pymof 0.2.2

Mass ratio variance-based outlier factor (MOF)

pymof

Updated by Mr. Supakit Sroynam ([e-mail]) and Krung Sinapiromsaran ([e-mail])
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University
Version 0.2: 23 September 2024

Mass-ratio-variance based outlier factor

Latest news

1. Documents are editted. 2D and 3D examples are added.
2. Suggest the package library before importing.
3. The package operates on fixed datasets containing fewer than 1000 data points.

Introduction

An outlier of a finite dataset in statistics is defined as a data point that differs significantly from others. It is normally surrounded by a few data points while normal ones are engulfed by others. This behavior leads to the proposed outlier factor called Mass-ratio-variance based Outlier Factor (MOF). A score is assigned to a data point from the variance of the mass-ratio distribution from the rest of data points. Within a sphere of an outlier, there will be few data points compared with a normal one. So, the mass-ratio of an outlier will be different from that of a normal data point. The algorithm to generate MOF requires no parameter and embraces the density concept.

Citation

If you use this package in your research, please consider citing the below papers.

BibTex for the package:

@inproceedings{changsakul2021mass,
  title={Mass-ratio-variance based Outlier Factor},
  author={Changsakul, Phichapop and Boonsiri, Somjai and Sinapiromsaran, Krung},
  booktitle={2021 18th International Joint Conference on Computer Science and Software Engineering (JCSSE)},
  pages={1--5},
  year={2021},
  organization={IEEE}
}

Installation

To install pymof, type the following command in the terminal

pip install pymof            # normal install
pip install --upgrade pymof  # or update if needed

Use on jupyter notebook

To make sure that the installed package can be called. A user must include the package path before import as

import sys
sys.path.append('/path/to/lib/python3.xx/site-packages')

Required Dependencies :

• Python 3.9 or higher
• numpy>=1.23
• numba>=0.56.0
• scipy>=1.8.0
• scikit-learn>=1.2.0
• matplotlib>=3.5

Documentation

---

The outlier score of each data point is calculated using the Mass-ratio-variance based Outlier Factor (MOF). MOF quantifies the global deviation of a data point's density relative to the rest of the dataset. This global perspective is crucial because an outlier's score depends on its overall isolation from all other data points. By analyzing the variance of the mass ratio, MOF can effectively identify data points with significantly lower density compared to their neighbors, indicating their outlier status.

MOF()

Initialize a model object MOF

Parameters :
Return :
        self : object
                object of MOF model

MOF.fit(Data)

Fit data to MOF model
Note The number of data points should not exceed 10000 due to the computation of all pair distances.

Parameters :
        Data  : numpy array of shape (n_points, d_dimensions)
                The input samples.
Return :
        self  : object
                fitted estimator

MOF.visualize()

Visualize data points with MOF's scores
Note cannot visualize data points having a dimension greather than 3

Parameters :
Return :
    decision_scores_ : numpy array of shape (n_samples)
                                decision score for each point

MOF attributes

Attributes	Type	Details
MOF.Data	numpy array of shape (n_points, d_dimensions)	input data for scoring
MOF.MassRatio	numpy array of shape (n_samples, n_points)	MassRatio for each pair of data points
MOF.decision_scores_	numpy array of shape (n_samples)	decision score for each point

Sample usage

# This example is from MOF paper.
import matplotlib.pyplot as plt
data = np.array([[0.0, 1.0], [1.0, 1.0], [2.0, 1.0], [3.0, 1.0],
                 [0.0, 0.0], [1.0, 0.0], [2.0, 0.0], [3.0, 0.0],
                 [0.0,-1.0], [1.0,-1.0], [2.0,-1.0], [3.0,-1.0], [8.0, 4.0]
                ])
model = MOF()
model.fit(data)
scores = model.decision_scores_
print(scores)
model.visualize()

# Create a figure and axes
fig, ax = plt.subplots()
data = model.MassRatio
# Iterate over each row and create a boxplot
for i in range(data.shape[0]):
    row = data[i, :]
    mask = np.isnan(row)
    ax.boxplot(row[~mask], positions=[i + 1], vert=False, widths=0.5)
# Set labels and title
ax.set_xlabel("MOF")
ax.set_ylabel("Data points")
ax.set_title("Boxplot of MassRatio distribution")
# Show the plot
plt.grid(True)
plt.show()

Output

[0.12844997, 0.06254347, 0.08142683, 0.20940997, 0.03981233, 0.0212412 , 0.025438  , 0.08894882, 0.11300615, 0.0500218, 0.05805704, 0.17226989, 2.46193377]

3D sample

# This example demonstrates  the usage of MOF
from pymof import MOF
import numpy as np
data = np.array([[-2.30258509,  7.01040212,  5.80242044],
                 [ 0.09531018,  7.13894636,  5.91106761],
                 [ 0.09531018,  7.61928251,  5.80242044],
                 [ 0.09531018,  7.29580291,  6.01640103],
                 [-2.30258509, 12.43197678,  5.79331844],
                 [ 1.13140211,  9.53156118,  7.22336862],
                 [-2.30258509,  7.09431783,  5.79939564],
                 [ 0.09531018,  7.50444662,  5.82037962],
                 [ 0.09531018,  7.8184705,   5.82334171],
                 [ 0.09531018,  7.25212482,  5.91106761]])
model = MOF()
model.fit(data)
scores = model.decision_scores_
print(scores)
model.visualize()

Output

[0.34541068 0.11101711 0.07193073 0.07520904 1.51480377 0.94558894 0.27585581 0.06242823 0.2204504  0.02247725]