1. FAUST Oblique Analytics are based on a linear or dot product, o Let X(X1...Xn) be a table.
FAUST Oblique analytics employ the ScalarPTreeSet (SPTS) of a valueTree, XoD  k=1..nXk*Dk, D=(D1...Dn) = a fixed vector.
FAUST Count Change (FC2) for clustering
Choose a nextD recursion plan to specify which D to use at each recursive step, e.g., if a cluster, C, needs further partitioning,
a. D = the diagonal producing the maximum Standard Deviation (STD(C)) or maximum STD(C)/Spread(C).
b. AM(C) (Average-to-Median)
c. AFFA(C) (Avg-FurthestFromAverage) [or FFAFFF(C) (FurthestFromAvg-FurthestFromFurthest)].
d. cycle thru diagonals: e1,...,..en, e1e2.. Or cycle thru AM, AFFA, FFAFFF or cycle through both.
Choose DensityThreshold(DT), DensityUniformityThreshold(DUT),Precipitous Count Change (PCC) def (PCCs include gaps).
ALGORITHM: If DT (and DUT) are not exceeded at cluster, C, partition by cutting at each PCC in CoD using the nextD.
FAUST Polygon Prediction (FP 2) for 1-class or multi-class classification. Let Xn+1= Class label column, C.
For each vector, D, let lD,kminCkoD (or the1st Precipitous_Count_Increase=PCI?); hD,k=hD,kmaxCkoD (or the last PCD?).
ALGORITHM: y is declared to be class=k iff yHullk where Hullk={z| lD,k  Doz  hD,k all D}.
(If y is in multiple hulls, Hi1..Hih, y isa Ck for the k maximizing OneCount{PCk&PHi..&PHih} or fuzzy classify using those OneCounts as k-weights)
Outlier Mining can mean:
1. Given a set of n objects and given a k, find the top k objects in terms of dissimilarity from the rest of the objects.
1.a This could mean the k object, xh, (h=1..k) most dissimilar [distant from] their individual complements, X-{xh}, or
1.b The top "set of k objects“, Sk, for which that set is most dissimilar from its complement, X-Sk.
2. Given a Training Set, identify outliers in each class (correctly classified but noticeably dissimilar to fellow class members).
3. Determine "fuzzy" clusters, i.e., assign a weight for each (object, cluster) pair. (A dendogram does that to some extent.).
Note: FC3 is a good outlier detector, since it identifies and removes large clusters so small clusters (outliers) appear.
FAUST Distance Analytics useSPTS of a distance valueTree. e.g., SquareDistanceToNearestNeighbor (D2NN)
FAUST Outlier Observer (FO2) uses D2NN. (L2 or Euclidean distance best, but L (EIN) works too.)
D2NN provides an instantaneous k-slider for 1.a (Find k objects, x, most dissimilar from X-{x}. It’s useful for the others too.