How to detect the singular value with wavelet analysis

Question

I have a series data

data=Uncompress[ FromCharacterCode[Flatten[ImageData[Import["https://i.sstatic.net/ApipY.png"], "Byte"]]]];

We can show it

ListPlot[data, PlotRange -> All]

Mathematica graphics

I put a singular value in position $20$ and $21$.As I know,wavelet analysis can detect it,but I don't know how to do it.

yode · Accepted Answer · 2017-04-14 19:31:22Z

Of course expected more professionnel answer,I just dig in documentation

Firstly,plots wavelet transform coefficients

dwd = DiscreteWaveletTransform[data]; WaveletListPlot[dwd]

Mathematica graphics

Select that basis index with minimal energy

{basisIndex} = Keys[MinimalBy[dwd["EnergyFraction"], Last]]

{{0, 1}}

Ugly to extract that x-value.

MaximalBy[ Cases[basisIndex /. dwd["ListPlot"], a_Line :> a, Infinity][[1,1]], Abs@*Last]

{{20.1, 1.00915}}

partida · Accepted Answer · 2017-09-18 12:14:19Z

1

Simple way not using wavelet

Position[data - MedianFilter[data, 3], x_ /; x > 1]

{{20}, {21}}

answered Sep 18, 2017 at 12:14

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