Example Data Table
| x | y | class | Meaning |
|---|---|---|---|
| 1.2 | 2.1 | A | First numeric feature, second feature, and known class. |
| 2.9 | 3.6 | B | A training point from another group. |
| 4.5 | 1.8 | C | A point that may support class C near the target. |
Formula Used
The calculator first computes the distance between the target point and every training point.
Euclidean: d = sqrt((x - xi)^2 + (y - yi)^2)
Manhattan: d = |x - xi| + |y - yi|
Minkowski: d = (|x - xi|^p + |y - yi|^p)^(1 / p)
After neighbors are selected, posterior probability is estimated by class support:
P(class c | target) = (class weight + alpha) / (total weight + alpha × number of classes)
Uniform voting gives each neighbor weight 1. Inverse distance uses 1 / (distance + epsilon). Gaussian weighting uses exp(-distance^2 / (2 × sigma^2)).
How To Use This Calculator
- Paste training data with x, y, and class columns.
- Enter the target point that needs classification.
- Select k, radius r, distance metric, and weighting method.
- Use scaling when feature ranges are very different.
- Press calculate to view probabilities above the form.
- Download CSV or PDF results when reporting is needed.
Understanding KNN Posterior Probability
Local Classification Estimate
KNN posterior probability is a local classification estimate. It studies the training points closest to a new observation. The calculator treats each row as evidence around the target point. It then estimates how likely each class is inside that local neighborhood.
Why Neighborhood Choice Matters
The method is useful when class shapes are irregular. It does not assume a straight decision boundary. Instead, the answer depends on distances, the selected value of k, and the optional radius r. Small neighborhoods can react quickly to local patterns. Larger neighborhoods are usually smoother and less sensitive to noise.
Advanced Controls
This tool supports several practical controls. Euclidean distance works well for balanced numeric features. Manhattan distance can be helpful when movement along axes matters. Minkowski distance gives extra flexibility through the p value. Radius mode lets you study only points inside a chosen local circle. The combined k within radius mode is strict, because it filters by r first and then keeps the closest neighbors.
Weights And Smoothing
Posterior probability is estimated from neighbor support. With uniform voting, every selected neighbor has equal influence. With inverse distance weighting, closer points matter more. Gaussian weighting also favors nearby observations, while reducing extreme jumps. Laplace smoothing can prevent zero probabilities when a class is not present in the selected neighborhood.
Interpreting Results
The result should be read as a neighborhood based probability estimate, not a permanent truth. It depends on feature scaling. A variable with a large numeric range can dominate distance. For reliable comparisons, scale features before pasting data. Also test several k and r values. Stable predictions across settings are usually more trustworthy.
Data Review
The example table shows how two numeric features and a class label can be entered. You may replace it with your own comma separated data. The result table lists each class, its votes, total weight, and posterior probability. The predicted class is the class with the largest probability.
Exporting Reports
Use the CSV export for spreadsheet review. Use the PDF export for reports or records. Keep the input data attached when sharing results, because posterior estimates only make sense with the selected training sample and settings. For stronger analysis, compare predicted classes with known labels. Repeated checks help reveal weak settings, outliers, or neighborhoods that need more data before making final decisions.
FAQs
What is posterior probability in KNN?
It is the estimated chance that a target point belongs to each class, based on nearby training points. In this calculator, it comes from votes or weighted votes inside the selected neighborhood.
What does radius r mean?
Radius r limits neighbors to points whose distance from the target is within the chosen radius. It helps focus the estimate on a local region instead of always using a fixed k.
Should I use k only or radius mode?
Use k only when you always want a fixed number of neighbors. Use radius mode when neighborhood size should depend on distance. Use k within radius for stricter local classification.
Why does feature scaling matter?
Distance methods are sensitive to numeric ranges. If one feature has much larger values, it can dominate the distance calculation. Scaling makes features more comparable before neighbors are selected.
What is Laplace alpha?
Laplace alpha adds smoothing to class probabilities. It prevents a class from receiving a zero probability only because no selected neighbor belongs to that class.
When should inverse distance weighting be used?
Use inverse distance weighting when closer neighbors should count more strongly than farther neighbors. It is useful when local evidence near the target should receive more influence.
What does the predicted class mean?
The predicted class is the class with the highest posterior probability. It is based only on the supplied training data, selected metric, k, r, weights, and smoothing settings.
Can I export the results?
Yes. The calculator includes CSV and PDF export options. The CSV is useful for spreadsheets, while the PDF is useful for reports, records, and quick sharing.