Kernel Classifier Predictor — Machine Learning/Classical Models

Kernel Classifier Predictor

Machine Learning / Classical Models

Evaluates a fitted binary kernel classifier at inference – what MATLAB's [label, score] = predict(Mdl, x) returns for a ClassificationKernel model (trained with fitckernel) and one observation. Such a model is a linear classifier on a random feature expansion of x that approximates a Gaussian kernel:

xs = (x − Mu) ./ Sigma (only for a model trained with 'Standardize', true),   f = Σ_c Beta_c·z_c(xs) + Bias,   score = [ T(−f) ; T(f) ],   label = ClassNames(2) when score(2) > score(1), ClassNames(1) otherwise – where T is the model's score transform and z is MATLAB's Fastfood expansion: for each Hadamard block i, T_i = H(H(xs·S_i)·G_i permuted by P_i)·B_i·√2/(KernelScale·√o), with H the Walsh–Hadamard transform of order o = 2^{⌈log2 D⌉} (x zero-padded to o entries), and the columns [cos T₁, sin T₁, cos T₂, sin T₂, …] cut to the first n = numel(Beta) and each scaled by 1/√(o·b). This is not the kernel SVM of SVM Predictor: there are no support vectors, only the explicit expansion.

The model is baked in as configuration. MATLAB keeps most of its numbers out of the model's public properties, and publishes them through saveLearnerForCoder(Mdl, 'kmdl'); then s = load('kmdl.mat').compactStruct holds every one below.

Ports

• x – one observation, a column [D,1] with one predictor per row, in the order the model was trained on. D decides the Hadamard order o, which must match the feature maps' width; at most 8 predictors.
• label – the predicted class, a scalar [1,1]: one of the two Class Names, as a number.
• score – the two class scores, a column [2,1] in Class Names order: row 1 is T(−f), the first class's score, and row 2 is T(f), the second class's. MATLAB returns the same pair as a row.

Parameters

• Feature Map S – the Fastfood scaling matrix, [b,o], one row per Hadamard block: s.FeatureMapper.S.
• Feature Map G – the Gaussian scaling matrix, [b,o]: s.FeatureMapper.G.
• Feature Map B – the random signs, [b,o]: s.FeatureMapper.B.
• Feature Map P – the permutations, [b,o], each row a permutation of 1…o (one-based, as MATLAB saves it): double(s.FeatureMapper.P).
• Kernel Scale – the model's KernelScale, a positive number (the resolved value when the model was fitted with 'auto').
• Beta – the linear coefficients, one per expanded feature, [n,1]: s.Impl.Beta. n is the model's NumExpansionDimensions, at most 256, and it must need exactly b = ⌈n/(2o)⌉ Hadamard blocks – the four feature maps and Beta come from the same model.
• Bias – the intercept, a scalar: s.Impl.Bias. Added after the sum.
• Mu – the predictor means, [1,D]: Mdl.Mu. [] (the default) for a model trained without 'Standardize', whose Mu is empty.
• Sigma – the predictor standard deviations, [1,D]: Mdl.Sigma, or [] with Mu. As in MATLAB, a predictor whose Sigma is 0 is centred and not divided.
• Class Names – the two class labels as numbers, in the model's own order: Mdl.ClassNames, copied as it is. The second is the class whose score is T(f), whatever order the names are in. The two must differ. Text or categorical labels are not numbers: use their positions, [1 2], and map them downstream.
• Score Transform – T, the model's ScoreTransform, spelled as MATLAB spells it. fitckernel sets logit for a logistic learner and none for an SVM learner. All eight act on the pair [−f, f]:
  • none – T(z) = z. The default.
  • logit – 1/(1 + e^−z), a probability.
  • doublelogit – 1/(1 + e^−2z); on a two-class pair also exactly what softmax gives.
  • symmetric – 2z − 1.
  • symmetriclogit – 2/(1 + e^−z) − 1.
  • sign – −1, 0 or +1 by the sign of z.
  • ismax – 1 for the larger of the pair and 0 for the other; on a tie the first gets the 1.
  • symmetricismax – as ismax, with −1 in place of 0.
  invlogit is not offered: it turns complex for any score outside (0,1), which MATLAB's own predict then returns (measured). A custom function handle cannot be pasted as a number either.
• 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 whole model is baked into the body at export time; there is no tunable parameter, so a refitted model means a re-export. The feature map is linear in x up to the cosine, so it is folded at export into one dense [D,o·b] matrix and every target writes the sum out term by term – D multiply-adds, one cosine and one sine per column pair. That is why D and n are capped: the limits bound the size of the generated code, not the math.

On the three HDL targets f is simulation-only real arithmetic: a cosine has no Q16.16 form to call. f is quantized to Q16.16 once; after that none, symmetric, sign, ismax and symmetricismax stay in fixed point, and logit, doublelogit and symmetriclogit are real again, quantized at the output port.

Simulink bridge

None. Simulink's ClassificationKernel Predict block (Statistics and Machine Learning Toolbox) exists, but its only model parameter, TrainedLearner, is the name of a fitted model object in the MATLAB workspace. That object cannot be built from these numbers – ClassificationKernel has no public constructor – and a parameter mapping carries one value to one parameter, so neither direction can cross. The bridge reports the block rather than dropping it silently, and it has no parity testbench, which is the documented consequence of that. The arithmetic is checked against MATLAB's own predict instead, and code export verification covers all ten languages in every transform. The Simulink block also has no SampleTime parameter.

Notes

• Algebraic and stateless: the outputs depend only on the current input. Nonlinear, and deliberately carries no state space: the label is a discontinuous function of x.
• The label compares the TRANSFORMED scores, as MATLAB does: at f = 0 exactly every transform ties and the first class wins, and under logit an f within about 10⁻¹⁶ of zero rounds both entries to 0.5 and also gives the first class.
• The label is discontinuous at the boundary, so the three HDL targets, which quantize x to Q16.16, can disagree with the simulation on a sample whose x lies within about one quantum (1.5×10⁻⁵) of the decision boundary: the label then differs by the whole distance between the two class names. That is inherent to reducing a continuous quantity to a decision in fixed point, not an export fault; threshold the score output downstream in floating point if an application cannot tolerate it.
• Fastfood only. Every model fitckernel builds uses it – the function has no option to choose another expansion. A model built with the undocumented Kitchen Sinks expansion keeps a matrix W instead of S, G, B and P, and is not carried.
• Prior and Cost do not enter the label (MATLAB labels by the first maximum score). MATLAB uses the prior only for an observation holding a NaN, which it labels with the most probable class; here a NaN makes both scores NaN and the label ClassNames(1).
• Binary only. fitckernel refuses more than two classes; several classes are an ECOC model of several of these.
• Agreement with predict is to rounding, not bit for bit: MATLAB applies the butterflies to each observation, this block applies their product, folded once. The two differ by about 10⁻¹⁵ in f.