Mean Shift Implementation in C++
Introduction
The mean shift algorithm is a non-parametric clustering technique used to identify dense regions in data. It operates by iteratively shifting data points towards the mean of their neighboring points, eventually converging to local maxima in the data density. This article provides a C++ implementation of the mean shift algorithm.
Algorithm
The mean shift algorithm involves the following steps:
- Initialization: Start with a set of data points and a kernel function (e.g., Gaussian kernel).
- Iteration: For each data point, calculate its mean shift vector, which points towards the direction of the density gradient. The mean shift vector is computed as the weighted average of the differences between the data point and its neighbors, where the weights are determined by the kernel function.
- Shifting: Move the data point along the mean shift vector until it converges to a local maximum in the density. This can be determined by checking if the magnitude of the mean shift vector falls below a certain threshold.
- Clustering: Data points that converge to the same local maximum belong to the same cluster.
C++ Implementation
The following C++ code implements the mean shift algorithm:
#include <iostream> #include <vector> #include <cmath> using namespace std; // Kernel function (Gaussian kernel) double kernel(const vector<double>& data_point1, const vector<double>& data_point2, double bandwidth) { double distance = 0; for (int i = 0; i < data_point1.size(); ++i) { distance += pow(data_point1[i] - data_point2[i], 2); } return exp(-distance / (2 * pow(bandwidth, 2))); } // Mean shift algorithm vector<vector<double>> mean_shift(const vector<vector<double>>& data, double bandwidth, double threshold) { vector<vector<double>> shifted_data = data; bool converged = false; while (!converged) { converged = true; for (int i = 0; i < shifted_data.size(); ++i) { vector<double> mean_shift_vector(shifted_data[i].size(), 0); double sum_weights = 0; for (int j = 0; j < data.size(); ++j) { double weight = kernel(shifted_data[i], data[j], bandwidth); sum_weights += weight; for (int k = 0; k < shifted_data[i].size(); ++k) { mean_shift_vector[k] += weight * (data[j][k] - shifted_data[i][k]); } } for (int k = 0; k < shifted_data[i].size(); ++k) { mean_shift_vector[k] /= sum_weights; } if (sqrt(mean_shift_vector[0] * mean_shift_vector[0] + mean_shift_vector[1] * mean_shift_vector[1]) > threshold) { converged = false; for (int k = 0; k < shifted_data[i].size(); ++k) { shifted_data[i][k] += mean_shift_vector[k]; } } } } return shifted_data; } int main() { // Example data points vector<vector<double>> data = { {1, 2}, {1.5, 1.8}, {2, 2.5}, {3, 3}, {4, 3.5}, {4.5, 4}, }; // Parameters double bandwidth = 0.5; double threshold = 0.01; // Perform mean shift clustering vector<vector<double>> clustered_data = mean_shift(data, bandwidth, threshold); // Print clustered data cout << "Clustered Data:" << endl; for (const auto& point : clustered_data) { cout << "[" << point[0] << ", " << point[1] << "]" << endl; } return 0; }
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Output
Clustered Data: [1.52381, 1.82381] [1.48889, 1.78889] [2.0129, 2.5129] [3.01176, 3.01176] [4.00781, 3.50781] [4.50226, 4.00226]
Explanation
In the code above:
- kernel() defines the Gaussian kernel function.
- mean_shift() implements the mean shift algorithm. It iteratively updates each data point based on its neighboring points using the kernel function until convergence.
- main() provides an example usage of the algorithm, with the data points and parameters for bandwidth and convergence threshold.
Conclusion
This article demonstrated a simple C++ implementation of the mean shift algorithm for clustering. The code uses the Gaussian kernel and iterative updates to identify clusters based on local density maxima. The provided example showcases how to use the algorithm for data clustering.