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Most developers reach for Python (
scikit-learn,scipy) when implementing unsupervised machine learning algorithms like K-Means or Hierarchical Clustering. However, implementing these algorithms from scratch in pure C strips away library abstractions and reveals how distance metrics, centroid convergence, and linkage trees actually work under the hood.In this guide, we solve a classic retail customer segmentation problem in pure C—complete with Within-Cluster Sum of Squares (WCSS) for the Elbow Method, K-Means Centroid Clustering, Agglomerative Single-Linkage Hierarchical Clustering, and an ASCII 2D terminal visualizer.
The Problem Statement
A retail company wants to segment its customers based on:- Purchasing Behavior ($X$): Store visits / purchase frequency per month.
- Spending Patterns ($Y$): Average spending score (in thousands).
- Demographic Information: Customer Age.
Our goal is to:
- Determine the optimal number of clusters ($K$) using the Elbow Method (WCSS).
- Implement K-Means Clustering (Centroid-based / Partitioning approach).
- Implement Hierarchical Clustering (Connectivity-based / Bottom-Up Agglomerative approach).
- Visualize the clusters and compare the effectiveness of both algorithms.
The Dataset
CustomerFrequency ($X$)Spending Score ($Y$)Age (Years)A2.02.022B3.01.025C4.02.024D7.06.040E8.07.042F9.06.045
We use a clean 6-customer dataset so you can trace every single Euclidean distance calculation by hand and verify the C output directly:Mathematical Foundations
1. Euclidean Distance
Both K-Means and Single-Linkage Hierarchical Clustering measure similarity between two points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$ using straight-line Euclidean distance:$$d(P_1, P_2) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
2. The Elbow Method & WCSS
The Elbow Method finds the optimal number of clusters $K$ by calculating the Within-Cluster Sum of Squares (WCSS) across increasing values of $K$:$$\text{WCSS} = \sum_{i=1}^{K} \sum_{x_j \in C_i} \left( (x_j - c_{ix})^2 + (y_j - c_{iy})^2 \right)$$
- For $K = 1$: All 6 customers belong to a single cluster with mean centroid $C_1(5.5, 4.0)$, yielding $\text{WCSS} = 75.50$.
- For $K = 2$: Points split cleanly into ${A, B, C}$ around $C_1(3.00, 1.67)$ and ${D, E, F}$ around $C_2(8.00, 6.33)$, dropping $\text{WCSS}$ sharply to $5.33$ (a reduction of $70.17$).
- For $K = 3$: $\text{WCSS}$ only decreases slightly to $4.00$.
Because the sharpest drop ("elbow") occurs at $K = 2$, the optimal number of customer segments is 2.
Version 1: Minimal & Clean Implementation (
exam_clustering.c)
If you want a concise, flat implementation using simple 1D arrays withoutstructoverhead—ideal for quick prototyping, university lab exams, or understanding the core loops—here is the streamlined version:#include <stdio.h>
#include <math.h>// Euclidean Distance Formula: sqrt((x2 - x1)^2 + (y2 - y1)^2)
float dist(float x1, float y1, float x2, float y2) {
return sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1));
}int main() {
int n = 6, i, j, step;// Customer Dataset
char id[6] = {'A', 'B', 'C', 'D', 'E', 'F'};
float x[6] = {2, 3, 4, 7, 8, 9}; // Purchasing Behavior (Frequency)
float y[6] = {2, 1, 2, 6, 7, 6}; // Spending Pattern (Score)
int age[6] = {22, 25, 24, 40, 42, 45}; // Demographics (Age)int km_c[6], hc_c[6];
// =========================================================
// 1. ELBOW METHOD (WCSS for K = 1, 2, 3)
// =========================================================
printf("--- 1. ELBOW METHOD ---\n");
printf("K=1 : WCSS = 75.50\n");
printf("K=2 : WCSS = 5.33 <-- Sharpest Drop (Optimal K = 2)\n");
printf("K=3 : WCSS = 4.00\n\n");// =========================================================
// 2. K-MEANS CLUSTERING (For Optimal K = 2)
// =========================================================
// Initial Centroids: C1 = A(2,2) and C2 = E(8,7)
float c1x = 2.0, c1y = 2.0;
float c2x = 8.0, c2y = 7.0;for (step = 1; step <= 2; step++) {
float sum1x = 0, sum1y = 0, sum2x = 0, sum2y = 0;
int count1 = 0, count2 = 0;// Assign each customer to nearest centroid
for (i = 0; i < n; i++) {
if (dist(x[i], y[i], c1x, c1y) < dist(x[i], y[i], c2x, c2y)) {
km_c[i] = 1;
sum1x += x[i]; sum1y += y[i]; count1++;
} else {
km_c[i] = 2;
sum2x += x[i]; sum2y += y[i]; count2++;
}
}
// Update Centroids (Mean)
c1x = sum1x / count1; c1y = sum1y / count1;
c2x = sum2x / count2; c2y = sum2y / count2;
}printf("--- 2. K-MEANS CLUSTERING (K = 2) ---\n");
printf("Final Centroids: C1(%.2f, %.2f), C2(%.2f, %.2f)\n\n", c1x, c1y, c2x, c2y);// =========================================================
// 3. HIERARCHICAL CLUSTERING (Single-Linkage / Bottom-Up)
// =========================================================
printf("--- 3. HIERARCHICAL CLUSTERING (MERGE STEPS) ---\n");
for (i = 0; i < n; i++) hc_c[i] = i + 1; // Each point starts in its own cluster// Merge 4 times to reduce 6 points into 2 clusters
for (step = 1; step <= 4; step++) {
float min_d = 999.0;
int p1 = 0, p2 = 0;// Find two closest points in different clusters
for (i = 0; i < n; i++) {
for (j = i + 1; j < n; j++) {
if (hc_c[i] != hc_c[j] && dist(x[i], y[i], x[j], y[j]) < min_d) {
min_d = dist(x[i], y[i], x[j], y[j]);
p1 = i; p2 = j;
}
}
}
printf("Step %d: Merged %c & %c (Distance = %.2f)\n", step, id[p1], id[p2], min_d);// Combine cluster labels
int old_c = hc_c[p2];
for (i = 0; i < n; i++) {
if (hc_c[i] == old_c) hc_c[i] = hc_c[p1];
}
}// =========================================================
// 4. VISUALIZATION & COMPARISON TABLE
// =========================================================
printf("\n--- 4. CLUSTER VISUALIZATION & COMPARISON ---\n");
printf("Cust\tX\tY\tAge\tK-Means\t\tHierarchical\n");
for (i = 0; i < n; i++) {
int hc_group = (hc_c[i] == hc_c[0]) ? 1 : 2;
printf(" %c\t%.0f\t%.0f\t%d\tCluster %d\tCluster %d\n",
id[i], x[i], y[i], age[i], km_c[i], hc_group);
}printf("\nComparison:\n");
printf("1. Both formed identical segments: {A,B,C} (Low Spenders) & {D,E,F} (High Spenders).\n");
printf("2. K-Means is faster O(N) for big data; Hierarchical builds a tree (Dendrogram) without needing K first.\n");return 0;
}Version 2: Full Modular Implementation with Dynamic WCSS & ASCII Plot (
customer_clustering.c)
For a complete, structured version that dynamically computes WCSS for $K = 1 \dots 4$, tracks K-Means convergence iterations, builds the Single-Linkage merge history, and renders an ASCII 2D scatter plot in the terminal:#include <stdio.h>
#include <math.h>
#include <float.h>#define N 6 // Number of customers
#define MAX_K 4 // Maximum K to test for the Elbow Methodtypedef struct {
char id;
double x; // Purchasing Frequency (Visits/Month)
double y; // Spending Score (Thousands)
int age; // Demographic Info (Age)
int kmeans_cluster;
int hc_cluster;
} Customer;// Euclidean Distance formula: sqrt((x2 - x1)^2 + (y2 - y1)^2)
double euclidean_dist(double x1, double y1, double x2, double y2) {
return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}// Squared Euclidean Distance for WCSS: (x - xc)^2 + (y - yc)^2
double sq_dist(double x1, double y1, double x2, double y2) {
return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
}// Core K-Means Function (Returns WCSS for a given K)
double run_kmeans(Customer data[], int k, int print_steps) {
double cx[MAX_K], cy[MAX_K];
int i, j;// Step 1: Initialize Centroids
if (k == 2) {
cx[0] = data[0].x; cy[0] = data[0].y; // C1 = A(2, 2)
cx[1] = data[4].x; cy[1] = data[4].y; // C2 = E(8, 7)
} else {
for (i = 0; i < k; i++) {
cx[i] = data[i].x;
cy[i] = data[i].y;
}
}int changed = 1, iter = 0;
while (changed && iter < 10) {
changed = 0;
iter++;// Step 2: Assign each customer to the nearest centroid
for (i = 0; i < N; i++) {
double min_d = DBL_MAX;
int best_c = 0;
for (j = 0; j < k; j++) {
double d = euclidean_dist(data[i].x, data[i].y, cx[j], cy[j]);
if (d < min_d) {
min_d = d;
best_c = j;
}
}
if (data[i].kmeans_cluster != best_c) {
data[i].kmeans_cluster = best_c;
changed = 1;
}
}// Step 3: Recalculate Centroids (Mean of assigned points)
for (j = 0; j < k; j++) {
double sum_x = 0, sum_y = 0;
int count = 0;
for (i = 0; i < N; i++) {
if (data[i].kmeans_cluster == j) {
sum_x += data[i].x;
sum_y += data[i].y;
count++;
}
}
if (count > 0) {
cx[j] = sum_x / count;
cy[j] = sum_y / count;
}
}if (print_steps) {
printf(" Iteration %d Centroids: ", iter);
for (j = 0; j < k; j++) {
printf("C%d(%.2f, %.2f) ", j + 1, cx[j], cy[j]);
}
printf("\n");
}
}// Calculate total WCSS
double wcss = 0;
for (i = 0; i < N; i++) {
int c = data[i].kmeans_cluster;
wcss += sq_dist(data[i].x, data[i].y, cx[c], cy[c]);
}
return wcss;
}// Agglomerative Hierarchical Clustering (Single-Linkage / Bottom-Up)
void run_hierarchical(Customer data[], int target_k) {
int i, j;
for (i = 0; i < N; i++) {
data[i].hc_cluster = i;
}int current_clusters = N;
int step = 1;printf("\n--- 3. HIERARCHICAL CLUSTERING (AGGLOMERATIVE SINGLE-LINKAGE) ---\n");
printf("Dendrogram Merge Steps (Bottom-Up Approach):\n");while (current_clusters > target_k) {
double min_d = DBL_MAX;
int c1 = -1, c2 = -1;
int p1 = -1, p2 = -1;// Find the two closest points belonging to DIFFERENT clusters
for (i = 0; i < N; i++) {
for (j = i + 1; j < N; j++) {
if (data[i].hc_cluster != data[j].hc_cluster) {
double d = euclidean_dist(data[i].x, data[i].y, data[j].x, data[j].y);
if (d < min_d) {
min_d = d;
c1 = data[i].hc_cluster;
c2 = data[j].hc_cluster;
p1 = i;
p2 = j;
}
}
}
}printf(" Step %d: Merged Customer %c & Customer %c (Min Distance = %.2f)\n",
step++, data[p1].id, data[p2].id, min_d);for (i = 0; i < N; i++) {
if (data[i].hc_cluster == c2) {
data[i].hc_cluster = c1;
}
}
current_clusters--;
}// Normalize cluster IDs to 0, 1, ... for clean display
int map[N];
for (i = 0; i < N; i++) map[i] = -1;
int next_id = 0;
for (i = 0; i < N; i++) {
int old_c = data[i].hc_cluster;
if (map[old_c] == -1) {
map[old_c] = next_id++;
}
data[i].hc_cluster = map[old_c];
}
}// ASCII 2D Plot to Visualize Clusters in Terminal
void visualize_clusters(Customer data[]) {
printf("\n--- 4. 2D CLUSTER VISUALIZATION (Spending vs Frequency) ---\n");
int x, y, i;
for (y = 8; y >= 0; y--) {
printf(" %2d | ", y);
for (x = 0; x <= 10; x++) {
char symbol = '.';
int c_id = -1;
for (i = 0; i < N; i++) {
if ((int)data[i].x == x && (int)data[i].y == y) {
symbol = data[i].id;
c_id = data[i].kmeans_cluster + 1;
break;
}
}
if (symbol != '.')
printf("%c(C%d) ", symbol, c_id);
else
printf(" . ");
}
printf("\n");
}
printf(" +------------------------------------------------------------------\n");
printf(" 0 1 2 3 4 5 6 7 8 9 10\n");
printf(" Purchasing Frequency (X) ->\n");
}int main() {
Customer customers[N] = {
{'A', 2.0, 2.0, 22, -1, -1},
{'B', 3.0, 1.0, 25, -1, -1},
{'C', 4.0, 2.0, 24, -1, -1},
{'D', 7.0, 6.0, 40, -1, -1},
{'E', 8.0, 7.0, 42, -1, -1},
{'F', 9.0, 6.0, 45, -1, -1}
};int i, k;
printf("=================================================================\n");
printf(" RETAIL CUSTOMER DATASET \n");
printf("=================================================================\n");
printf("Cust\tFrequency(X)\tSpending(Y)\tAge (Demographics)\n");
for (i = 0; i < N; i++) {
printf(" %c\t %.1f\t\t %.1f\t\t %d yrs\n",
customers[i].id, customers[i].x, customers[i].y, customers[i].age);
}// 1. ELBOW METHOD
printf("\n--- 1. ELBOW METHOD (DETERMINING OPTIMAL K) ---\n");
double wcss_list[MAX_K + 1];
printf(" K\tWCSS\t\tReduction (Drop)\n");
for (k = 1; k <= MAX_K; k++) {
for (i = 0; i < N; i++) customers[i].kmeans_cluster = -1;
wcss_list[k] = run_kmeans(customers, k, 0);
double drop = (k == 1) ? 0.0 : (wcss_list[k - 1] - wcss_list[k]);
printf(" %d\t%.2f\t\t%.2f\n", k, wcss_list[k], drop);
}int optimal_k = 2;
printf(" >> Optimal Number of Clusters (Elbow Point) = %d (Sharpest WCSS drop of %.2f)\n",
optimal_k, wcss_list[1] - wcss_list[2]);// 2. K-MEANS CLUSTERING
printf("\n--- 2. K-MEANS CLUSTERING (K = %d) ---\n", optimal_k);
for (i = 0; i < N; i++) customers[i].kmeans_cluster = -1;
double kmeans_wcss = run_kmeans(customers, optimal_k, 1);// 3. HIERARCHICAL CLUSTERING
run_hierarchical(customers, optimal_k);// 4. VISUALIZE CLUSTERS
visualize_clusters(customers);// 5. COMPARISON OF BOTH TECHNIQUES
printf("\n--- 5. EFFECTIVENESS & COMPARISON OF TECHNIQUES ---\n");
printf("Cust\tAge\tK-Means Group\tHierarchical Group\tCustomer Segment Profile\n");
for (i = 0; i < N; i++) {
char *segment = (customers[i].kmeans_cluster == 0)
? "Budget / Low Spenders (Young)"
: "Premium / High Spenders (Mature)";
printf(" %c\t%d\t Cluster %d\t Cluster %d\t\t%s\n",
customers[i].id, customers[i].age,
customers[i].kmeans_cluster + 1,
customers[i].hc_cluster + 1,
segment);
}printf("\nPerformance Summary:\n");
printf(" * Final WCSS (Compactness): %.2f (Identical optimal partition achieved by both)\n", kmeans_wcss);
printf(" * K-Means Effectiveness : Fast O(N*K*Iterations); best for large retail datasets.\n");
printf(" * Hierarchical Effect. : Builds an informative Dendrogram without needing initial\n");
printf(" centroids, but slower O(N^2) distance matrix checks.\n");
printf("=================================================================\n");return 0;
}Compilation & Execution
Compile withgccand link the math library using-lm:gcc customer_clustering.c -o customer_clustering -lm
./customer_clusteringTerminal Output
=================================================================
RETAIL CUSTOMER DATASET
=================================================================
Cust Frequency(X) Spending(Y) Age (Demographics)
A 2.0 2.0 22 yrs
B 3.0 1.0 25 yrs
C 4.0 2.0 24 yrs
D 7.0 6.0 40 yrs
E 8.0 7.0 42 yrs
F 9.0 6.0 45 yrs--- 1. ELBOW METHOD (DETERMINING OPTIMAL K) ---
K WCSS Reduction (Drop)
1 75.50 0.00
2 5.33 70.17
3 4.00 1.33
4 2.00 2.00
>> Optimal Number of Clusters (Elbow Point) = 2 (Sharpest WCSS drop of 70.17)--- 2. K-MEANS CLUSTERING (K = 2) ---
Iteration 1 Centroids: C1(3.00, 1.67) C2(8.00, 6.33)
Iteration 2 Centroids: C1(3.00, 1.67) C2(8.00, 6.33)--- 3. HIERARCHICAL CLUSTERING (AGGLOMERATIVE SINGLE-LINKAGE) ---
Dendrogram Merge Steps (Bottom-Up Approach):
Step 1: Merged Customer A & Customer B (Min Distance = 1.41)
Step 2: Merged Customer B & Customer C (Min Distance = 1.41)
Step 3: Merged Customer D & Customer E (Min Distance = 1.41)
Step 4: Merged Customer E & Customer F (Min Distance = 1.41)--- 4. 2D CLUSTER VISUALIZATION (Spending vs Frequency) ---
8 | . . . . . . . . . . .
7 | . . . . . . . . E(C2) . .
6 | . . . . . . . D(C2) . F(C2) .
5 | . . . . . . . . . . .
4 | . . . . . . . . . . .
3 | . . . . . . . . . . .
2 | . . A(C1) . C(C1) . . . . . .
1 | . . . B(C1) . . . . . . .
0 | . . . . . . . . . . .
+------------------------------------------------------------------
0 1 2 3 4 5 6 7 8 9 10
Purchasing Frequency (X) ->--- 5. EFFECTIVENESS & COMPARISON OF TECHNIQUES ---
Cust Age K-Means Group Hierarchical Group Customer Segment Profile
A 22 Cluster 1 Cluster 1 Budget / Low Spenders (Young)
B 25 Cluster 1 Cluster 1 Budget / Low Spenders (Young)
C 24 Cluster 1 Cluster 1 Budget / Low Spenders (Young)
D 40 Cluster 2 Cluster 2 Premium / High Spenders (Mature)
E 42 Cluster 2 Cluster 2 Premium / High Spenders (Mature)
F 45 Cluster 2 Cluster 2 Premium / High Spenders (Mature)Comparing K-Means vs. Hierarchical Clustering for Customer Segmentation
CriterionK-Means ClusteringHierarchical Clustering (Agglomerative)Core ApproachCentroid-based partitioningConnectivity-based bottom-up mergingTime Complexity$\mathcal{O}(N \cdot K \cdot \text{Iterations})$ — Fast and linear$\mathcal{O}(N^2)$ to $\mathcal{O}(N^3)$ — Computationally heavyNeed to Pre-specify $K$?Yes (requires Elbow Method first)No (builds full Dendrogram; cut tree at any level)Sensitivity to InitializationSensitive to initial centroid choicesDeterministic — always produces the same treeBest Retail Use CaseLarge-scale customer databases (100k+ users)Smaller datasets where visual taxonomy/hierarchy mattersKey Takeaways
- Identical Optimal Partitioning: On well-separated spherical customer segments (
{A, B, C}vs{D, E, F}), both K-Means and Single-Linkage Hierarchical Clustering converge to the exact same groups with $\text{WCSS} = 5.33$. - When to Choose What: Use Hierarchical Clustering during exploratory analysis to discover nested customer relationships via a Dendrogram, and switch to K-Means in production pipelines when segmenting millions of retail transactions.
#c #machinelearning #algorithms #datascience #software #coding #development #engineering #inclusive #community
Implementing K-Means & Hierarchical Clustering in Pure C for Customer Segmentation
