Linear Classifier Predictor — Machine Learning/Classical Models

Linear Classifier Predictor

Machine Learning / Classical Models

Evaluates a fitted binary linear classifier at inference – what MATLAB's [label, score] = predict(Mdl, x) returns for a ClassificationLinear model and one observation:

f = Σ_j Beta_j·x_j + 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.

The model is baked in as configuration: paste Mdl.Beta, Mdl.Bias, Mdl.ClassNames and Mdl.ScoreTransform from a model trained with fitclinear. Nothing is fitted here and no model file is read.

Ports

• x – one observation, a column [D,1] with one predictor per row, in the order the model was trained on. D must equal the number of entries of Beta.
• 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

• Beta – the linear coefficients, one per predictor: the model's Beta property, [D,1]. A row is accepted too. A matrix with more than one column is refused – that is a model fitted over several regularization strengths; pick one with selectModels(Mdl, idx) first. The Simulink block refuses such a model as well.
• Bias – the intercept, a scalar: the model's Bias property.
• 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) – that holds whatever order the names are in (a model trained with 'ClassNames',[7 3] scores 3 with T(f)). 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. fitclinear 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 this is also exactly what softmax gives, so use it for a model whose transform is softmax.
  • 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 takes the logarithm of z/(1−z) and turns complex for any score outside (0,1), which is every raw linear score of one sign. 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 HDL story depends on the transform. f is a multiply-accumulate and the three HDL targets always compute it in genuine Q16.16 fixed point. With none, symmetric, sign, ismax and symmetricismax the whole block stays in fixed point. logit, doublelogit and symmetriclogit have an exponential, so those three HDL bodies are simulation-only real arithmetic after f, quantized again at the output port.

Simulink bridge

None. Simulink's ClassificationLinear 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 Beta, Bias, the class names and the transform – ClassificationLinear 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.
• The label compares the TRANSFORMED scores, as MATLAB does, and that is not always the same as the sign of f: at f = 0 exactly every transform ties and the first class wins, and under logit a score 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 one quantum (about 1.5×10⁻⁵) of the decision hyperplane: 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.
• Nonlinear, and deliberately carries no state space: the label is a discontinuous function of x.
• No predictor standardization exists for these models (fitclinear takes no such option), and the learner changes how Beta was found, never how it is used. Prior and Cost do not enter the label either; 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. A ClassificationLinear model has two classes; several classes are an ECOC model of several of these.