鲁棒峰值检测算法(使用z-scores)
I came up with an algorithm that works very well for these types of datasets. It is based on the principle of dispersion: if a new datapoint is a given x number of standard deviations away from some moving mean, the algorithm signals (also called z-score). The algorithm is very robust because it constructs a separate moving mean and deviation, such that signals do not corrupt the threshold. Future signals are therefore identified with approximately the same accuracy, regardless of the amount of previous signals. The algorithm takes 3 inputs: lag = the lag of the moving window, threshold = the z-score at which the algorithm signals and influence = the influence (between 0 and 1) of new signals on the mean and standard deviation. For example, a lag of 5 will use the last 5 observations to smooth the data. A threshold of 3.5 will signal if a datapoint is 3.5 standard deviations away from the moving mean. And an influence of 0.5 gives signals half of the influence that normal datapoints have. Likewise, an influence of 0 ignores signals completely for recalculating the new threshold. An influence of 0 is therefore the most robust option (but assumes stationarity); putting the influence option at 1 is least robust. For non-stationary data, the influence option should therefore be put somewhere between 0 and 1.
其工作原理如下:
伪代码
# Let y be a vector of timeseries data of at least length lag+2
# Let mean() be a function that calculates the mean
# Let std() be a function that calculates the standard deviaton
# Let absolute() be the absolute value function
# Settings (these are examples: choose what is best for your data!)
set lag to 5; # average and std. are based on past 5 observations
set threshold to 3.5; # signal when data point is 3.5 std. away from average
set influence to 0.5; # between 0 (no influence) and 1 (full influence)
# Initialize variables
set signals to vector 0,...,0 of length of y; # Initialize signal results
set filteredY to y(1),...,y(lag) # Initialize filtered series
set avgFilter to null; # Initialize average filter
set stdFilter to null; # Initialize std. filter
set avgFilter(lag) to mean(y(1),...,y(lag)); # Initialize first value average
set stdFilter(lag) to std(y(1),...,y(lag)); # Initialize first value std.
for i=lag+1,...,t do
if absolute(y(i) - avgFilter(i-1)) > threshold*stdFilter(i-1) then
if y(i) > avgFilter(i-1) then
set signals(i) to +1; # Positive signal
else
set signals(i) to -1; # Negative signal
end
set filteredY(i) to influence*y(i) + (1-influence)*filteredY(i-1);
else
set signals(i) to 0; # No signal
set filteredY(i) to y(i);
end
set avgFilter(i) to mean(filteredY(i-lag+1),...,filteredY(i));
set stdFilter(i) to std(filteredY(i-lag+1),...,filteredY(i));
end
下面是为数据选择良好参数的经验法则。
Demo
这个演示的Matlab代码可以在这里找到。要使用演示，只需运行它并单击上面的图表自己创建一个时间序列。算法在绘制滞后观测数后开始工作。
结果
对于原始问题，当使用以下设置时，该算法将给出以下输出:滞后= 30，阈值= 5，影响= 0:
在不同编程语言中的实现:
Matlab (me)
R (me)
Golang (Xeoncross)
Golang [efficient version] (Micah Parks)
Python (R Kiselev)
Python [efficient version] (delica)
Swift (me)
Groovy (JoshuaCWebDeveloper)
C++ [interactive parameters] (Jason C)
C++ (Animesh Pandey)
Rust (swizard)
Scala (Mike Roberts)
Kotlin (leoderprofi)
Ruby (Kimmo Lehto)
Fortran [for resonance detection] (THo)
Julia (Matt Camp)
C# (Ocean Airdrop)
C (DavidC)
Java (takanuva15)
JavaScript (Dirk Lüsebrink)
TypeScript (Jerry Gamble)
Perl (Alen)
PHP (radhoo)
PHP (gtjamesa)
Dart (Sga)
配置算法的经验法则
lag: the lag parameter determines how much your data will be smoothed and how adaptive the algorithm is to changes in the long-term average of the data. The more stationary your data is, the more lags you should include (this should improve the robustness of the algorithm). If your data contains time-varying trends, you should consider how quickly you want the algorithm to adapt to these trends. I.e., if you put lag at 10, it takes 10 'periods' before the algorithm's treshold is adjusted to any systematic changes in the long-term average. So choose the lag parameter based on the trending behavior of your data and how adaptive you want the algorithm to be.
influence: this parameter determines the influence of signals on the algorithm's detection threshold. If put at 0, signals have no influence on the threshold, such that future signals are detected based on a threshold that is calculated with a mean and standard deviation that is not influenced by past signals. If put at 0.5, signals have half the influence of normal data points. Another way to think about this is that if you put the influence at 0, you implicitly assume stationarity (i.e. no matter how many signals there are, you always expect the time series to return to the same average over the long term). If this is not the case, you should put the influence parameter somewhere between 0 and 1, depending on the extent to which signals can systematically influence the time-varying trend of the data. E.g., if signals lead to a structural break of the long-term average of the time series, the influence parameter should be put high (close to 1) so the threshold can react to structural breaks quickly.
threshold: the threshold parameter is the number of standard deviations from the moving mean above which the algorithm will classify a new datapoint as being a signal. For example, if a new datapoint is 4.0 standard deviations above the moving mean and the threshold parameter is set as 3.5, the algorithm will identify the datapoint as a signal. This parameter should be set based on how many signals you expect. For example, if your data is normally distributed, a threshold (or: z-score) of 3.5 corresponds to a signaling probability of 0.00047 (from this table), which implies that you expect a signal once every 2128 datapoints (1/0.00047). The threshold therefore directly influences how sensitive the algorithm is and thereby also determines how often the algorithm signals. Examine your own data and choose a sensible threshold that makes the algorithm signal when you want it to (some trial-and-error might be needed here to get to a good threshold for your purpose).
警告:上面的代码每次运行时都会遍历所有的数据点。在实现这段代码时，请确保将信号的计算拆分为一个单独的函数(没有循环)。然后当一个新的数据点到达时，更新filteredY, avgFilter和stdFilter一次。不要每次有新的数据点时都重新计算所有数据的信号(就像上面的例子一样)，这在实时应用程序中是非常低效和缓慢的。
其他修改算法的方法(为了潜在的改进)有:
使用中位数而不是平均值
使用稳健的尺度测量，如中位数绝对偏差(MAD)，而不是标准偏差
使用信号裕度，这样信号就不会频繁切换
更改影响参数的工作方式
区别对待上下信号(不对称处理)
创建一个单独的影响参数的平均值和标准(在这个Swift翻译)
(已知)学术引用此StackOverflow的答案:
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其他工作使用的算法从这个答案
Bergamini, E. and E. Mourlon-Druol (2021). Talking about Europe: exploring 70 years of news archives. Working Paper 04/2021, Bruegel.
Cox, G. (2020). Peak Detection in a Measured Signal. Online article on https://www.baeldung.com/cs/signal-peak-detection.
Raimundo, D. W. (2020). SwitP: Mobile Application for Real-Time Swimming Analysis.. Semester Thesis, ETH Zürich.
Bernardi, D. (2019). A feasibility study on pairing a smartwatch and a mobile device through multi-modal gestures. Master thesis, Aalto University.
Lemmens, E. (2018). Outlier detection in event logs by using statistical methods, Master thesis, University of Eindhoven.
Willems, P. (2017). Mood controlled affective ambiences for the elderly, Master thesis, University of Twente.
Ciocirdel, G. D. and Varga, M. (2016). Election Prediction Based on Wikipedia Pageviews. Project paper, Vrije Universiteit Amsterdam.
算法的其他应用从这个答案
Avo审计dbt包。Avo公司(下一代分析治理)。
用OpenBCI系统合成语音，SarahK01。
Python包:机器学习金融实验室，基于De Prado, m.l.(2018)的工作。金融机器学习的进展。John Wiley & Sons。
Adafruit CircuitPlayground Library, Adafruit board (Adafruit Industries)
步长跟踪算法，Android App (jeeshnair)
R包:《动物追踪者》(乔·钱皮恩、西娅·苏基安托)
链接到其他峰值检测算法
噪声正弦时间序列中的实时峰值检测
如何引用该算法:
Brakel, J.P.G. van(2014)。使用z分数的鲁棒峰值检测算法。堆栈溢出。下载地址:https://stackoverflow.com/questions/22583391/peak-signal-detection-in-realtime-timeseries-data/22640362#22640362(版本:2020-11-08)。
助理
@misc{brakel2014，作者= {Brakel, J.P.G van}，标题={使用z-scores的鲁棒峰值检测算法}，url = {https://stackoverflow.com/questions/22583391/peak-signal-detection-in-realtime-timeseries-data/22640362#22640362}，语言= {en}，年份= {2014}，urldate ={2022-04-12}，期刊= {Stack Overflow}， howpublished = {https://stackoverflow.com/questions/22583391/peak-signal-detection-in-realtime-timeseries-data/22640362#22640362}}
如果你在某个地方使用这个功能，请使用上面的参考资料来感谢我。如果你对算法有任何问题，请在下面的评论中发表，或在LinkedIn上与我联系。
