A data scientist is preparing a dataset for a K-Means clustering algorithm, which uses Euclidean distance to group data points. The dataset includes customer_age (ranging from 18 to 85) and annual_income (ranging from 25,000 to 250,000 in USD). If the data scientist proceeds without applying any feature scaling, what is the most likely impact on the model's performance?
The Euclidean distance metric will automatically normalize the features, resulting in balanced clusters.
The clustering algorithm will fail to execute because the features have different units and scales.
The annual_income feature will disproportionately influence the distance calculations, minimizing the effect of customer_age.
The customer_age feature will dominate the clustering process because of its smaller numerical range.
The correct answer is that the annual_income feature will disproportionately influence the distance calculations. The Euclidean distance is calculated as the square root of the sum of the squared differences between the coordinates of two points. Because the annual_income values are several orders of magnitude larger than the customer_age values, the squared difference in income will be vastly larger than the squared difference in age. Consequently, the income feature will almost entirely determine the distance between points, and the age feature will have a negligible impact on the final cluster assignments. To prevent this, data scientists should apply feature scaling techniques like standardization or normalization so that all features contribute more equally to the distance metric. The algorithm will not fail to execute, but the results will be skewed. The feature with the larger range, not the smaller one, will dominate. The distance metric itself does not perform normalization; this is a separate preprocessing step.
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