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Unveiling Outliers: Exploring Alternatives to MaskedArray.anom()


Purpose

  • Calculates the deviations (anomalies) of elements in a masked array from the mean along a specified axis.

What are Masked Arrays?

  • Masked values are excluded from calculations by ma.MaskedArray.anom().
  • They combine a regular NumPy array with a mask, which is another boolean array indicating the validity of each element in the main array.
  • Masked arrays are a special data structure in NumPy that can handle missing or invalid data points.

Function Parameters

  • dtype (dtype, optional): This defines the data type used for calculations. Defaults to float32 for integer arrays and the original data type for float arrays.
  • axis (int, optional): This specifies the axis along which the anomalies are computed. By default (axis=None), the mean of the flattened array is used as the reference.

Return Value

  • The mask is propagated from the input array.
  • The data part contains the anomalies (deviations from the mean).
  • It returns a new masked array with the same shape as the input array.

Example

import numpy.ma as ma

# Create a masked array
data = [1, 2, None, 4]
mask = [False, False, True, False]
arr = ma.array(data, mask=mask)

# Calculate anomalies along axis 0 (default)
anomalies = arr.anom()

print(anomalies)

This code will output:

masked_array(data=[-1., 0., nan, 1.], mask=[False, False,  True, False],
              fill_value=1e+20)

As you can see, the masked value (None) is excluded from the calculation, and it remains masked (NaN) in the output.

  • Remember to consider the axis argument and data type if needed for specific calculations.
  • It helps to analyze masked data effectively by excluding invalid points.
  • ma.MaskedArray.anom() is useful for identifying outliers or deviations from the central tendency in masked datasets.

Example 1: Specifying the axis

import numpy.ma as ma

# Create a 2D masked array
data = [[1, 2, None], [4, None, 5]]
mask = [[False, False, True], [False, True, False]]
arr = ma.array(data, mask=mask)

# Calculate anomalies along axis 1 (columns)
anomalies_by_column = arr.anom(axis=1)

print(anomalies_by_column)

This code calculates anomalies for each column (axis=1) independently. The masked values will be excluded within each column.

Example 2: Specifying the data type

import numpy.ma as ma

# Create a masked array with integer data
data = [10, 20, 30, None]
mask = [False, False, False, True]
arr = ma.array(data, mask=mask, dtype=int)

# Calculate anomalies using float32 for calculations
anomalies_float = arr.anom(dtype=float32)

print(anomalies_float)

In this example, even though the data is integer (dtype=int), specifying dtype=float32 forces the calculations to be done in floating-point precision for potentially more accurate results.

import numpy.ma as ma

# Create a masked array with all elements masked
data = [None, None, None]
mask = [True, True, True]
arr = ma.array(data, mask=mask)

# Anomalies calculation with all-masked data
anomalies = arr.anom()

print(anomalies.mask)  # Print only the mask

Manual Calculation

import numpy.ma as ma
import numpy as np

# Create a masked array
data = [1, 2, None, 4]
mask = [False, False, True, False]
arr = ma.array(data, mask=mask)

# Calculate mean excluding masked values
mean = np.ma.mean(arr, masked=True)

# Calculate standard deviation excluding masked values
std = np.ma.std(arr, masked=True)

# Calculate anomalies (absolute deviations from the mean)
anomalies = np.abs(arr - mean) / std

print(anomalies)

This approach gives you more control over the calculations and allows for customization (e.g., using median instead of mean).

IQR (Interquartile Range) based Outlier Detection

import numpy.ma as ma
from scipy import stats

# Create a masked array
data = [1, 2, 100, 4]
mask = [False, False, False, False]
arr = ma.array(data, mask=mask)

# Remove masked values before IQR calculation
data_clean = arr.compressed()

# Calculate IQR
q1, q3 = stats.iqr(data_clean)
iqr = q3 - q1

# Identify outliers based on IQR thresholds (e.g., 1.5 * IQR)
lower_bound = q1 - 1.5 * iqr
upper_bound = q3 + 1.5 * iqr

outliers = arr[(arr < lower_bound) | (arr > upper_bound)]

print(outliers)

This approach utilizes the IQR to define thresholds for identifying outliers within the masked array.

Choosing the Right Approach

The best alternative depends on your specific needs:

  • If you require more control over the calculations or want to use alternative metrics like IQR, consider manual calculations or libraries like scipy.stats.
  • If you need a simple and built-in solution for anomaly detection based on mean and standard deviation, ma.MaskedArray.anom() is a good choice.