Optimal One Dimensional K Means Calculator
Partition scalar observations into contiguous sorted clusters with the globally minimum squared error.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Sort observations and use dynamic programming over every contiguous cluster boundary.
DP[k,j]=min_i(DP[k−1,i]+SSE of sorted positions i…j−1)
Worked example
1,2,3 and10,11,12 form two clusters centered at2 and11 with total SSE4.
Assumptions and input details
Scalar Euclidean squared error only, equal observation weights. Ties can admit several optimal partitions; the first encountered boundary is retained. No automatic choice of k or multidimensional clustering.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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