Local Outlier Factor Score — Machine Learning/Anomaly Detection

Local Outlier Factor Score

Machine Learning / Anomaly Detection

Scores how much sparser a sample's neighbourhood is than its neighbours' own neighbourhoods – the density-ratio form of novelty detection:

LOF(u) = mean(lrd_i) / lrd(u) over the k nearest training points, with lrd(u) = 1 / mean(max(kdist_i, d_i)).

This is LocalOutlierFactor(novelty=True).score_samples negated, with _fit_X, _distances_fit_X_[:, -1] and _lrd pasted in. Around 1 means the sample sits in as dense a region as the points around it; well above 1 means it does not, which is the whole idea. Unlike a distance threshold, it adapts to regions of different density – a point far from a sparse cluster is not automatically odd.

Ports

• u – the sample, a column [d,1] matching the d columns of Training Set.
• lof – a scalar [1,1]: the factor itself. Report it, plot it, or threshold it downstream; it is a ratio, so it carries no units.
• outlier – a scalar [1,1]: 1 when lof exceeds Novelty Threshold, otherwise 0. The decision, kept beside the evidence, exactly as One Class SVM Score does.

Parameters

• Training Set – the [N,d] matrix, one training sample per row, which is sklearn's orientation.
• K Distances – an [N,1] column: each training row's distance to its own k-th nearest neighbour, as fitted. In sklearn this is _distances_fit_X_[:, -1].
• Local Reachability Densities – an [N,1] column: each training row's fitted _lrd.
• Neighbors – k, a whole number ≥ 1. It must be the same k the fit used, or the two baked columns describe a different model than the one being evaluated – nothing can detect that mismatch for you.
• Novelty Threshold – the operating point for outlier. 1 is the neutral value; 1.5 is a common starting point.
• 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, both fitted columns, k and the threshold are baked in at export time.

No backend divides at run time. The reciprocal that defines lrd(u) cancels against the mean it is divided by, leaving (Σ lrd)(Σ reach) / k² with 1/k² folded into a constant – two sums and two multiplies.

The three HDL targets are simulation-only real arithmetic, quantizing only at the port boundary, because the reachability distance is summed rather than merely ranked and so cannot stay squared. The same escape hatch Mahalanobis Distance takes, and for the same reason. The seven software targets are exact.

Simulink bridge

None. Local Outlier Factor belongs to the Statistics and Machine Learning Toolbox, which is not installed here, and its interface takes a fitted model object rather than parameters – which no parameter rule could carry even if it were present. The bridge reports the block rather than dropping it silently, and it has no parity testbench, which is the documented consequence of Support::None rather than a gap.

Notes

• Algebraic and stateless: the score depends only on the current sample.
• The fit is baked, not recomputed. k-distances and local reachability densities are properties of the training set measured against itself, so deriving them here would mean re-running the whole fit every sample. Paste them from the fitted model.
• k must match the fit. The two columns were computed at a particular k; evaluating at a different one silently mixes two models. Nothing in the block can detect that, which is why it is said here.
• The selection is KNN Classifier's, verbatim: rank by counting, ties broken toward the lower training row, ranking done on squared distances so it needs no roots.
• Cost is O(N²·d) per sample, inherent to ranking without a stored order – fine for the small baked sets this family targets.