peak detection for growing time series using Swift
有人会有一个好的算法来测量使用swift(v3)的增长时间序列数据的峰值吗？因此，在数据流入时检测峰值。
例如，平滑Z波算法的快速版本。那个算法似乎是合适的。
我需要检测峰值，如下所示。数据包含正数和负数。输出应该是峰值的计数器，和/或该特定样本的真/假。
。
示例数据集(上一系列的摘要)：
1 2 3 4 5 6 7 8 9 10 | 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] |
最新消息：感谢Jean-Paul为Swift提供了最初的港口。但不确定z波算法是否适合这个数据集。对于数据集的最后一个系列，
问题是：由于存在很大的延迟，第一个数据样本不包括在内，我需要每个峰值一个信号，算法需要进一步的工作来提高效率。
例如，完整数据集、使用python代码和(例如)
氧化镁
完整数据集(应产生25个峰值)：
1 | 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] |
号
因此，我不确定z波算法是否是这种数据集的正确方法。
将平滑z-分数算法转换为swift
好吧，快来帮你：这里有一个将algo翻译成swift的版本：在swift沙箱中演示
警告：我决不是一个快速的程序员，所以可能有错误在那里！
还要注意，我已经关闭了负信号，至于OP的目的，我们只需要正信号。
银行代码：
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 | 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)\t\t sample: \(samples[i]) \t 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)\t\(samples[i])\t\(signals[i])\t\(avgFilter[i])\t\(stdFilter[i]) ") } |
样本数据的结果(对于
。
通过对平均值和标准差的
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | // 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) } |
号
然后使用例如
氧化镁