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[![Go Reference](https://pkg.go.dev/badge/github.com/MicahParks/peakdetect.svg)](https://pkg.go.dev/github.com/MicahParks/peakdetect) [![Go Report Card](https://goreportcard.com/badge/github.com/MicahParks/peakdetect)](https://goreportcard.com/report/github.com/MicahParks/peakdetect)
# peakdetect
Detect peaks in realtime timeseries data using z-scores. This is a Golang implementation for the algorithm described
by [this StackOverflow answer](https://stackoverflow.com/a/22640362/14797322).
Unlike some implementations, a goal is to minimize the memory footprint and allow for the processing of new data points
without reprocessing old ones.
```go
import "github.com/MicahParks/peakdetect"
```
# Configuration
`Lag` determines how much your data will be smoothed and how adaptive the algorithm is to change 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 threshold
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` 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 stationary (
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` 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)
# Usage
```go
package main
import (
"fmt"
"log"
"github.com/MicahParks/peakdetect"
)
// This example is the equivalent of the R example from the algorithm's author.
// https://stackoverflow.com/a/54507329/14797322
func main() {
data := []float64{1, 1, 1.1, 1, 0.9, 1, 1, 1.1, 1, 0.9, 1, 1.1, 1, 1, 0.9, 1, 1, 1.1, 1, 1, 1, 1, 1.1, 0.9, 1, 1.1, 1, 1, 0.9, 1, 1.1, 1, 1, 1.1, 1, 0.8, 0.9, 1, 1.2, 0.9, 1, 1, 1.1, 1.2, 1, 1.5, 1, 3, 2, 5, 3, 2, 1, 1, 1, 0.9, 1, 1, 3, 2.6, 4, 3, 3.2, 2, 1, 1, 0.8, 4, 4, 2, 2.5, 1, 1, 1}
// Algorithm configuration from example.
const (
lag = 30
threshold = 5
influence = 0
)
// Create then initialize the peak detector.
detector := peakdetect.NewPeakDetector()
err := detector.Initialize(influence, threshold, data[:lag]) // The length of the initial values is the lag.
if err != nil {
log.Fatalf("Failed to initialize peak detector.\nError: %s", err)
}
// Start processing new data points and determine what signal, if any they produce.
//
// This method, .Next(), is best for when data are being processed in a stream, but this simply iterates over a
// slice.
nextDataPoints := data[lag:]
for i, newPoint := range nextDataPoints {
signal := detector.Next(newPoint)
var signalType string
switch signal {
case peakdetect.SignalNegative:
signalType = "negative"
case peakdetect.SignalNeutral:
signalType = "neutral"
case peakdetect.SignalPositive:
signalType = "positive"
}
println(fmt.Sprintf("Data point at index %d has the signal: %s", i+lag, signalType))
}
// This method, .NextBatch(), is a helper function for processing many data points at once. It's returned slice
// should produce the same signal outputs as the loop above.
signals := detector.NextBatch(nextDataPoints)
println(fmt.Sprintf("1:1 ratio of batch inputs to signal outputs: %t", len(signals) == len(nextDataPoints)))
}
```
# Testing
```
$ go test -cover -race
PASS
coverage: 100.0% of statements
ok github.com/MicahParks/peakdetect 0.019s
```
# Performance
To further improve performance, this algorithm uses Welford's algorithm on initialization
and an adaptation of [this StackOverflow answer](https://stackoverflow.com/a/14638138/14797322) to calculate the mean
and population standard deviation for the lag period (sliding window). This appears to improve performance by more than
a factor of 10!
`v0.0.4`
```
goos: linux
goarch: amd64
pkg: github.com/MicahParks/peakdetect
cpu: AMD Ryzen 9 7950X 16-Core Processor
BenchmarkPeakDetector_NextBatch-32 1000000000 0.0000221 ns/op
PASS
ok github.com/MicahParks/peakdetect 0.003s
```
`v0.1.0`
```
goos: linux
goarch: amd64
pkg: github.com/MicahParks/peakdetect
cpu: AMD Ryzen 9 7950X 16-Core Processor
BenchmarkPeakDetector_NextBatch-32 1000000000 0.0000011 ns/op
PASS
ok github.com/MicahParks/peakdetect 0.003s
```
# References
Brakel, J.P.G. van (2014). "Robust peak detection algorithm using z-scores". Stack Overflow. Available
at: https://stackoverflow.com/questions/22583391/peak-signal-detection-in-realtime-timeseries-data/22640362#22640362
(version: 2020-11-08).
* [StackOverflow: Peak detection in realtime timeseries data](https://stackoverflow.com/a/22640362/14797322).
* [StackOverflow: sliding window for online algorithm to calculate mean and standard devation](https://stackoverflow.com/a/14638138/14797322).
* [Welford's algorithm related blog post](https://www.johndcook.com/blog/standard_deviation/).
* Yeah, I used [Wikipedia](https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance) too.

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package peakdetect
import (
"errors"
"fmt"
"math"
)
const (
// SignalNegative indicates that a particular value is a negative peak.
SignalNegative Signal = -1
// SignalNeutral indicates that a particular value is not a peak.
SignalNeutral Signal = 0
// SignalPositive indicates that a particular value is a positive peak.
SignalPositive Signal = 1
)
// Signal is a set of enums that indicates what type of peak, if any a particular value is.
type Signal int8
// ErrInvalidInitialValues indicates that the initial values provided are not valid to initialize a PeakDetector.
var ErrInvalidInitialValues = errors.New("the initial values provided are invalid")
type peakDetector struct {
index uint
influence float64
lag uint
movingMeanStdDev *movingMeanStdDev
prevMean float64
prevStdDev float64
prevValue float64
threshold float64
}
// PeakDetector detects peaks in realtime timeseries data using z-scores.
//
// This is a Golang interface for the algorithm described by this StackOverflow answer:
// https://stackoverflow.com/a/22640362/14797322
//
// Brakel, J.P.G. van (2014). "Robust peak detection algorithm using z-scores". Stack Overflow. Available
// at: https://stackoverflow.com/questions/22583391/peak-signal-detection-in-realtime-timeseries-data/22640362#22640362
// (version: 2020-11-08).
type PeakDetector interface {
// Initialize initializes the PeakDetector with its configuration and initialValues. The initialValues are the first
// values to be processed by the PeakDetector. The length of these values are used to configure the PeakDetector's
// lag (see description below). The PeakDetector will never return any signals for the initialValues.
//
// influence 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 stationary (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 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).
//
// lag determines how much your data will be smoothed and how adaptive the algorithm is to change 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
// threshold 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.
Initialize(influence, threshold float64, initialValues []float64) error
// Next processes the next value and determines its signal.
Next(value float64) Signal
// NextBatch processes the next values and determines their signals. Their signals will be returned in a slice equal
// to the length of the input.
NextBatch(values []float64) []Signal
}
// NewPeakDetector creates a new PeakDetector. It must be initialized before use.
func NewPeakDetector() PeakDetector {
return &peakDetector{
movingMeanStdDev: &movingMeanStdDev{},
}
}
func (p *peakDetector) Initialize(influence, threshold float64, initialValues []float64) error {
p.lag = uint(len(initialValues))
if p.lag == 0 {
return fmt.Errorf("the length of the initial values is zero, the length is used as the lag for the algorithm: %w", ErrInvalidInitialValues)
}
p.influence = influence
p.threshold = threshold
p.prevMean, p.prevStdDev = p.movingMeanStdDev.initialize(initialValues)
p.prevValue = initialValues[p.lag-1]
return nil
}
func (p *peakDetector) Next(value float64) (signal Signal) {
p.index++
if p.index == p.lag {
p.index = 0
}
if math.Abs(value-p.prevMean) > p.threshold*p.prevStdDev {
if value > p.prevMean {
signal = SignalPositive
} else {
signal = SignalNegative
}
value = p.influence*value + (1-p.influence)*p.prevValue
} else {
signal = SignalNeutral
}
p.prevMean, p.prevStdDev = p.movingMeanStdDev.next(value)
p.prevValue = value
return signal
}
func (p *peakDetector) NextBatch(values []float64) []Signal {
signals := make([]Signal, len(values))
for i, v := range values {
signals[i] = p.Next(v)
}
return signals
}
// meanStdDev determines the mean and population standard deviation for the given population.
type movingMeanStdDev struct {
cache []float64
cacheLen float64
cacheLenU uint
index uint
prevMean float64
prevVariance float64
}
// initialize creates the needed assets for the movingMeanStdDev. It also computes the resulting mean and population
// standard deviation using Welford's method.
//
// https://www.johndcook.com/blog/standard_deviation/
func (m *movingMeanStdDev) initialize(initialValues []float64) (mean, stdDev float64) {
m.cacheLenU = uint(len(initialValues))
m.cacheLen = float64(m.cacheLenU)
m.cache = make([]float64, m.cacheLenU)
copy(m.cache, initialValues)
mean = initialValues[0]
prevMean := mean
var sumOfSquares float64
for i := uint(2); i <= m.cacheLenU; i++ {
value := initialValues[i-1]
mean = prevMean + (value-prevMean)/float64(i)
sumOfSquares = sumOfSquares + (value-prevMean)*(value-mean)
prevMean = mean
}
m.prevMean = mean
m.prevVariance = sumOfSquares / m.cacheLen
return mean, math.Sqrt(m.prevVariance)
}
// Next computes the next mean and population standard deviation. It uses a sliding window and is based on Welford's
// method.
//
// https://stackoverflow.com/a/14638138/14797322
func (m *movingMeanStdDev) next(value float64) (mean, stdDev float64) {
outOfWindow := m.cache[m.index]
m.cache[m.index] = value
m.index++
if m.index == m.cacheLenU {
m.index = 0
}
newMean := m.prevMean + (value-outOfWindow)/m.cacheLen
m.prevVariance = m.prevVariance + (value-newMean+outOfWindow-m.prevMean)*(value-outOfWindow)/(m.cacheLen)
m.prevMean = newMean
return m.prevMean, math.Sqrt(m.prevVariance)
}