Presentation slides for "DAOC: Stable Clustering of Large Networks". Presented at IEEE BigData 2019, Special Session on Intelligent Data Mining. The clustering algorithm is designed to build human perception-adapted taxonomies of large networks (i.e., graphs) without any manual tuning.

1. Artem Lutov, Mourad Khayati and Philippe Cudré-Mauroux
eXascale Infolab, University of Fribourg, Switzerland
https://github.com/eXascaleInfolab/daoc
https://bit.ly/daoc-slides

2. Stability includes both robustness and determinism in our paper:
● Robustness means that the forming clusters should evolve gracefully
and without any surges on minor perturbations (i.e., some
changes in the links or nodes) of the input network (i.e., graph).
● Determinism represents both non-stochastic and input
order-independent (i.e., reshuffling-resistant) results.
2

3. Stable (i.e., robust and deterministic) clustering of large networks:
DAOC - Deterministic and Agglomerative Overlapping Clustering
● Mutual Maximal Gain, to ensure robustness while being capable of
identifying micro-scale clusters
● Overlap Decomposition, to identify fine-grained clusters in a
deterministic way, while capturing multiple optima even for the
algorithms whose optimization function is not supported overlaps
3

4. Human perception-adapted Taxonomy construction
for large Evolving Networks by Incremental Clustering
● Stable
● Fully-automatic
● Browsable
● Large
● Multi-viewpoint
● Narrow (7 ± 2 rule)
4
● Robust + Determ.
● Parameter-free
● Hierarchical
● Near-linear runtime
● Overlapping
● Fine-grained

5. Human perception-adapted Taxonomy construction
for large Evolving Networks by Incremental Clustering
● Stable
● Fully-automatic
● Browsable
● Large
● Multi-viewpoint
● Narrow (7 ± 2 rule)
5
● Robust + Determ.
● Parameter-free
● Hierarchical
● Near-linear runtime
● Overlapping
● Fine-grained
Louvain

6. 6
Modularity:
Modularity gain:
Mutual Maximal(⬦) Gain:

7. Decomposition of a node of degree d=3 into K=3 fragments:
7
OD
constraints:

8. The following algorithms are evaluated on synthetic (multiple instances of each category) and
real-world networks using open-source benchmarking framework, Clubmark:
8
* the feature is partially available, parameters tuning might be required for specific cases
◦ the feature is not supported by the original implementation of the algorithm

9. 9
F1h (average value and deviation)
for subsequent perturbations (link
removals) of a synthetic network.
Stable algorithms (among non-
stochastic and ensemble) are
outlined with a bold line and
expected to have a gracefully
decreasing F1h without surges.

10. 10

11. 11

12. DAOC is a novel clustering algorithm design for a stable (both robust
and deterministic) clustering of large networks aiming to construct
human perception-adapted taxonomies without any manual tuning.
● DAOC is 25% more accurate on average than state-of-the-art
non-stochastic clustering algorithms being on par with the most
accurate existing (including stochastic) clustering algorithms
● DAOC is one the least memory consuming and fastest state-of-
the-art clustering algorithms being applicable to large networks
12

13. Artem Lutov <artem.lutov@unifr.ch>
https://github.com/eXascaleInfolab/daoc
13

14. 14

15. 1515
Racing cars
Overlapping Clusters Clusters on Various Resolutions
Blue cars
Jeeps
Cars
Racing cars
Bikes
Racing &
blue cars
Bikes

16. Matching the clusterings (unordered sets of elements) even with the
elements having a single membership may yield multiple best matches:
=> Strictclusterslabeling is not
always possible and undesirable.
Many dedicated accuracy metrics
are designed but few of them are
applicable for the elements with
multiplemembership.
16
Produced Ground-truth
Dark or Cyan?
Yellow

17. ● Applicable for the elements having multiple membership
● Applicable for Large Datasets: ideally O(N), runtime up to O(N2
)
Families with the accuracy metrics satisfying our requirements:
● Pair Counting Based Metrics: Omega Index [Collins,1988]
● Cluster Matching Based Metrics: Average F1 score [Yang,2013]
● Information Theory Based Metrics: Generalized NMI
[Esquivel,2012]
Problem: accuracy values interpretability and the metric selection. 17

18. Omega Index (𝛀) counts the number of pairs of elements occurring
in exactly the same number of clusters as in the number of categories
and adjusted to the expected number of such pairs:
18
,
,
C’ - ground-truth
(categories)
C - produced cls.

19. Soft Omega Index take into account pairs present in different
number of clusters by normalizing smaller number of occurrences of
each pair of elements in all clusters of one clustering by the larger
number of occurrences in another clustering:
19
,

20. F1a is defined as the average of the weighted F1 scores of a) the best
matching ground-truth clusters to the formed clusters and b) the best
matching formed clusters to the ground-truth clusters:
20
,
F1 - F1-measure
[Rijsbergen, 1974]

21. F1h uses harmonic instead of the arithm. mean to address F1a ≳ 0.5
for the clusters produced from all combinations of the nodes (F1C‘,C
=
1 since for each category there exists the exactly matching cluster,
F1C,C’
→0 since majority of the clusters have low similarity to the
categories):
21
, for the contribution m of the nodes:

22. F1p is the harmonic mean of the average over each clustering of the
best local probabilities (f1 ➞ pprob) for each cluster:
22

23. Purpose: O(N(|C’| + |C|)) ➞ O(N)
Cluster
mbs # Member nodes, const
cont #Members contrib, const
counter # Contribs counter
Counter
orig # Originating cluster
ctr # Raw counter, <= mbs
C
23
..
...
a
for a in g2.mbs: for c in cls(C.a):
cc = c.counter;
if cc.orig != g2:
cc.ctr=0; cc.orig=g2
cc.ctr += 1 / |C.a| if ovp else 1
fmatch(cc.ctr, c.cont, g2.cont)
g2
c1
c3
C’

24. SNAP DBLP (Nodes: 317,080
Edges: 1,049,866 Clusters:
13,477) ground-truth vs
clustering by the Louvain.
Evaluation on Intel Xeon
E5-2620 (32 logical CPUs)
@ 2.10 GHz, apps compiled
using GCC 5.4 with -O3 flag.
24

25. NMI is Mutual Information I(C’:C) normalized by the max or mean
value of the unconditional entropy H of the clusterings C’, C:
25
,
,
GNMI
[Esquivel,2012]
uses a stochastic
process to
compute MI.

26. (Soft) 𝛀
MF1
GNMI
26
O(N2
), performs purely for the
multi-resolution clusterings.
Evaluates the best-matching
clusters only (unfair advantage
for the larger clusters).
Biased to the number of clusters,
non-deterministic results, the
convergence is not guaranteed in
the stochastic implementation.
values are not affected by the
number of clusters.
O(N), F1p satisfiers more
formal constraints than others.
Highly parallelized, evaluates
full matches, well-grounded
theoretically.