A reimplementation of Genie - a robust and outlier resistant
clustering algorithm (see Gagolewski, Bartoszuk, Cena, 2016).
The Genie algorithm is based on a minimum spanning tree (MST) of the
pairwise distance graph of a given point set.
Just like the single linkage, it consumes the edges
of the MST in an increasing order of weights. However, it prevents
the formation of clusters of highly imbalanced sizes; once the Gini index
(see gini_index()) of the cluster size distribution
raises above gini_threshold, a forced merge of a point group
of the smallest size is performed. Its appealing simplicity goes hand
in hand with its usability; Genie often outperforms
other clustering approaches on benchmark data,
such as https://github.com/gagolews/clustering-benchmarks.
The clustering can now also be computed with respect to the
mutual reachability distance (based, e.g., on the Euclidean metric),
which is used in the definition of the HDBSCAN* algorithm
(see Campello et al., 2013). If M > 1, then the mutual reachability
distance \(m(i,j)\) with smoothing factor M is used instead of the
chosen "raw" distance \(d(i,j)\). It holds \(m(i,j)=\max(d(i,j), c(i), c(j))\),
where \(c(i)\) is \(d(i,k)\) with \(k\) being the
(M-1)-th nearest neighbour of \(i\).
This makes "noise" and "boundary" points being "pulled away" from each other.
The Genie correction together with the smoothing factor M > 1 (note that
M = 2 corresponds to the original distance) gives a robustified version of
the HDBSCAN* algorithm that is able to detect a predefined number of
clusters. Hence it does not dependent on the DBSCAN's somewhat magical
eps parameter or the HDBSCAN's min_cluster_size one.
gclust(d, ...)# S3 method for default
gclust(
d,
gini_threshold = 0.3,
distance = c("euclidean", "l2", "manhattan", "cityblock", "l1", "cosine"),
cast_float32 = TRUE,
verbose = FALSE,
...
)
# S3 method for dist
gclust(d, gini_threshold = 0.3, verbose = FALSE, ...)
# S3 method for mst
gclust(d, gini_threshold = 0.3, verbose = FALSE, ...)
genie(d, ...)
# S3 method for default
genie(
d,
k,
gini_threshold = 0.3,
distance = c("euclidean", "l2", "manhattan", "cityblock", "l1", "cosine"),
M = 1L,
postprocess = c("boundary", "none", "all"),
detect_noise = M > 1L,
cast_float32 = TRUE,
verbose = FALSE,
...
)
# S3 method for dist
genie(
d,
k,
gini_threshold = 0.3,
M = 1L,
postprocess = c("boundary", "none", "all"),
detect_noise = M > 1L,
verbose = FALSE,
...
)
# S3 method for mst
genie(
d,
k,
gini_threshold = 0.3,
postprocess = c("boundary", "none", "all"),
detect_noise = FALSE,
verbose = FALSE,
...
)
gclust() computes the whole clustering hierarchy; it
returns a list of class hclust,
see hclust. Use cutree to obtain
an arbitrary k-partition.
genie() returns a k-partition - a vector with elements in 1,...,k,
whose i-th element denotes the i-th input point's cluster identifier.
Missing values (NA) denote noise points (if detect_noise
is TRUE).
a numeric matrix (or an object coercible to one,
e.g., a data frame with numeric-like columns) or an
object of class dist, see dist
or an object of class mst, see mst().
further arguments passed to other methods.
threshold for the Genie correction, i.e., the Gini index of the cluster size distribution; Threshold of 1.0 disables the correction. Low thresholds highly penalise the formation of small clusters.
metric used to compute the linkage, one of:
"euclidean" (synonym: "l2"),
"manhattan" (a.k.a. "l1" and "cityblock"),
"cosine".
logical; whether to compute the distances using 32-bit instead of 64-bit precision floating-point arithmetic (up to 2x faster).
logical; whether to print diagnostic messages and progress information.
the desired number of clusters to detect, k = 1 with M > 1
acts as a noise point detector.
smoothing factor; M <= 2 gives the selected distance;
otherwise, the mutual reachability distance is used.
one of "boundary" (default), "none"
or "all"; in effect only if M > 1.
By default, only "boundary" points are merged
with their nearest "core" points (A point is a boundary point if it is
a noise point and it's amongst its adjacent vertex's
M-1 nearest neighbours). To force a classical
k-partition of a data set (with no notion of noise),
choose "all".
whether the minimum spanning tree's leaves
should be marked as noise points, defaults to TRUE if M > 1
for compatibility with HDBSCAN*.
Marek Gagolewski and other contributors
Note that, as in the case of all the distance-based methods, the standardisation of the input features is definitely worth giving a try.
If d is a numeric matrix or an object of class dist,
mst() will be called to compute an MST, which generally
takes at most \(O(n^2)\) time (the algorithm we provide is parallelised,
environment variable OMP_NUM_THREADS controls the number of threads
in use). However, see emst_mlpack() for a very fast alternative
in the case of Euclidean spaces of (very) low dimensionality and M = 1.
Given an minimum spanning tree, the algorithm runs in \(O(n \sqrt{n})\) time.
Therefore, if you want to test different gini_thresholds,
(or ks), it is best to explicitly compute the MST first.
According to the algorithm's original definition,
the resulting partition tree (dendrogram) might violate
the ultrametricity property (merges might occur at levels that
are not increasing w.r.t. a between-cluster distance).
gclust() automatically corrects departures from
ultrametricity by applying height = rev(cummin(rev(height))).
Gagolewski M., Bartoszuk M., Cena A., Genie: A new, fast, and outlier-resistant hierarchical clustering algorithm, Information Sciences 363, 2016, 8-23, tools:::Rd_expr_doi("10.1016/j.ins.2016.05.003").
Campello R.J.G.B., Moulavi D., Sander J., Density-based clustering based on hierarchical density estimates, Lecture Notes in Computer Science 7819, 2013, 160-172, tools:::Rd_expr_doi("10.1007/978-3-642-37456-2_14").
Gagolewski M., Cena A., Bartoszuk M., Brzozowski L., Clustering with minimum spanning trees: How good can it be?, Journal of Classification, 2024, in press, tools:::Rd_expr_doi("10.1007/s00357-024-09483-1").
The official online manual of genieclust at https://genieclust.gagolewski.com/
Gagolewski M., genieclust: Fast and robust hierarchical clustering, SoftwareX 15:100722, 2021, tools:::Rd_expr_doi("10.1016/j.softx.2021.100722").
mst() for the minimum spanning tree routines.
adjusted_rand_score() (amongst others) for external
cluster validity measures (partition similarity scores).
library("datasets")
data("iris")
X <- iris[1:4]
h <- gclust(X)
y_pred <- cutree(h, 3)
y_test <- iris[,5]
plot(iris[,2], iris[,3], col=y_pred,
pch=as.integer(iris[,5]), asp=1, las=1)
adjusted_rand_score(y_test, y_pred)
pair_sets_index(y_test, y_pred)
# Fast for low-dimensional Euclidean spaces:
# h <- gclust(emst_mlpack(X))
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