以下是平滑z-score算法的Scala版本(非惯用):
/**
* Smoothed zero-score alogrithm shamelessly copied from https://stackoverflow.com/a/22640362/6029703
* Uses a rolling mean and a rolling deviation (separate) to identify peaks in a vector
*
* @param y - The input vector to analyze
* @param lag - The lag of the moving window (i.e. how big the window is)
* @param threshold - The z-score at which the algorithm signals (i.e. how many standard deviations away from the moving mean a peak (or signal) is)
* @param influence - The influence (between 0 and 1) of new signals on the mean and standard deviation (how much a peak (or signal) should affect other values near it)
* @return - The calculated averages (avgFilter) and deviations (stdFilter), and the signals (signals)
*/
private def smoothedZScore(y: Seq[Double], lag: Int, threshold: Double, influence: Double): Seq[Int] = {
val stats = new SummaryStatistics()
// the results (peaks, 1 or -1) of our algorithm
val signals = mutable.ArrayBuffer.fill(y.length)(0)
// filter out the signals (peaks) from our original list (using influence arg)
val filteredY = y.to[mutable.ArrayBuffer]
// the current average of the rolling window
val avgFilter = mutable.ArrayBuffer.fill(y.length)(0d)
// the current standard deviation of the rolling window
val stdFilter = mutable.ArrayBuffer.fill(y.length)(0d)
// init avgFilter and stdFilter
y.take(lag).foreach(s => stats.addValue(s))
avgFilter(lag - 1) = stats.getMean
stdFilter(lag - 1) = Math.sqrt(stats.getPopulationVariance) // getStandardDeviation() uses sample variance (not what we want)
// loop input starting at end of rolling window
y.zipWithIndex.slice(lag, y.length - 1).foreach {
case (s: Double, i: Int) =>
// if the distance between the current value and average is enough standard deviations (threshold) away
if (Math.abs(s - avgFilter(i - 1)) > threshold * stdFilter(i - 1)) {
// this is a signal (i.e. peak), determine if it is a positive or negative signal
signals(i) = if (s > avgFilter(i - 1)) 1 else -1
// filter this signal out using influence
filteredY(i) = (influence * s) + ((1 - influence) * filteredY(i - 1))
} else {
// ensure this signal remains a zero
signals(i) = 0
// ensure this value is not filtered
filteredY(i) = s
}
// update rolling average and deviation
stats.clear()
filteredY.slice(i - lag, i).foreach(s => stats.addValue(s))
avgFilter(i) = stats.getMean
stdFilter(i) = Math.sqrt(stats.getPopulationVariance) // getStandardDeviation() uses sample variance (not what we want)
}
println(y.length)
println(signals.length)
println(signals)
signals.zipWithIndex.foreach {
case(x: Int, idx: Int) =>
if (x == 1) {
println(idx + " " + y(idx))
}
}
val data =
y.zipWithIndex.map { case (s: Double, i: Int) => Map("x" -> i, "y" -> s, "name" -> "y", "row" -> "data") } ++
avgFilter.zipWithIndex.map { case (s: Double, i: Int) => Map("x" -> i, "y" -> s, "name" -> "avgFilter", "row" -> "data") } ++
avgFilter.zipWithIndex.map { case (s: Double, i: Int) => Map("x" -> i, "y" -> (s - threshold * stdFilter(i)), "name" -> "lower", "row" -> "data") } ++
avgFilter.zipWithIndex.map { case (s: Double, i: Int) => Map("x" -> i, "y" -> (s + threshold * stdFilter(i)), "name" -> "upper", "row" -> "data") } ++
signals.zipWithIndex.map { case (s: Int, i: Int) => Map("x" -> i, "y" -> s, "name" -> "signal", "row" -> "signal") }
Vegas("Smoothed Z")
.withData(data)
.mark(Line)
.encodeX("x", Quant)
.encodeY("y", Quant)
.encodeColor(
field="name",
dataType=Nominal
)
.encodeRow("row", Ordinal)
.show
return signals
}
下面是一个测试，返回与Python和Groovy版本相同的结果:
val y = List(1d, 1d, 1.1d, 1d, 0.9d, 1d, 1d, 1.1d, 1d, 0.9d, 1d, 1.1d, 1d, 1d, 0.9d, 1d, 1d, 1.1d, 1d, 1d,
1d, 1d, 1.1d, 0.9d, 1d, 1.1d, 1d, 1d, 0.9d, 1d, 1.1d, 1d, 1d, 1.1d, 1d, 0.8d, 0.9d, 1d, 1.2d, 0.9d, 1d,
1d, 1.1d, 1.2d, 1d, 1.5d, 1d, 3d, 2d, 5d, 3d, 2d, 1d, 1d, 1d, 0.9d, 1d,
1d, 3d, 2.6d, 4d, 3d, 3.2d, 2d, 1d, 1d, 0.8d, 4d, 4d, 2d, 2.5d, 1d, 1d, 1d)
val lag = 30
val threshold = 5d
val influence = 0d
smoothedZScore(y, lag, threshold, influence)
这里的要点
