问题描述
这个问题是关于确定数字序列中最大值的数量和位置的算法。因此,该问题具有统计意义,但它更倾向于编程,因为我对特定的统计特性不感兴趣,并且解决方案必须在R中。使用统计数据来回答这个问题是可以的,
我想提取时间序列数据(即数字的有序序列)中循环的最大值。这种数据的一个例子是太阳耀斑时间序列(约11年的周期,介于9到14年之间)。循环不会以理想的间隔重复,并且峰的高度并不总是相同。
我发现了一篇最近的论文,描述了为此的算法,并且论文实际上以太阳耀斑为例(图5,Scholkmann等,2012,算法)。我希望该算法或同等有效的算法可以作为R包使用。
链接到Scholkmann的论文基于多尺度的自动峰检测 $ b
This question is about an algorithm for determining the number and location of maxima in a sequence of numbers. Thus, there is a statistical flavor to the question, but it is more leaning towards programming, because I am not interested in the specific statistical properties, and the solution needs to be in R. The use of statistics to answer this question is OK, but not a requirement.
I want to extract maxima of cycles in time series data (i.e., an ordered sequence of numbers). An example of such data is the solar flare time series (~11 year cycle, between 9 & 14 years). The cycles don't repeat at a perfect interval, and the peaks aren't always the same height.
I found a recent paper describing an algorithm for this, and the paper actually uses solar flares as an example (Figure 5, Scholkmann et al. 2012, Algorithms). I was hoping that this algorithm, or an equally effective algorithm, was available as an R package.
Link to Scholkmann paper on "automatic multiscale-based peak detection"http://www.mdpi.com/1999-4893/5/4/588
I've tried the "turningpoints" function in the "pastecs" package but it seemed to be too sensitive (i.e., detected too many peaks). I thought of trying to smooth the time series first, but I'm not sure if this is the best approach (I'm no expert).
Thanks for any pointers.
Here is a solution involving the wmtsa
package in R. I added my own little function to facilitate the searching of maxima once the wmtsa::wavCWTPeaks
got it close.
PeakCycle <- function(Data=as.vector(sunspots), SearchFrac=0.02){
# using package "wmtsa"
#the SearchFrac parameter just controls how much to look to either side
#of wavCWTPeaks()'s estimated maxima for a bigger value
#see dRange
Wave <- wavCWT(Data)
WaveTree <- wavCWTTree(Wave)
WavePeaks <- wavCWTPeaks(WaveTree, snr.min=5)
WavePeaks_Times <- attr(WavePeaks, which="peaks")[,"iendtime"]
NewPeakTimes <- c()
dRange <- round(SearchFrac*length(Data))
for(i in 1:length(WavePeaks_Times)){
NewRange <- max(c(WavePeaks_Times[i]-dRange, 1)):min(c(WavePeaks_Times[i]+dRange, length(Data)))
NewPeakTimes[i] <- which.max(Data[NewRange])+NewRange[1]-1
}
return(matrix(c(NewPeakTimes, Data[NewPeakTimes]), ncol=2, dimnames=list(NULL, c("PeakIndices", "Peaks"))))
}
dev.new(width=6, height=4)
par(mar=c(4,4,0.5,0.5))
plot(seq_along(as.vector(sunspots)), as.vector(sunspots), type="l")
Sunspot_Ext <- PeakCycle()
points(Sunspot_Ext, col="blue", pch=20)
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