KNN Classifier — Machine Learning/Classical Models

KNN Classifier

Machine Learning / Classical Models

Classifies a sample by the majority label of its k nearest training points:

d²_i = Σ_j (u_j − X_ij)², then the k smallest distances vote.

This is KNeighborsClassifier.predict with _fit_X and _y pasted in as config. kNN is the one classical model with no fitted parameters – the training set is the model – which is why the configuration here is a matrix and a label column rather than coefficients.

Ports

• u – the sample, a column [d,1] matching the d columns of Training Set.
• cls – a scalar [1,1]: the winning class, plus Index Base.
• votes – a scalar [1,1]: how many of the k neighbours carried the winning label. At most k, at least one. Read it as a confidence – 2 of 5 is a far weaker answer than 5 of 5.

Parameters

• Training Set – the [N,d] matrix, one training sample per row, which is sklearn's orientation. N rows is the number of stored examples, d columns the feature count the input must match.
• Training Labels – an [N,1] column giving each row's class position, counted from 0 whatever the index base. It is the only source of the class count: C is one past the largest label, so no separate setting can disagree with the data beside it.
• Neighbors – k, a whole number ≥ 1: how many nearest points vote. Larger k smooths the boundary; k above N simply lets every point vote.
• Index Base – what the first class is called:
  • Zero-based (PyTorch, numpy) – the first class is 0. The default.
  • One-based (MATLAB) – the first class is 1.
  It shifts the reported class and nothing else; the labels are always counted from 0.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. The training set, the labels, k and the base are baked into the body at export time; there is no tunable parameter, because the training set determines how much code is emitted.

The three HDL targets are genuine synthesizable Q16.16: the distance is squared and never rooted, so the block is multiplies, adds and comparisons with no division and no transcendental anywhere.

Simulink bridge

None, and for two independent reasons. Nearest-neighbour classification lives in the Statistics and Machine Learning Toolbox, which is not installed on this machine; and its block takes a fitted model object rather than parameters, which no parameter rule could carry across even if the toolbox were present. There is therefore no parameter set to map onto and no reference to run a parity testbench against. A model carrying this block exports with the block reported rather than silently dropped.

Notes

• Algebraic and stateless: the outputs depend only on the current sample.
• Two tie rules, and both are part of the contract. Among equal distances the lower training-set row counts as nearer; among equal vote counts the lowest class index wins, which is Argmax Decision's rule. Both are decided by counting rather than by sorting, so every backend agrees on exactly which points tie.
• The distance is squared and never rooted, exactly as in K Means Assign. Ranking is monotone under squaring, so the root would change no answer while costing every backend its exactness.
• Cost is O(N²·d) per sample – inherent to ranking without storing a sorted order, and fine for the small baked sets this family targets. A training set of hundreds of rows belongs behind a real index rather than in a block, and will emit a great deal of code.
• Nonlinear and discontinuous, and deliberately carries no state space: the class steps rather than varies, so no A/B/C/D describes it and model reduction correctly refuses the block.
• At a near-tie in distance the HDL targets can rank differently. They compare Q16.16 values, one quantum of which is about 1.5e-5, where the in-app run compares doubles – so two training points closer together than that can swap places and change the vote. This is inherent to a discrete decision taken in fixed point, and it is the same caveat Argmax Decision carries.