Accumulate Absolute Differences

Accumulating absolute differences involves calculating the running sum of absolute differences between elements in a sequence.

For a sequence a1, a2, …, an, the accumulate absolute differences is:

accum = 0 for i from 1 to n: accum += abs(ai - ai-1)

This metric measures variability in a sequence and has applications in statistics and signal processing.

Example in Java:

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int[] a = {2, 4, 6, 9};

int accumDiff = 0;
for(int i=1; i < a.length; i++) {
  accumDiff += Math.abs(a[i] - a[i-1]); 
}

// accumDiff = 5

Example in C++:

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vector<double> a{1.2, 3.4, -5.0, 8.4}; 

double accumDiff = 0;
for(int i=1; i < a.size(); ++i) {
  accumDiff += abs(a[i] - a[i-1]);
}

// accumDiff = 9.8

Example in Python:

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a = [10, 20, 30, 15]

accum_diff = 0
for i in range(1, len(a)):
  accum_diff += abs(a[i] - a[i-1])
  
# accum_diff = 25  

In summary, accumulating absolute differences sums the change between consecutive elements in a sequence. It measures variability.

Accumulate Absolute Differences

Accumulate Absolute Differences refers to the process of summing up the absolute differences between elements in two arrays or lists of equal length. This concept is commonly used in data analysis, machine learning, and image processing to measure the similarity or dissimilarity between two sets of data points.

Why is it Important?

Comparison: Helps in comparing two data sets or sequences.
Data Analysis: Used in feature extraction and anomaly detection.
Efficiency: Typically straightforward to implement and computationally efficient.

Formula

The formula for accumulating absolute differences between two arrays ( A ) and ( B ) of length ( n ) is:

[ \text{Accumulated Difference} = \sum_{i=0}^{n-1} | A[i] - B[i] | ]

Example Code

Java

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public class Main {
    public static int accumulateAbsoluteDifferences(int[] A, int[] B) {
        int sum = 0;
        for (int i = 0; i < A.length; i++) {
            sum += Math.abs(A[i] - B[i]);
        }
        return sum;
    }
  
    public static void main(String[] args) {
        int[] A = {1, 2, 3};
        int[] B = {4, 5, 6};
        int result = accumulateAbsoluteDifferences(A, B);
        System.out.println("Accumulated Absolute Difference: " + result);
    }
}

C++

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#include <iostream>
#include <cmath>
using namespace std;

int accumulateAbsoluteDifferences(int A[], int B[], int n) {
    int sum = 0;
    for (int i = 0; i < n; ++i) {
        sum += abs(A[i] - B[i]);
    }
    return sum;
}

int main() {
    int A[] = {1, 2, 3};
    int B[] = {4, 5, 6};
    int n = sizeof(A)/sizeof(A[0]);
    int result = accumulateAbsoluteDifferences(A, B, n);
    cout << "Accumulated Absolute Difference: " << result << endl;
    return 0;
}

Python

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def accumulate_absolute_differences(A, B):
    return sum(abs(a - b) for a, b in zip(A, B))

A = [1, 2, 3]
B = [4, 5, 6]
result = accumulate_absolute_differences(A, B)
print(f"Accumulated Absolute Difference: {result}")

Key Takeaways

Accumulate Absolute Differences is useful for comparing two sequences.
Implementation is straightforward and can be done efficiently.
The concept is widely applicable in data science, computer vision, and machine learning.