Change Point Detector — Machine Learning/Anomaly Detection

Change Point Detector

Machine Learning / Anomaly Detection

Finds the single best split of the last W samples into two segments and reports where it is:

k̂ = argmin_k [ SSE(y₁…y_k−1) + SSE(y_k…y_W) ]

This is MATLAB's findchangepts(x, 'MaxNumChanges', 1), and k follows that function's own convention: the 1-based index of the first sample of the SECOND segment, counted from the oldest sample of the window.

Ports

• u – the sampled signal. Scalar: one channel and its own window – see Notes.
• k – the change point, 1…W, or 0 when no split beats Minimum Improvement. Scalar.
• residual – the total within-segment residual of the reported segmentation: the two-segment cost when k is nonzero, the whole-window cost when it is 0. This is MATLAB's second output. Scalar.
• improvement – the whole-window cost minus the best two-segment cost, always reported even when k is 0 so a threshold can be chosen by watching it. Scalar, never negative.

Parameters

• Window Length – W, how many samples the search sees. A whole number from 4 to 48. Bounded above because the sweep is unrolled at export.
• Statistic – what a segment is fitted with, and therefore what counts as a change:
  • mean – each segment by its own mean. A change is a level shift. This is MATLAB's default.
  • linear – each segment by its own least-squares line. A change is a shift in level or slope, so a ramp that changes gradient is found where mean would see nothing. Each segment needs two points, so the split runs 3…W−1 rather than 2…W.
• Minimum Improvement – how much better the two-segment fit must be before a change point is reported at all. Zero or more; 0 always reports the best split. It is in the units of the residual, which are the square of the signal's units.
• 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.

No generated core divides, and none solves anything. The sample positions are fixed by the window length, so every 1/n, every segment midpoint and every 1/Σ(t−t̄)² is a number computed at export time and inlined; a core keeps three running sums and compares. The statistic and the window length are structural – they decide how many comparisons the core contains – so re-export after changing either.

The three HDL targets are simulation-only real arithmetic. That is not about cost: the answer is an argmin over candidates that are often nearly equal, so one Q16.16 quantum on a cost changes which candidate wins and the index then differs by a whole sample – a large error produced by an arithmetic difference of 10⁻⁵.

Simulink bridge

None (Support::None). findchangepts is a Signal Processing Toolbox function and that toolbox ships no Simulink library, so there is no path a diagram could name. The bridge reports this block rather than dropping it silently, and it therefore has no parity testbench; code export verification still covers it across all ten languages.

Notes

• Stateful, and discrete by nature (setDiscreteOnlyBlock(true)): the window advances once per sample.
• ⚠ This is not an alarm, and it is not Drift Detector. Drift Detector – beside this block – and CUSUM Detector are sequential monitors: they accumulate evidence sample by sample and fire when it crosses a threshold, answering has something changed?. This block is retrospective: it re-examines the whole window every sample and answers where?. It will happily move its answer backwards as later samples arrive, which an alarm must never do. Use one of those two to trigger something; use this one to say when it happened.
• ⚠ k moves, and that is the block working rather than failing. The window slides, so the same real change appears at k = W, then W−1, and finally leaves. Watch improvement rather than k to know whether there is a change at all.
• ⚠ MATLAB's other two statistics are absent, with a reason. rms and std score a segment by the logarithm of a segment statistic – findchangepts with 'rms' answers a negative residual on ordinary data, which is what a sum of logs looks like – so each candidate split would put a logarithm in every generated core, W−1 of them per sample. mean and linear are the two that reduce to prefix sums.
• ⚠ A tie keeps the smallest k. A window with no change at all is a tie among every candidate, so something has to decide it; the rule is the same in all ten targets and in this block's own simulation.
• The window is zero-prefilled, so the first W−1 answers of a run describe a window that is partly zeros.
• Scalar only. One channel and its own history; wire one block per channel.
• No state space. An argmin is not a linear map of the window, so model reduction correctly declines to merge it.