Centrality vs. Ranking Quality

Data set	Dimensionality
Euclidean, Manhattan and Arc-Cosine distance
All-Relevant	10d 20d 40d 80d 160d 320d 640d
10-Relevant	10d 20d 40d 80d 160d 320d 640d
Cyc-Relevant	10d 20d 40d 80d 160d 320d 640d
Half-Relevant	10d 20d 40d 80d 160d 320d 640d
All-Dependent	10d 20d 40d 80d 160d 320d 640d
10-Dependent	10d 20d 40d 80d 160d 320d 640d
SNN with s=200 based on the given distance
All-Relevant	10d 20d 40d 80d 160d 320d 640d
10-Relevant	10d 20d 40d 80d 160d 320d 640d
Cyc-Relevant	10d 20d 40d 80d 160d 320d 640d
Half-Relevant	10d 20d 40d 80d 160d 320d 640d
All-Dependent	10d 20d 40d 80d 160d 320d 640d
10-Dependent	10d 20d 40d 80d 160d 320d 640d

Comparing dimensionality

The following plots have for one data set and one distance function three dimensionalities at the same time.

All-Relevant	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine
10-Relevant	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine
Cyc-Relevant	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine
Half-Relevant	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine
All-Dependent	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine
10-Dependent	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine

SNN and dimensionality

The following plots have for one data set and one base distance function at 160 dimensions for different SNN s values at the same time.

All-Relevant	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine
10-Relevant	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine
Cyc-Relevant	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine
Half-Relevant	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine
All-Dependent	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine
10-Dependent	Manhattan	Euclidean	L^0.6	L^0.8	Arccosine

Notes:

Centrality is based on the distribution density (at data generation) and part of the ground truth. Central points are typical to the cluster (high density). Points are ordered by their density, no absolute values are used.

Many plots - especially at high dimensionality - are not very interesting.

The Cyc-relevant plots are much less stable because of the smaller data set size compared to the others (1:10).

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