matplotlib: disregard outliers when plotting

Question

I'm plotting some data from various tests. Sometimes in a test I happen to have one outlier (say 0.1), while all other values are three orders of magnitude smaller.

With matplotlib, I plot against the range [0, max_data_value]

How can I just zoom into my data and not display outliers, which would mess up the x-axis in my plot?

Should I simply take the 95 percentile and have the range [0, 95_percentile] on the x-axis?

Answer 1

There's no single "best" test for an outlier. Ideally, you should incorporate a-priori information (e.g. "This parameter shouldn't be over x because of blah...").

Most tests for outliers use the median absolute deviation, rather than the 95th percentile or some other variance-based measurement. Otherwise, the variance/stddev that is calculated will be heavily skewed by the outliers.

Here's a function that implements one of the more common outlier tests.

def is_outlier(points, thresh=3.5):
    """
    Returns a boolean array with True if points are outliers and False 
    otherwise.

    Parameters:
    -----------
        points : An numobservations by numdimensions array of observations
        thresh : The modified z-score to use as a threshold. Observations with
            a modified z-score (based on the median absolute deviation) greater
            than this value will be classified as outliers.

    Returns:
    --------
        mask : A numobservations-length boolean array.

    References:
    ----------
        Boris Iglewicz and David Hoaglin (1993), "Volume 16: How to Detect and
        Handle Outliers", The ASQC Basic References in Quality Control:
        Statistical Techniques, Edward F. Mykytka, Ph.D., Editor. 
    """
    if len(points.shape) == 1:
        points = points[:,None]
    median = np.median(points, axis=0)
    diff = np.sum((points - median)**2, axis=-1)
    diff = np.sqrt(diff)
    med_abs_deviation = np.median(diff)

    modified_z_score = 0.6745 * diff / med_abs_deviation

    return modified_z_score > thresh

As an example of using it, you'd do something like the following:

import numpy as np
import matplotlib.pyplot as plt

# The function above... In my case it's in a local utilities module
from sci_utilities import is_outlier

# Generate some data
x = np.random.random(100)

# Append a few "bad" points
x = np.r_[x, -3, -10, 100]

# Keep only the "good" points
# "~" operates as a logical not operator on boolean numpy arrays
filtered = x[~is_outlier(x)]

# Plot the results
fig, (ax1, ax2) = plt.subplots(nrows=2)

ax1.hist(x)
ax1.set_title('Original')

ax2.hist(filtered)
ax2.set_title('Without Outliers')

plt.show()