@@ -234,6 +234,67 @@ of 2D panes to provide extra helper tools. These overlays are extensions of the
234234of the author of LitFX is rivaled only possibly by the author's stunning
235235lumberjack good looks. A few of these helper tools are shown below:
236236
237+ ### Probability Density and Cumulative Distribution Functions
238+
239+ ![ Trinity-PDFCDF-Generator] ( /media/Trinity-PDFCDF-Generator.png )
240+
241+ ### Joint Probability Density Grid
242+
243+ A Joint PDF shows how two variables tend to behave together. It shows
244+ relationships between different variables/dimensions. This then helps identify
245+ redundant metrics (those that behave almost the same) or complementary metrics
246+ (those that capture different aspects of network similarity). It can reveal
247+ nonlinear patterns that a simple average correlation might miss.
248+
249+ ![ Trinity-JointPDFGenerator] ( /media/Trinity-JointPDFGenerator.png )
250+
251+ This grid of Joint PDFs is a diagnostic dashboard for understanding and
252+ improving systems of variables (or scores). Each plot thumbnail shows how two of the dimensions
253+ of a vector system behave together across many samples. The color pattern
254+ indicates a density of occurrence and can indicate strength of presence over time.
255+
256+ A Pearson correlation coefficient for each pair of variables/dimensions is computed.
257+ This provides a correlation score between -1 and 1:
258+
259+ +1: Perfect positive relationship (metrics move together).
260+
261+ 0: No relationship.
262+
263+ -1: Perfect negative relationship (as one goes up, the other goes down).
264+
265+ This allows Trinity to order the combinations by correlation and establish a
266+ ranking. Correlation ranking illuminates which metrics overlap in meaning versus
267+ which ones bring new perspective.
268+
269+ Ranking:
270+
271+ Descending (high → low correlation):
272+
273+ Pairs at the top are most similar — possibly redundant metrics.
274+ Pairs at the bottom are least related — they provide unique information.
275+
276+ Ascending (low → high correlation):
277+
278+ Pairs at the top are most distinct — potentially the most valuable for diversifying how we measure similarity.
279+ Pairs at the bottom are redundant — maybe candidates for pruning or simplifying the model.
280+
281+
282+ ### Similarity and Divergence Matrix
283+
284+ ![ Trinity-SimilarityMatrix] ( /media/Trinity-SimilarityMatrix.png )
285+
286+ The Similarity Matrix is a heatmap where every row/column is one similarity
287+ feature computed between two features of your vectors. Each square shows how
288+ strongly two features “move together” across all samples of a "cohort".
289+ How to read:
290+ - Bright/hot = those two features usually agree
291+ - Dark/cold = they tell different stories
292+
293+ Per-cell JPDF surface (3D “joint probability” view): clicking any square opens
294+ a surface plot for just that pair of features. It shows where the data actually
295+ lives when you look at those two similarity scores together for all network-pairs.
296+ Think of it as the shape of agreement/disagreement between two metrics.
297+
237298### Natural Language Query
238299
239300There is a command terminal that you can enter natural language queries to using
@@ -305,6 +366,7 @@ inverse FFT, can be tessellated into the Hypersurface on demand.
305366- Sean M Phillips
306367- Melanie Lockhart
307368- Samuel Matos
369+ - David Penn
308370- Gene Whipps
309371- Griffin Milsap
310372- David Newcomer
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