我目前正在一个小项目中，想要比较两个时间序列的相似度。相似性测量非常模糊，如果这两个时间序列大致相同，则认为它们是相似的。
所以我想：“如果它们只需要具有相同的形状，那么我只需要比较两个时间序列的峰值，如果峰值位于同一位置，那么这两个时间序列肯定是相似的。”
我的问题现在是找到一种好的峰值检测算法。我用了谷歌搜索，但只找到了这篇论文：Simple Algorithms for Peak Detection in Time-Series。问题在于，该论文中描述的算法适用于极端和尖锐的峰值，但在大多数情况下，我的时间序列具有相当平坦的峰值，因此不会被检测到。
有人知道我可以在哪里找到或搜索能检测以下图像中显示的峰值的算法吗？
List<Point> points = ... //all the points in your curve
List<Point> extremes = new ArrayList<Point> ();
double previous = null;
double previousSlope = 0;
for (Point p : points) {
if (previous == null) { previous = p; continue; }
double slope = p.getValue() - previous.getValue();
if (slope * previousSlope < 0) { //look for sign changes
extremes.add(previous);
}
previousSlope = slope;
previous = p;
}
您可以在此处阅读有关回报相关性的更多信息。总之，如果您的价值为：
Series 1 Series 2
100 50
98 49
100 52
102 54
Series 1 Series 2
-2.00% -2.00%
+2.04% +6.12%
+2.00% +3.85%
你需要计算这两个回报系列的相关性（在本例中为0.96），以衡量这两个曲线有多相似。你可能需要调整方差的结果（即，如果一个形状的范围比另一个宽得多）。
// those are your points:
double[] f = {1, 2, 3, 4, 5, 6, 5, 4, 7, 8, 9, 3, 1, 4, 6, 8, 9, 7, 4, 1};
List<Integer> ext = new ArrayList<Integer> ();
for (int i = 0; i<f.length-2; i++) {
if ((f[i+1]-f[i])*(f[i+2]-f[i+1]) <= 0) { // changed sign?
ext.add(i+1);
}
}
// now you have the indices of the extremes in your list `ext`
这对于平滑系列非常有效。如果您的数据有一定的变化，您应该先通过低通滤波器处理它。一个非常简单的低通滤波器实现是移动平均值（每个点都被最近k个值的平均值替换，其中k是窗口大小）。
Eli Billauer提出的peakdet算法非常有效且易于实现：
http://www.billauer.co.il/peakdet.html
该算法在处理噪声信号时表现尤为优秀，而使用一阶导数的方法则会失败。
List<XYDataItem> maxPoints = ... //list to store the maximums
XYDataItem leftPeakPoint = new XYDataItem(0, 0);
int leftPeakPointIndex = 0;
XYDataItem rightPeakPoint = new XYDataItem(0, 0);
boolean first = true;
int index = -1;
List<XYDataItem> pointList = (List<XYDataItem>) lrpSeries.getItems();
for (XYDataItem point : pointList) {
index++;
if (first) {
//initialize the first point
leftPeakPoint = point;
leftPeakPointIndex = index;
first = false;
continue;
}
if (leftPeakPoint.getYValue() < point.getYValue()) {
leftPeakPoint = point;
leftPeakPointIndex = index;
rightPeakPoint = point;
} else if (leftPeakPoint.getYValue() == point.getYValue()) {
rightPeakPoint = point;
} else {
//determine if we are coming down off of a peak by looking at the Y value of the point before the
//left most point that was detected as a part of a peak
if (leftPeakPointIndex > 0) {
XYDataItem prev = pointList.get(leftPeakPointIndex - 1);
//if two points back has a Y value that is less than or equal to the left peak point
//then we have found the end of the peak and we can process as such
if (prev.getYValue() <= leftPeakPoint.getYValue()) {
double peakx = rightPeakPoint.getXValue() - ((rightPeakPoint.getXValue() - leftPeakPoint.getXValue()) / 2D);
maxPoints.add(new XYDataItem(peakx, leftPeakPoint.getYValue()));
}
}
leftPeakPoint = point;
leftPeakPointIndex = index;
rightPeakPoint = point;
}
}