statsmodels.graphics.functional.hdrboxplot(data, ncomp=2, alpha=None, threshold=0.95, bw=None, xdata=None, labels=None, ax=None)
High Density Region boxplot
The median curve is the curve with the highest probability on the reduced space of a Principal Component Analysis (PCA).
Outliers are defined as curves that fall outside the band corresponding to the quantile given by
The non-outlying region is defined as the band made up of all the non-outlying curves.
Behind the scene, the dataset is represented as a matrix. Each line corresponding to a 1D curve. This matrix is then decomposed using Principal Components Analysis (PCA). This allows to represent the data using a finite number of modes, or components. This compression process allows to turn the functional representation into a scalar representation of the matrix. In other words, you can visualize each curve from its components. Each curve is thus a point in this reduced space. With 2 components, this is called a bivariate plot (2D plot).
In this plot, if some points are adjacent (similar components), it means that back in the original space, the curves are similar. Then, finding the median curve means finding the higher density region (HDR) in the reduced space. Moreover, the more you get away from this HDR, the more the curve is unlikely to be similar to the other curves.
Using a kernel smoothing technique, the probability density function (PDF) of the multivariate space can be recovered. From this PDF, it is possible to compute the density probability linked to the cluster of points and plot its contours.
Finally, using these contours, the different quantiles can be extracted along with the median curve and the outliers.
Steps to produce the HDR boxplot include:
Load the El Nino dataset. Consists of 60 years worth of Pacific Ocean sea surface temperature data.
>>> import matplotlib.pyplot as plt >>> import statsmodels.api as sm >>> data = sm.datasets.elnino.load()
Create a functional boxplot. We see that the years 1982-83 and 1997-98 are outliers; these are the years where El Nino (a climate pattern characterized by warming up of the sea surface and higher air pressures) occurred with unusual intensity.
>>> fig = plt.figure() >>> ax = fig.add_subplot(111) >>> res = sm.graphics.hdrboxplot(data.raw_data[:, 1:], ... labels=data.raw_data[:, 0].astype(int), ... ax=ax)
>>> ax.set_xlabel("Month of the year") >>> ax.set_ylabel("Sea surface temperature (C)") >>> ax.set_xticks(np.arange(13, step=3) - 1) >>> ax.set_xticklabels(["", "Mar", "Jun", "Sep", "Dec"]) >>> ax.set_xlim([-0.2, 11.2])
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© 2006 Jonathan E. Taylor
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