Distance metrics play a crucial role in several Machine Learning (ML) techniques, aimed at recognising patterns, extracting information, and more. Recommendations systems and facial recognition technologies rely heavily on ML to offer accurate data to users. Nonetheless, it is essential to maintain some minimal separation from the data while working with ML algorithms, so that it can effectively differentiate between distinct materials based on their similarities, a concept known as “distance metric”.
A precise calculation of the distance between different data points is crucial for identifying patterns and drawing credible conclusions from input data, ultimately leading to a more reliable outcome. This, in turn, boosts the efficacy of both supervised and unsupervised machine learning algorithms employeed for tasks such as clustering, classification, and information retrieval. To know more about the comparison between deep learning and machine learning, check out our blog on “The Final Showdown: Deep Learning vs. Machine Learning”.
Within this article, we will delve into the realm of distance metrics, explore their various types, and scrutinise their mathematical computations as well as their relevance in machine learning algorithms. Consequently, readers will be able to make sound decisions while selecting the most suitable distance metric for their machine learning model.
Understanding the Basic Concept of Euclidean Distance
Among the various approaches in the field of mathematics, the Euclidean distance measure holds a pre-eminent position. This technique of calculating distance utilises the Pythagorean theorem, which provides the shortest route between two points in a given coordinate system. By using this theory, the Euclidean distance measure can accurately generate the shortest distance between two points, rendering it highly effective.
Several Machine Learning algorithms employ Euclidean Distance as the default distance metric for measuring the proximity between two observed data points. This type of metric excels at determining the distinctions between two columns of numerical data, such as height, weight, and salaries, that comprise continuous, numerical variables. In essence, Euclidean Distance is a highly effective method for evaluating the proximity of two data points with numerical values.
If you were assigned to write an equivalent code in Python, the Python code block would resemble the following:
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import numpy as np
#Function to calculate the Euclidean Distance between two points
def euclidean(p,q)->float:
distance = 0
for index, feature in enumerate(p):
d =(feature - q[index])**2
distance = distance + d
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return np.sqrt(distance)
Google Maps demonstrates the elegance of the Euclidean distance metric, which calculates the separation between two vectors with real values.
Analogous to a Journey to Manhattan with Different Metrics
The distance between the two points on a grid can be measured in two different ways – either by using Manhattan distance or cityblock distance.
When dealing with datasets composed of binary or discrete attributes, this method is advantageous, as the path created using the attribute values is self-explanatory.
The given code snippet can be utilised to compute this metric:
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import numpy as np
#Function to calculate the Manhattan Distance between two points
def manhattan(a,b)->int:
distance = 0
for index, feature in enumerate(a):
d = np.abs(feature - b[index])
distance = distance + d
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return distance
One should keep in mind that the Manhattan distance cannot be solely relied upon to measure distance for datasets containing floating properties. It can serve as a substitute for the more efficient Euclidean distance, but it is not recommendable while working with high dimensional data.
The expression “taxicab distance” describes the commuting duration between two locations in Manhattan colloquially. This phrase originates from the idea that a taxi driver chooses the shortest distance between two points, reducing the travel time between them.
The Minkowski Distance Calculation
The Minkowski distance rating is an enhanced form of both the Manhattan and Euclidean metrics, which enables the analysis of spatial differences between two or more vectors. In machine learning, this metric is frequently used to determine the proximity of two objects, providing a precise assessment of their distance from each other. Using the Minkowski equation, the distance calculation can be determined with accuracy, enabling the comparison of the relative position of two objects.
The p-norm vector is also known as the p-norm, which is a measure of the norm’s order. By allowing the parameter p to be inserted, this vector may be used to compute various types of distances.
where
When travelling in Manhattan, p=1.
For calculating the Euclidean distance, p=2.
When the Chebyshev distance’s parameter p is infinite, the distance is also infinite.
The Chebyshev distance refers to the utmost separation achieved along an axes in any given space.
To calculate the Minkowski distance, use the Python function provided below:
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def minkowski_distance(a, b, p):
return sum(abs(e1-e2)**p for e1, e2 in zip(a,b))**(1/p)
#OR
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from scipy.spatial import minkowski_distance
dist = minkowski_distance(row1, row2)
print(dist)
Measuring the Distance between Hammers
Using Hamming distance to compare same-length strings is a straightforward technique for assessing the similarity of two data points. This distance metric calculates the number of values that vary between the two points, providing a clear representation of the dissimilarity between them.
For instance:
Consider the following examples:
A = [1, 2, 5, 8, 9, 0]
B = [1, 3, 5, 7, 9, 0]
As there are two differing values between the given binary strings, the Hamming distance between them is 2 in the above example.
The Hamming distance can be calculated with the following formula:
d = min{xC, yC, xy}. We can obtain d(x,y) with this formula.
Using the Hamming distance is useful in identifying communication errors between computers. However, it is crucial to compare only similar data sets for accurate outcomes. Additionally, if the feature size is substantial, the Hamming distance may not be the appropriate distance measure to use.
The Hamming distance function in Python can be defined as:
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def hamming_distance(a, b):
return sum(abs(e1 - e2) for e1, e2 in zip(a, b)) / len(a)
#OR
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from scipy.spatial.distance import hamming
dist = hamming(row1, row2)
print(dist)
In constructing a machine learning model, it is crucial to have knowledge regarding various distance measurements and how to select the most appropriate metrics for your dataset. Having familiarity with the properties of each distance metric and knowing how to implement them in Python can provide the essential insights in determining the best distance metric choice for the specific model being developed.
Check out our blog post on building a machine learning model to learn more.
