, -0.99, -0.84,-0.75, -2.59, -1.34, -0.08, -0.36, -0.50, -1.89, -1.60, -0.55, -0.78, -1.46, -0.96, -0.97, -1.18, -0.98, -1.10, -1.07, -1.06, -1.79, -1.78, -1.54, -1.25, -1.00, -0.46, -0.27, -0.20, -0.15, -0.13, -0.11, -0.13, -0.09, -0.09, -0.05, 0.02, 0.20, -0.31, -1.35, -0.03, 1.34, 0.52, 0.80, -0.91, -1.26, -0.10, -0.10, 0.53, 0.93, 0.60, -0.83, -1.87, -0.21, 1.26, 0.44, 0.86, 0.73, -2.05, -1.66, 0.31, 1.04, 0.72, 0.63, -0.01, -2.14, -0.48, 0.77, 0.63, 0.58, 0.66, -1.01, -1.28, 0.18, 0.44, 0.09, -0.27, -0.06、0.06、-0.18、-0.01、-0.08、-0.07, -0.06, -0.06, -0.07, -0.07, -0.06, -0.05, -0.04, -0.03, -0.02, -0.02, -0.03, -0.03, -0.01, 0.01, 0.00, 0.01, 0.05,0.12, 0.16, 0.25, 0.29, -0.16, -0.69, -1.05, -0.84, -0.54, -0.07, 0.46, 1.12, 1.05, 0.77, 0.68, 0.63, 0.39, -0.96, -1.61, -0.68, -0.14, -0.03, 0.22, 0.31, 0.15, -0.02, 0.11, 0.14, 0.00, 0.04, 0.18, 0.27, 0.14, -0.05, -0.03, -0.08, -0.41, -0.94, -1.03, -0.50, 0.02, 0.52, 1.10, 1.03, 0.79, 0.69, 0.55, -0.34, -1.17, -0.89, -0.54, -0.22, 0.37, 0.47, 0.39, 0.23, 0.00, -0.02, 0.05, 0.10, 0.12, 0.09, -0.12, -0.50, -0.89, -0.89, -0.48, 0.00, 0.43, 1.03, 0.95, 0.67, 0.64, 0.47, -0.07, -0.85, -1.02, -0.73, -0.08, 0.38, 0.46, 0.32, 0.15, 0.01, -0.01, 0.09, 0.20, 0.23, 0.19, 0.12, -0.50, -1.17, -0.97, -0.12, 0.15, 0.70, 1.31, 0.97, 0.45, 0.27, -0.73, -1.00, -0.5, -0.27, 0.10, 0.33, 0.34, 0.23, 0.07, -0.04, -0.27, -0.24, 0.10, 0.21, 0.05, -0.07, 0.04, 0.21, 0.29, 0.16, -0.45, -1.13, -0.93, -0.28, 0.04, 0.72, 1.35, 1.05, 0.56, 0.43, 0.17, -0.59, -1.38, -0.76, 0.10, 0.44,0.46、0.35、0.12、-0.07、-0.05、-0.01、-0.07、-0.04、0.01、0.01、0.06、0.02、-0.03、-0.05、0.00、0.01、-0.02、-0.03、-0.02、-0.01, 0.00, -0.01, 0.00, -0.01, 0.00, -0.01, -0.01, 0.00, 0.01, -0.01, -0.01, 0.00, 0.00, 0.01, 0.01, 0.01, 0.04, 0.06, 0.05, 0.05, 0.04, 0.00, -0.12, -0.16, -0.09, -0.01, 0.14, 0.07, 0.06, 0.00, -0.03, 0.00, 0.06, 0.06, -0.04, -0.11, -0.02, 0.13, 0.18, 0.21, 0.01, -0.31, -0.92, -1.35, -0.62, 0.03, 0.78, 1.36, 1.07, 0.59, 0.75, 0.42, -1.65, -3.16, -0.97, 0.24, 1.44, 1.50, 0.84, 0.47, 0.506, 0.40, -, -2.71, -1.22, 0.01, 1.20, 1.55, 0.92, 0.44, 0.66, 0.73, -0.43, -2.34, -2.28, -0.72, 0.36, 1.41, 1.56, 0.89, 0.54, 0.67, 0.39, -1.7-2.75, -1.07, -0.07, 1.16, 1.65, 0.80, 0.47, 0.73, 0.86, -0.24, -1.52, -1.68, -0.39, 0.02, 0.38, 0.60, 0.49, 0.02, -0.42, -0.31, -0.01、0.08、0.00、-0.07、-0.05、-0.01、-0.02、-0.04、-0.05、-0.02、-0.01、-0.02、-0.02、-0.03、-0.05、-0.04、-0.03、-0.01, -0.01, 0.00, -0.01, 0.00, 0.01, 0.00, 0.00, 0.00, 0.01, 0.01, -0.01, -0.03, -0.02, -0.01, 0.00, 0.00, 0.00, -0.01, 0.01, 0.00, -0.01, 0.02, 0.07, 0.15, 0.28, 0.31, 0.08, -0.26, -0.54, -0.96, -1.08, -0.27, 0.01,0.45, 1.18, 1.07, 0.71, 0.65, 0.20, -0.80, -1.30, -0.74, -0.24, 0.29, 0.47, 0.34, 0.15, 0.02, 0.03, -0.02, -0.16, -0.13, 0.05, 0.09, -0.01, -0.08, -0.06, 0.03, 0.13, 0.19, 0.23, 0.18, 0.10, -0.07, -0.44, -0.91, -1.05, -0.64, -0.08, 0.50, 1.12, 1.35, 0.89, 0.58, 0.54,-0.58, -1.27, -1.20, -0.48, 0.19, 0.62, 0.62, 0.37, -0.01, -0.35, -0.33, 0.07, 0.29, 0.10, -0.14, -0.10, 0.07, 0.07, 0.01, 0.03, 0.09, 0.20, 0.32, 0.26, -0.02, -0.32, -0.78, -1.25, -0.93, -0.16, 0.30, 0.88, 1.40, 1.14, 0.72, 0.48, -0.54, -1.21, -1.13, -0.41, 0.18, 0.51, 0.53, 0.36, 0.11, -0.03, -0.09, -0.28, -0.11, 0.11, 0.15, 0.04, -0.08, -0.04, 0.04, 0.09, 0.16, 0.26, 0.43, 0.09, -0.88, -1.46, -0.64, -0.16, 0.43, 1.37, 1.34, 0.84, 0.52, -0.17, -0.87, -1.22, -0.76, 0.03, 0.47, 0.60, 0.36, 0.04, -0.09, -0.03, 0.02, -0.04,0.04, 0.12, 0.13, 0.19, 0.27, 0.31, 0.18, -0.42, -0.99, -1.13, -0.75,-0.22, 0.50, 1.42, 1.41, 0.98, 0.51, 0.29, -0.69, -1.59, -0.88, -0.13, 0.31, 0.49, 0.46, 0.30, 0.05, -0.08, -0.03, 0.01, -0.04, -0.060.02, 0.03, 0.01, -0.02, 0.01, 0.04, 0.06, 0.04, 0.03, 0.02, 0.03, 0.03, 0.01, -0.01, 0.00, 0.02, 0.00, 0.02, 0.02, 0.02, -0.02，0.02,0.01,0.02,0.04,0.02,0.01,0.02,0.04,0.01,0.01,0.01,0.02,0.01,0.00,0.01,0.01,00.00,0.00,0.01,0.00,0.00,0.01,0.01，0.00,0.02,00.00,0.01,0.01,00.00,0.01,0.01,00.00,000,0.00,0.01,0.01,00. 0.01,00.00,0.01,0.01,0.01,0.01,0.01,0.01,0.00,0.01,0.01,0.01,0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.01, 0.01, 0.01, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00]

因此，我不确定 z-wave 算法是否适合这种数据集.

解决方案

平滑z-score算法翻译成Swift

好吧，为了快速帮助您:这里是算法到 Swift 的翻译:Swift Sandbox 中的演示

警告:我绝不是一个快速的程序员，所以可能会有错误！

另请注意，我已关闭负面信号，因为 OP 的目的我们只想要正面信号.

Swift 代码:

import Glibc//或 Darwin/Foundation/Cocoa/UIKit (取决于操作系统)//计算算术平均值的函数func算术平均值(数组:[双])->双倍的 {var总计:双= 0对于数组中的数字 {总计 += 数量}返回总计/双(array.count)}//计算标准差的函数func standardDeviation(array: [Double]) ->双倍的{让长度 = Double(array.count)让 avg = array.reduce(0, {$0 + $1})/长度让 sumOfSquaredAvgDiff = array.map { pow($0 - avg, 2.0)}.reduce(0, {$0 + $1})返回 sqrt(sumOfSquaredAvgDiff/长度)}//从数组中提取某个范围的函数func subArray<T>(数组: [T], s: Int, e: Int) ->[T] {如果 e >数组.count {返回 []}return Array(array[s..([整数]，[双]，[双]){//创建数组var 信号 = 数组(重复:0，计数:y.count)var filtersY = Array(重复:0.0，计数:y.count)var avgFilter = Array(重复:0.0，计数:y.count)var stdFilter = Array(重复:0.0，计数:y.count)//初始化变量对于我在 0...lag-1 {信号[i] = 0过滤Y[i] = y[i]}//开始过滤avgFilter[lag-1] =算术平均值(数组:subArray(数组:y，s:0，e:lag-1))stdFilter[lag-1] = standardDeviation(array: subArray(array: y, s: 0, e: lag-1))因为我滞后...y.count-1 {如果 abs(y[i] - avgFilter[i-1]) >阈值*stdFilter[i-1] {如果 y[i] >avgFilter[i-1] {信号[i] = 1//正信号} 别的 {//此应用程序关闭负信号//signals[i] = -1//负信号}filtersY[i] = 影响*y[i] + (1-influence)*filteredY[i-1]} 别的 {信号[i] = 0//无信号过滤Y[i] = y[i]}//调整过滤器avgFilter[i] =算术平均值(数组:子数组(数组:filteredY，s:i-lag，e:i))stdFilter[i] = 标准偏差(数组:子数组(数组:filteredY，s:i-lag，e:i))}返回(信号，avgFilter，stdFilter)}//演示让样本 = [0.01, -0.02, -0.02, 0.01, -0.01, -0.01, 0.00, 0.10, 0.31,-0.10, -0.73, -0.68, 0.21, 1.22, 0.67, -0.59, -1.04, 0.06, 0.42, 0.07,0.03, -0.18, 0.11, -0.06, -0.02, 0.16, 0.21, 0.03, -0.68, -0.89, 0.18,1.31、0.66、0.07、-1.62、-0.16、0.67、0.19、-0.42、0.23、-0.05、-0.01、0.03、0.06、0.27、0.15、-0.50、-1.18、0.11、1.30、0.93、0.16、-1.32、-0.10, 0.55, 0.23, -0.03, -0.23, 0.16, -0.04, 0.01, 0.12, 0.35, -0.38,-1.11, 0.07, 1.46, 0.61, -0.68, -1.16, 0.29, 0.54, -0.05, 0.02, -0.01,0.12、0.23、0.29、-0.75、-0.95、0.11、1.51、0.70、-0.30、-1.48、0.13、0.50, 0.18, -0.06, -0.01, -0.02, 0.03, -0.02, 0.06, 0.03, 0.03, 0.02,-0.01, 0.01, 0.02, 0.01]//运行过滤器让(信号，avgFilter，stdFilter)= ThresholdingAlgo(y:样本，滞后:10，阈值:3，影响:0.2)//打印输出到控制台print("
输出:
")对于我在 0...signals.count - 1 {print("数据点(i)		样本:(samples[i])	信号:(signals[i])
")}//用于在 Excel 中创建绘图的原始数据print("
 
 用于在 Excel 中创建绘图的原始数据:
 ")对于我在 0...signals.count - 1 {print("(i+1)	(samples[i])	(signals[i])	(avgFilter[i])	(stdFilter[i])
")}

对于样本数据的结果(对于 lag = 10, threshold = 3, influence = 0.2):

更新

您可以通过对均值和标准差的lag 使用不同的值来提高算法的性能.例如:

//平滑 z 分数阈值过滤器func ThresholdingAlgo(y:[Double]，lagMean:Int，lagStd:Int，阈值:Double，influenceMean:Double，influenceStd:Double)->([整数]，[双]，[双]){//创建数组var 信号 = 数组(重复:0，计数:y.count)var filtersYmean = Array(重复:0.0，计数:y.count)var filtersYstd = Array(重复:0.0，计数:y.count)var avgFilter = Array(重复:0.0，计数:y.count)var stdFilter = Array(重复:0.0，计数:y.count)//初始化变量对于我在 0...lagMean-1 {信号[i] = 0过滤Ymean[i] = y[i]过滤Ystd[i] = y[i]}//开始过滤avgFilter[lagMean-1] =算术平均值(数组:subArray(数组:y，s:0，e:lagMean-1))stdFilter[lagStd-1] = standardDeviation(array: subArray(array: y, s: 0, e: lagStd-1))对于 i in max(lagMean,lagStd)...y.count-1 {如果 abs(y[i] - avgFilter[i-1]) >阈值*stdFilter[i-1] {如果 y[i] >avgFilter[i-1] {信号[i] = 1//正信号} 别的 {信号[i] = -1//负信号}过滤的Ymean[i] = 影响平均*y[i] + (1-影响平均)*过滤的Ymean[i-1]filtersYstd[i] =fluenceStd*y[i] + (1-influenceStd)*filteredYstd[i-1]} 别的 {信号[i] = 0//无信号过滤Ymean[i] = y[i]过滤Ystd[i] = y[i]}//调整过滤器avgFilter[i] =算术平均值(数组:子数组(数组:filteredYmean，s:i-lagMean，e:i))stdFilter[i] = standardDeviation(数组:subArray(数组:filteredYstd，s:i-lagStd，e:i))}返回(信号，avgFilter，stdFilter)}

然后使用例如 let (signals,avgFilter,stdFilter) = ThresholdingAlgo(y: samples, lagMean: 10, lagStd: 100, threshold: 2, impactMean: 0.5, impactStd: 0.1) 可以给出更好的结果:

Would anyone have a good algorithm to measure peaks in growing time series data using Swift (v3)? So, detect peaks as the data is streaming in.

E.g. a Swift version of the smooth z-wave algorithm. That algorithm seems to be suitable.

I would need to detect the peaks as shown below. The data contains positive and negative numbers. Output should be a counter of the peaks, and/or true/false for that specific sample.

Sample dataset (summary of the last series):

let samples = [0.01, -0.02, -0.02, 0.01, -0.01, -0.01, 0.00, 0.10, 0.31,
  -0.10, -0.73, -0.68, 0.21, 1.22, 0.67, -0.59, -1.04, 0.06, 0.42, 0.07, 
  0.03, -0.18, 0.11, -0.06, -0.02, 0.16, 0.21, 0.03, -0.68, -0.89, 0.18, 
  1.31, 0.66, 0.07, -1.62, -0.16, 0.67, 0.19, -0.42, 0.23, -0.05, -0.01,
  0.03, 0.06, 0.27, 0.15, -0.50, -1.18, 0.11, 1.30, 0.93, 0.16, -1.32, 
  -0.10, 0.55, 0.23, -0.03, -0.23, 0.16, -0.04, 0.01, 0.12, 0.35, -0.38,
  -1.11, 0.07, 1.46, 0.61, -0.68, -1.16, 0.29, 0.54, -0.05, 0.02, -0.01,
  0.12, 0.23, 0.29, -0.75, -0.95, 0.11, 1.51, 0.70, -0.30, -1.48, 0.13,
  0.50, 0.18, -0.06, -0.01, -0.02, 0.03, -0.02, 0.06, 0.03, 0.03, 0.02,
  -0.01, 0.01, 0.02, 0.01]

Update: Thanks to Jean-Paul for the initial Swift port. But not sure the z-wave algo is the right one for this dataset. lag=10,threshold=3,influence=0.2 works fine for the last series of the dataset, but I have not been able to find a combination that comes close for the complete dataset.

The issues: with a big lag the first data samples are not included, I need one signal per peak and the algorithm would need further work to be made more efficient.

E.g. result for full dataset, using the Python code, and (e.g.) lag=5,threshold=2.5,influence=0.7 is missing peaks for series 1 and 2, and showing too many false positives in the quiet periods:

Full dataset (should result in 25 peaks):

let samples = [-1.38, -0.97, -1.20, -2.06, -2.26, -0.99, 0.11, -0.47, -0.95, -2.61, -0.88, -0.74, -1.12, -1.19, -1.12, -1.04, -0.72, -1.21, -2.61, -1.41, -0.23, -0.27, -0.43, -1.77, -2.75, -0.61, -0.73, -1.53, -1.02, -1.14, -1.12, -1.06, -0.78, -0.72, -2.41, -1.55, -0.01, -0.44, -0.47, -2.02, -1.66, -0.43, -0.93, -1.51, -0.86, -1.06, -1.10, -0.88, -0.84, -1.26, -2.59, -0.92, 0.29, -0.50, -1.31, -2.40, -0.88, -0.56, -1.09, -1.14, -1.09, -0.90, -0.99, -0.84, -0.75, -2.59, -1.34, -0.08, -0.36, -0.50, -1.89, -1.60, -0.55, -0.78, -1.46, -0.96, -0.97, -1.18, -0.98, -1.10, -1.07, -1.06, -1.79, -1.78, -1.54, -1.25, -1.00, -0.46, -0.27, -0.20, -0.15, -0.13, -0.11, -0.13, -0.09, -0.09, -0.05, 0.02, 0.20, -0.31, -1.35, -0.03, 1.34, 0.52, 0.80, -0.91, -1.26, -0.10, -0.10, 0.53, 0.93, 0.60, -0.83, -1.87, -0.21, 1.26, 0.44, 0.86, 0.73, -2.05, -1.66, 0.31, 1.04, 0.72, 0.63, -0.01, -2.14, -0.48, 0.77, 0.63, 0.58, 0.66, -1.01, -1.28, 0.18, 0.44, 0.09, -0.27, -0.06, 0.06, -0.18, -0.01, -0.08, -0.07, -0.06, -0.06, -0.07, -0.07, -0.06, -0.05, -0.04, -0.03, -0.02, -0.02, -0.03, -0.03, -0.01, 0.01, 0.00, 0.01, 0.05, 0.12, 0.16, 0.25, 0.29, -0.16, -0.69, -1.05, -0.84, -0.54, -0.07, 0.46, 1.12, 1.05, 0.77, 0.68, 0.63, 0.39, -0.96, -1.61, -0.68, -0.14, -0.03, 0.22, 0.31, 0.15, -0.02, 0.11, 0.14, 0.00, 0.04, 0.18, 0.27, 0.14, -0.05, -0.03, -0.08, -0.41, -0.94, -1.03, -0.50, 0.02, 0.52, 1.10, 1.03, 0.79, 0.69, 0.55, -0.34, -1.17, -0.89, -0.54, -0.22, 0.37, 0.47, 0.39, 0.23, 0.00, -0.02, 0.05, 0.10, 0.12, 0.09, 0.05, -0.12, -0.50, -0.89, -0.89, -0.48, 0.00, 0.43, 1.03, 0.95, 0.67, 0.64, 0.47, -0.07, -0.85, -1.02, -0.73, -0.08, 0.38, 0.46, 0.32, 0.15, 0.01, -0.01, 0.09, 0.20, 0.23, 0.19, 0.12, -0.50, -1.17, -0.97, -0.12, 0.15, 0.70, 1.31, 0.97, 0.45, 0.27, -0.73, -1.00, -0.52, -0.27, 0.10, 0.33, 0.34, 0.23, 0.07, -0.04, -0.27, -0.24, 0.10, 0.21, 0.05, -0.07, 0.04, 0.21, 0.29, 0.16, -0.45, -1.13, -0.93, -0.28, 0.04, 0.72, 1.35, 1.05, 0.56, 0.43, 0.17, -0.59, -1.38, -0.76, 0.10, 0.44, 0.46, 0.35, 0.12, -0.07, -0.05, -0.01, -0.07, -0.04, 0.01, 0.01, 0.06, 0.02, -0.03, -0.05, 0.00, 0.01, -0.02, -0.03, -0.02, -0.01, 0.00, -0.01, 0.00, -0.01, 0.00, -0.01, -0.01, 0.00, 0.01, -0.01, -0.01, 0.00, 0.00, 0.01, 0.01, 0.01, 0.04, 0.06, 0.05, 0.05, 0.04, 0.03, 0.00, -0.12, -0.16, -0.09, -0.01, 0.14, 0.07, 0.06, 0.00, -0.03, 0.00, 0.06, 0.06, -0.04, -0.11, -0.02, 0.13, 0.18, 0.21, 0.01, -0.31, -0.92, -1.35, -0.62, 0.03, 0.78, 1.36, 1.07, 0.59, 0.75, 0.42, -1.65, -3.16, -0.97, 0.24, 1.44, 1.50, 0.84, 0.47, 0.56, 0.40, -1.50, -2.71, -1.22, 0.01, 1.20, 1.55, 0.92, 0.44, 0.66, 0.73, -0.43, -2.34, -2.28, -0.72, 0.36, 1.41, 1.56, 0.89, 0.54, 0.67, 0.39, -1.78, -2.75, -1.07, -0.07, 1.16, 1.65, 0.80, 0.47, 0.73, 0.86, -0.24, -1.52, -1.68, -0.39, 0.02, 0.38, 0.60, 0.49, 0.02, -0.42, -0.31, -0.01, 0.08, 0.00, -0.07, -0.05, -0.01, -0.02, -0.04, -0.05, -0.02, -0.01, -0.02, -0.02, -0.03, -0.05, -0.04, -0.03, -0.01, -0.01, 0.00, -0.01, 0.00, 0.01, 0.00, 0.00, 0.00, 0.01, 0.01, -0.01, -0.03, -0.02, -0.01, 0.00, 0.00, 0.00, -0.01, 0.01, 0.00, -0.01, 0.02, 0.07, 0.15, 0.28, 0.31, 0.08, -0.26, -0.54, -0.96, -1.08, -0.27, 0.01, 0.45, 1.18, 1.07, 0.71, 0.65, 0.20, -0.80, -1.30, -0.74, -0.24, 0.29, 0.47, 0.34, 0.15, 0.02, 0.03, -0.02, -0.16, -0.13, 0.05, 0.09, -0.01, -0.08, -0.06, 0.03, 0.13, 0.19, 0.23, 0.18, 0.10, -0.07, -0.44, -0.91, -1.05, -0.64, -0.08, 0.50, 1.12, 1.35, 0.89, 0.58, 0.54, -0.58, -1.27, -1.20, -0.48, 0.19, 0.62, 0.62, 0.37, -0.01, -0.35, -0.33, 0.07, 0.29, 0.10, -0.14, -0.10, 0.07, 0.07, 0.01, 0.03, 0.09, 0.20, 0.32, 0.26, -0.02, -0.32, -0.78, -1.25, -0.93, -0.16, 0.30, 0.88, 1.40, 1.14, 0.72, 0.48, -0.54, -1.21, -1.13, -0.41, 0.18, 0.51, 0.53, 0.36, 0.11, -0.03, -0.09, -0.28, -0.11, 0.11, 0.15, 0.04, -0.08, -0.04, 0.04, 0.09, 0.16, 0.26, 0.43, 0.09, -0.88, -1.46, -0.64, -0.16, 0.43, 1.37, 1.34, 0.84, 0.52, -0.17, -0.87, -1.22, -0.76, 0.03, 0.47, 0.60, 0.36, 0.04, -0.09, -0.03, 0.02, -0.04, 0.04, 0.12, 0.13, 0.19, 0.27, 0.31, 0.18, -0.42, -0.99, -1.13, -0.75, -0.22, 0.50, 1.42, 1.41, 0.98, 0.51, 0.29, -0.69, -1.59, -0.88, -0.13, 0.31, 0.49, 0.46, 0.30, 0.05, -0.08, -0.03, 0.01, -0.04, -0.06, 0.02, 0.03, 0.01, -0.02, 0.01, 0.04, 0.06, 0.04, 0.03, 0.02, 0.03, 0.03, 0.01, -0.01, 0.00, 0.02, 0.00, 0.02, 0.02, 0.02, -0.02, -0.01, 0.02, 0.02, 0.01, 0.02, 0.02, 0.02, 0.02, 0.04, 0.03, 0.01, 0.01, 0.02, 0.01, 0.01, 0.01, 0.02, 0.01, 0.00, 0.01, 0.01, 0.00, 0.00, 0.01, 0.00, 0.00, 0.01, 0.00, 0.02, 0.00, 0.00, 0.01, 0.01, 0.00, 0.00, 0.01, 0.01, 0.00, 0.00, 0.00, 0.01, 0.01, 0.00, 0.01, 0.00, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.01, 0.01, 0.01, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00]

I am therefore not sure the z-wave algorithm is the right approach for this kind of dataset.

解决方案

Translation of smooth z-score algo into Swift

Well, to quickly help you out: here is a translation of the algo into Swift: Demo in Swift Sandbox

Warning: I am by no means a swift programmer, so there could be mistakes in there!

Also note that I have turned off negative signals, as for OP's purpose we only want positive signals.

Swift code:

import Glibc // or Darwin/ Foundation/ Cocoa/ UIKit (depending on OS)

// Function to calculate the arithmetic mean
func arithmeticMean(array: [Double]) -> Double {
    var total: Double = 0
    for number in array {
        total += number
    }
    return total / Double(array.count)
}

// Function to calculate the standard deviation
func standardDeviation(array: [Double]) -> Double
{
    let length = Double(array.count)
    let avg = array.reduce(0, {$0 + $1}) / length
    let sumOfSquaredAvgDiff = array.map { pow($0 - avg, 2.0)}.reduce(0, {$0 + $1})
    return sqrt(sumOfSquaredAvgDiff / length)
}

// Function to extract some range from an array
func subArray<T>(array: [T], s: Int, e: Int) -> [T] {
    if e > array.count {
        return []
    }
    return Array(array[s..<min(e, array.count)])
}

// Smooth z-score thresholding filter
func ThresholdingAlgo(y: [Double],lag: Int,threshold: Double,influence: Double) -> ([Int],[Double],[Double]) {

    // Create arrays
    var signals   = Array(repeating: 0, count: y.count)
    var filteredY = Array(repeating: 0.0, count: y.count)
    var avgFilter = Array(repeating: 0.0, count: y.count)
    var stdFilter = Array(repeating: 0.0, count: y.count)

    // Initialise variables
    for i in 0...lag-1 {
        signals[i] = 0
        filteredY[i] = y[i]
    }

    // Start filter
    avgFilter[lag-1] = arithmeticMean(array: subArray(array: y, s: 0, e: lag-1))
    stdFilter[lag-1] = standardDeviation(array: subArray(array: y, s: 0, e: lag-1))

    for i in lag...y.count-1 {
        if abs(y[i] - avgFilter[i-1]) > threshold*stdFilter[i-1] {
            if y[i] > avgFilter[i-1] {
                signals[i] = 1      // Positive signal
            } else {
                // Negative signals are turned off for this application
                //signals[i] = -1       // Negative signal
            }
            filteredY[i] = influence*y[i] + (1-influence)*filteredY[i-1]
        } else {
            signals[i] = 0          // No signal
            filteredY[i] = y[i]
        }
        // Adjust the filters
        avgFilter[i] = arithmeticMean(array: subArray(array: filteredY, s: i-lag, e: i))
        stdFilter[i] = standardDeviation(array: subArray(array: filteredY, s: i-lag, e: i))
    }

    return (signals,avgFilter,stdFilter)
}

// Demo
let samples = [0.01, -0.02, -0.02, 0.01, -0.01, -0.01, 0.00, 0.10, 0.31,
  -0.10, -0.73, -0.68, 0.21, 1.22, 0.67, -0.59, -1.04, 0.06, 0.42, 0.07, 
  0.03, -0.18, 0.11, -0.06, -0.02, 0.16, 0.21, 0.03, -0.68, -0.89, 0.18, 
  1.31, 0.66, 0.07, -1.62, -0.16, 0.67, 0.19, -0.42, 0.23, -0.05, -0.01,
  0.03, 0.06, 0.27, 0.15, -0.50, -1.18, 0.11, 1.30, 0.93, 0.16, -1.32, 
  -0.10, 0.55, 0.23, -0.03, -0.23, 0.16, -0.04, 0.01, 0.12, 0.35, -0.38,
  -1.11, 0.07, 1.46, 0.61, -0.68, -1.16, 0.29, 0.54, -0.05, 0.02, -0.01,
  0.12, 0.23, 0.29, -0.75, -0.95, 0.11, 1.51, 0.70, -0.30, -1.48, 0.13,
  0.50, 0.18, -0.06, -0.01, -0.02, 0.03, -0.02, 0.06, 0.03, 0.03, 0.02,
  -0.01, 0.01, 0.02, 0.01]

// Run filter
let (signals,avgFilter,stdFilter) = ThresholdingAlgo(y: samples, lag: 10, threshold: 3, influence: 0.2)
// Print output to console
print("
Output: 
 ")
for i in 0...signals.count - 1 {
    print("Data point (i)		 sample: (samples[i]) 	 signal: (signals[i])
")
}

// Raw data for creating a plot in Excel
print("
 
 Raw data for creating a plot in Excel: 
 ")
for i in 0...signals.count - 1 {
    print("(i+1)	(samples[i])	(signals[i])	(avgFilter[i])	(stdFilter[i])
")
}

With the result for the sample data (for lag = 10, threshold = 3, influence = 0.2):

Update

You can improve the performance of the algorithm by using different values for the lag of the mean and the standard deviation. E.g.:

// Smooth z-score thresholding filter
func ThresholdingAlgo(y: [Double], lagMean: Int, lagStd: Int, threshold: Double, influenceMean: Double, influenceStd: Double) -> ([Int],[Double],[Double]) {

    // Create arrays
    var signals   = Array(repeating: 0, count: y.count)
    var filteredYmean = Array(repeating: 0.0, count: y.count)
    var filteredYstd = Array(repeating: 0.0, count: y.count)
    var avgFilter = Array(repeating: 0.0, count: y.count)
    var stdFilter = Array(repeating: 0.0, count: y.count)

    // Initialise variables
    for i in 0...lagMean-1 {
        signals[i] = 0
        filteredYmean[i] = y[i]
        filteredYstd[i] = y[i]
    }

    // Start filter
    avgFilter[lagMean-1] = arithmeticMean(array: subArray(array: y, s: 0, e: lagMean-1))
    stdFilter[lagStd-1] = standardDeviation(array: subArray(array: y, s: 0, e: lagStd-1))

    for i in max(lagMean,lagStd)...y.count-1 {
        if abs(y[i] - avgFilter[i-1]) > threshold*stdFilter[i-1] {
            if y[i] > avgFilter[i-1] {
                signals[i] = 1      // Positive signal
            } else {
                signals[i] = -1       // Negative signal
            }
            filteredYmean[i] = influenceMean*y[i] + (1-influenceMean)*filteredYmean[i-1]
            filteredYstd[i] = influenceStd*y[i] + (1-influenceStd)*filteredYstd[i-1]
        } else {
            signals[i] = 0          // No signal
            filteredYmean[i] = y[i]
            filteredYstd[i] = y[i]
        }
        // Adjust the filters
        avgFilter[i] = arithmeticMean(array: subArray(array: filteredYmean, s: i-lagMean, e: i))
        stdFilter[i] = standardDeviation(array: subArray(array: filteredYstd, s: i-lagStd, e: i))
    }

    return (signals,avgFilter,stdFilter)
}

Then using for example let (signals,avgFilter,stdFilter) = ThresholdingAlgo(y: samples, lagMean: 10, lagStd: 100, threshold: 2, influenceMean: 0.5, influenceStd: 0.1) can give a lot better results:

DEMO

这篇关于使用 Swift 对增长的时间序列进行峰值检测的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！

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