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About Author +Source Code (GitHub) +Bug Tracker and Feature Suggestions +PyPI Entry +CRAN Entry :::: @@ -149,11 +153,7 @@ rapi :maxdepth: 1 :caption: See Also -Source Code (GitHub) -Bug Tracker and Feature Suggestions -PyPI Entry -CRAN Entry -Clustering Benchmarks +Clustering Benchmarks Data Wrangling in Python :::: diff --git a/.devel/sphinx/news.md b/.devel/sphinx/news.md index 337f4a3c..4d707831 100644 --- a/.devel/sphinx/news.md +++ b/.devel/sphinx/news.md @@ -1,10 +1,10 @@ # What Is New in *genieclust* -## 1.1.x (under development) +## 1.1.0 (2022-09-05) -- [GENERAL] ..TO DO.. We now mention that the partition similarity scores - are discussed in more detail at + +- [GENERAL] The cluster validity measures are discussed in more detail at . - [Python and R] New function: @@ -12,7 +12,7 @@ - [Python and R] Implementations of the so-called internal cluster validity measures discussed in - DOI:[10.1016/j.ins.2021.10.004](https://doi.org/10.1016/j.ins.2021.10.004); + DOI: [10.1016/j.ins.2021.10.004](https://doi.org/10.1016/j.ins.2021.10.004); see our (GitHub-only) [CVI](https://github.com/gagolews/optim_cvi) package for R. In particular, the generalised Dunn indices are based on the code originally authored by Maciej Bartoszuk. Thanks. @@ -47,7 +47,7 @@ - [GENERAL] A paper on the `genieclust` package is now available: M. Gagolewski, genieclust: Fast and robust hierarchical clustering, - *SoftwareX* **15**, 100722, 2021, DOI: + SoftwareX 15, 100722, 2021, DOI: [10.1016/j.softx.2021.100722](https://doi.org/10.1016/j.softx.2021.100722). - [Python] `plots.plot_scatter` now uses a more accessible default palette diff --git a/.devel/sphinx/rapi/comparing_partitions.md b/.devel/sphinx/rapi/comparing_partitions.md index b67db077..2a092d40 100644 --- a/.devel/sphinx/rapi/comparing_partitions.md +++ b/.devel/sphinx/rapi/comparing_partitions.md @@ -36,11 +36,11 @@ normalizing_permutation(x, y = NULL) ## Arguments -| | | -|-----------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| -| `x` | an integer vector of length n (or an object coercible to) representing a K-partition of an n-set (e.g., a reference partition), or a confusion matrix with K rows and L columns (see [`table(x, y)`](https://stat.ethz.ch/R-manual/R-devel/library/base/html/table.html)) | -| `y` | an integer vector of length n (or an object coercible to) representing an L-partition of the same set (e.g., the output of a clustering algorithm we wish to compare with `x`), or NULL (if x is an K\*L confusion matrix) | -| `whether` | to assume E=1 in the definition of the pair sets index index, i.e., use Eq. (20) instead of (18); see (Rezaei, Franti, 2016). | +| | | +|--------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| +| `x` | an integer vector of length n (or an object coercible to) representing a K-partition of an n-set (e.g., a reference partition), or a confusion matrix with K rows and L columns (see [`table(x, y)`](https://stat.ethz.ch/R-manual/R-devel/library/base/html/table.html)) | +| `y` | an integer vector of length n (or an object coercible to) representing an L-partition of the same set (e.g., the output of a clustering algorithm we wish to compare with `x`), or NULL (if x is an K\*L confusion matrix) | +| `simplified` | whether to assume E=1 in the definition of the pair sets index index, i.e., use Eq. (20) instead of (18); see (Rezaei, Franti, 2016). | ## Details @@ -80,7 +80,7 @@ Each cluster validity measure is a single numeric value. Gagolewski M., *A Framework for Benchmarking Clustering Algorithms*, 2022, . -Gagolewski M., Adjusted asymmetric accuracy: An interpretable external cluster validity measure, 2022, submitted for publication. +Gagolewski M., Adjusted asymmetric accuracy: A well-behaving external cluster validity measure, 2022, submitted for publication. Hubert L., Arabie P., Comparing partitions, *Journal of Classification* 2(1), 1985, 193-218, esp. Eqs. (2) and (4). diff --git a/DESCRIPTION b/DESCRIPTION index f3b162ba..d8df0d39 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,8 +1,8 @@ Package: genieclust Type: Package Title: Fast and Robust Hierarchical Clustering with Noise Points Detection -Version: 1.0.0.9001 -Date: 2022-08-29 +Version: 1.1.0 +Date: 2022-09-05 Authors@R: c( person("Marek", "Gagolewski", role = c("aut", "cre", "cph"), diff --git a/MANIFEST b/MANIFEST index 3b48a1ac..562dd38c 100644 --- a/MANIFEST +++ b/MANIFEST @@ -2,13 +2,13 @@ LICENSE MANIFEST.in NEWS -README.rst requirements.txt setup.cfg setup.py genieclust/__init__.py genieclust/c_argfuns.pxd genieclust/c_compare_partitions.pxd +genieclust/c_cvi.pxd genieclust/c_disjoint_sets.pxd genieclust/c_genie.pxd genieclust/c_gini_disjoint_sets.pxd @@ -16,6 +16,7 @@ genieclust/c_inequity.pxd genieclust/c_mst.pxd genieclust/c_postprocess.pxd genieclust/c_preprocess.pxd +genieclust/cluster_validity.pyx genieclust/compare_partitions.pyx genieclust/genie.py genieclust/inequity.pyx @@ -25,6 +26,7 @@ genieclust/tools.pyx src/c_argfuns.h src/c_common.h src/c_compare_partitions.h +src/c_cvi.h src/c_disjoint_sets.h src/c_distance.h src/c_genie.h diff --git a/NEWS b/NEWS index 337f4a3c..4d707831 100644 --- a/NEWS +++ b/NEWS @@ -1,10 +1,10 @@ # What Is New in *genieclust* -## 1.1.x (under development) +## 1.1.0 (2022-09-05) -- [GENERAL] ..TO DO.. We now mention that the partition similarity scores - are discussed in more detail at + +- [GENERAL] The cluster validity measures are discussed in more detail at . - [Python and R] New function: @@ -12,7 +12,7 @@ - [Python and R] Implementations of the so-called internal cluster validity measures discussed in - DOI:[10.1016/j.ins.2021.10.004](https://doi.org/10.1016/j.ins.2021.10.004); + DOI: [10.1016/j.ins.2021.10.004](https://doi.org/10.1016/j.ins.2021.10.004); see our (GitHub-only) [CVI](https://github.com/gagolews/optim_cvi) package for R. In particular, the generalised Dunn indices are based on the code originally authored by Maciej Bartoszuk. Thanks. @@ -47,7 +47,7 @@ - [GENERAL] A paper on the `genieclust` package is now available: M. Gagolewski, genieclust: Fast and robust hierarchical clustering, - *SoftwareX* **15**, 100722, 2021, DOI: + SoftwareX 15, 100722, 2021, DOI: [10.1016/j.softx.2021.100722](https://doi.org/10.1016/j.softx.2021.100722). - [Python] `plots.plot_scatter` now uses a more accessible default palette diff --git a/R/RcppExports.R b/R/RcppExports.R index acc4d056..a8c7120b 100644 --- a/R/RcppExports.R +++ b/R/RcppExports.R @@ -91,7 +91,7 @@ #' Gagolewski M., \emph{A Framework for Benchmarking Clustering Algorithms}, #' 2022, \url{https://clustering-benchmarks.gagolewski.com}. #' -#' Gagolewski M., Adjusted asymmetric accuracy: An interpretable external +#' Gagolewski M., Adjusted asymmetric accuracy: A well-behaving external #' cluster validity measure, 2022, submitted for publication. #' #' Hubert L., Arabie P., Comparing partitions, @@ -126,7 +126,7 @@ #' clustering algorithm we wish to compare with \code{x}), #' or NULL (if x is an K*L confusion matrix) #' -#' @param whether to assume E=1 in the definition of the pair sets index index, +#' @param simplified whether to assume E=1 in the definition of the pair sets index index, #' i.e., use Eq. (20) instead of (18); see (Rezaei, Franti, 2016). #' #' diff --git a/README.md b/README.md index a10e45c3..5ee04a95 100644 --- a/README.md +++ b/README.md @@ -231,7 +231,7 @@ Gagolewski M., Bartoszuk M., Cena A., Are cluster validity measures (in)valid?, *Information Sciences* **581**, 2021, 620–636. [DOI: 10.1016/j.ins.2021.10.004](https://doi.org/10.1016/j.ins.2021.10.004). -Gagolewski M., *Adjusted asymmetric accuracy: An interpretable external +Gagolewski M., *Adjusted asymmetric accuracy: A well-behaving external cluster validity measure*, 2022, submitted for publication. 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@@ -247,7 +361,7 @@

Notes

-

See genieclust.compare_partitions.compare_partitions for more details.

+

See compare_partitions() for more details.

@@ -279,13 +393,13 @@

Notes

-

See genieclust.compare_partitions.compare_partitions for more details.

+

See compare_partitions() for more details.

genieclust.compare_partitions.compare_partitions(C)
-

Computes a series of partition similarity scores

+

Computes a series of external cluster validity measures

Parameters
@@ -312,10 +426,16 @@
'ami'

Adjusted mutual information \((\mathrm{AMI}_\mathrm{sum})\)

-
'nacc'

Normalised accuracy (purity)

+
'nacc'

Normalised (set-matching) accuracy

'psi'

Pair sets index

+
'spsi'

Simplified pair sets index

+
+
'aaa'

Adjusted asymmetric accuracy (or nan if \(K \neq L\)); +it is assumed that rows in C represent the ground-truth +partition

+
@@ -326,8 +446,13 @@
genieclust.compare_partitions.confusion_matrix

Computes a confusion matrix

+
genieclust.compare_partitions.normalized_confusion_matrix

Determines the confusion matrix and permutes the rows and columns so that the sum of the elements of the main diagonal is the largest possible

+
genieclust.compare_partitions.compare_partitions2

A wrapper around this function that accepts two label vectors on input

+
genieclust.compare_partitions.adjusted_asymmetric_accuracy
+
genieclust.compare_partitions.normalized_accuracy
+
genieclust.compare_partitions.pair_sets_index
genieclust.compare_partitions.adjusted_rand_score
genieclust.compare_partitions.rand_score
genieclust.compare_partitions.adjusted_fm_score
@@ -335,8 +460,6 @@
genieclust.compare_partitions.mi_score
genieclust.compare_partitions.normalized_mi_score
genieclust.compare_partitions.adjusted_mi_score
-
genieclust.compare_partitions.normalized_accuracy
-
genieclust.compare_partitions.pair_sets_index

Notes

@@ -345,70 +468,86 @@ nonempty and pairwise disjoint subsets. For instance, these can be two clusterings of a dataset with \(n\) observations specified as vectors of labels. Moreover, let C be the -confusion matrix (with \(K\) rows and \(L\) columns, \(K \leq L\)) -corresponding to x and y, see also -genieclust.compare_partitions.confusion_matrix.

+confusion matrix (with \(K\) rows and \(L\) columns, +\(K \leq L\)) corresponding to x and y; see also +confusion_matrix().

This function implements a few scores that aim to quantify -the similarity between x and y. -Partition similarity scores can be used as external cluster validity -measures — for comparing the outputs of clustering algorithms -with reference (ground truth) labels, see, e.g., -https://github.com/gagolews/clustering_benchmarks_v1 -for a suite of benchmark datasets.

-

Every index except mi_score (which computes the mutual -information score) outputs 1 given two identical partitions. +the similarity between x and y.

+

These functions can be used as external cluster +validity measures, where we assume that x is +the reference (ground-truth) partition; compare [5].

+

Each index except adjusted_asymmetric_accuracy +can act as a pairwise partition similarity score: it is symmetric, +i.e., index(x, y) == index(y, x).

+

Each index except mi_score (which computes the mutual information score) +outputs the value of 1.0 if two identical partitions are given. Note that partitions are always defined up to a bijection of the set of possible labels, e.g., (1, 1, 2, 1) and (4, 4, 2, 4) represent the same 2-partition.

+

adjusted_asymmetric_accuracy [2] +only accepts \(K = L\). It is an external cluster validity measure +which assumes that the label vector x (or rows in the confusion +matrix) represents the reference (ground truth) partition. +It is a corrected-for-chance summary of the proportion of correctly +classified points in each cluster (with cluster matching based on the +solution to the maximal linear sum assignment problem; see +normalize_confusion_matrix()), given by: +\((\max_\sigma \sum_{i=1}^K (c_{i, \sigma(i)}/(c_{i, 1}+...+c_{i, K})) - 1)/(K - 1)\), +where \(C\) is the confusion matrix.

+

normalized_accuracy is a measure defined as +\((\mathrm{Accuracy}(C_\sigma)-1/L)/(1-1/L)\), +where \(C_\sigma\) is a version of the confusion matrix +for given x and y, \(K \leq L\), with columns permuted +based on the solution to the maximal linear sum assignment problem. +Note that the \(\mathrm{Accuracy}(C_\sigma)\) part +is sometimes referred to as set-matching classification +rate or pivoted accuracy.

+

pair_sets_index gives the Pair Sets Index (PSI) +adjusted for chance [3], \(K \leq L\). +Pairing is based on the solution to the linear sum assignment problem +of a transformed version of the confusion matrix. +Its simplified version assumes E=1 in the definition of the index, +i.e., uses Eq. (20) instead of (18); see [3].

rand_score gives the Rand score (the “probability” of agreement between the two partitions) and adjusted_rand_score is its version -corrected for chance [1] (especially Eqs. (2) and (4) therein): +corrected for chance [1] (especially Eqs. (2) and (4) therein): its expected value is 0.0 for two independent partitions. Due to the adjustment, the resulting index might also be negative for some inputs.

Similarly, fm_score gives the Fowlkes-Mallows (FM) score -and adjusted_fm_score is its adjusted-for-chance version [1].

+and adjusted_fm_score is its adjusted-for-chance version [1].

Note that both the (unadjusted) Rand and FM scores are bounded from below by \(1/(K+1)\) if \(K = L\), hence their adjusted versions are preferred.

mi_score, adjusted_mi_score and normalized_mi_score are information-theoretic indices based on mutual information, see the definition of \(\mathrm{AMI}_\mathrm{sum}\) -and \(\mathrm{NMI}_\mathrm{sum}\) in [4].

-

normalized_accuracy is defined as -\((\mathrm{Accuracy}(C_\sigma)-1/L)/(1-1/L)\), -where \(C_\sigma\) is a version of the confusion matrix -for given x and y, \(K \leq L\), with columns permuted -based on the solution to the Maximal Linear Sum Assignment Problem. -\(\mathrm{Accuracy}(C_\sigma)\) is sometimes referred to as Purity, -e.g., in [2].

-

pair_sets_index gives the Pair Sets Index (PSI) -adjusted for chance [3], \(K \leq L\). -Pairing is based on the solution to the Linear Sum Assignment Problem -of a transformed version of the confusion matrix.

+and \(\mathrm{NMI}_\mathrm{sum}\) in [4].

References

-
1(1,2)
+
1(1,2)

Hubert L., Arabie P., Comparing Partitions, Journal of Classification 2(1), 1985, 193-218.

-
2
-

Rendon E., Abundez I., Arizmendi A., Quiroz E.M., -Internal versus external cluster validation indexes, -International Journal of Computers and Communications 5(1), 2011, -27-34.

+
2
+

Gagolewski M., Adjusted asymmetric accuracy: A well-behaving external +cluster validity measure, 2022, submitted for publication.

-
3
+
3(1,2)

Rezaei M., Franti P., Set matching measures for external cluster validity, IEEE Transactions on Knowledge and Data Mining 28(8), 2016, -2173-2186. doi:10.1109/TKDE.2016.2551240.

+2173-2186. https://doi.org/10.1109/TKDE.2016.2551240.

-
4
+
4

Vinh N.X., Epps J., Bailey J., Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance, Journal of Machine Learning Research 11, 2010, 2837-2854.

+
5
+

Gagolewski M., A Framework for Benchmarking Clustering Algorithms, +https://clustering-benchmarks.gagolewski.com

+

Examples

>>> x = np.r_[1, 1, 2, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2]
@@ -419,12 +558,12 @@
        [ 8,  2]])
 >>> {k : round(v, 2) for k, v in
 ...      genieclust.compare_partitions.compare_partitions(C).items()}
-{'ar': 0.49, 'r': 0.74, 'fm': 0.73, 'afm': 0.49, 'mi': 0.29, 'nmi': 0.41, 'ami': 0.39, 'nacc': 0.71, 'psi': 0.65}
+{'ar': 0.49, 'r': 0.74, 'fm': 0.73, 'afm': 0.49, 'mi': 0.29, 'nmi': 0.41, 'ami': 0.39, 'nacc': 0.71, 'psi': 0.65, 'spsi': 0.63, 'aaa': 0.71}
 >>> {k : round(v, 2) for k, v in
 ...      genieclust.compare_partitions.compare_partitions2(x,y).items()}
-{'ar': 0.49, 'r': 0.74, 'fm': 0.73, 'afm': 0.49, 'mi': 0.29, 'nmi': 0.41, 'ami': 0.39, 'nacc': 0.71, 'psi': 0.65}
->>> round(genieclust.compare_partitions.adjusted_rand_score(x, y), 2)
-0.49
+{'ar': 0.49, 'r': 0.74, 'fm': 0.73, 'afm': 0.49, 'mi': 0.29, 'nmi': 0.41, 'ami': 0.39, 'nacc': 0.71, 'psi': 0.65, 'spsi': 0.63, 'aaa': 0.71}
+>>> round(genieclust.compare_partitions.adjusted_asymmetric_accuracy(x, y), 2)
+0.71
 
@@ -455,11 +594,13 @@
genieclust.compare_partitions.confusion_matrix

Determines the contingency table

+
genieclust.compare_partitions.normalized_confusion_matrix

Determines the confusion matrix and permutes the rows and columns so that the sum of the elements of the main diagonal is the largest possible

+

Notes

-

Calls genieclust.compare_partitions.compare_partitions(C), -where C = genieclust.compare_partitions.confusion_matrix(x, y).

+

Calls compare_partitions() on the result of +returned by confusion_matrix().

@@ -485,7 +626,7 @@

See also

-
genieclust.compare_partitions.normalize_confusion_matrix

Applies pivoting

+
genieclust.compare_partitions.normalize_confusion_matrix

Permutes the rows and columns of a confusion matrix so that the sum of the elements of the main diagonal is the largest possible

@@ -530,7 +671,7 @@

Notes

-

See genieclust.compare_partitions.compare_partitions for more details.

+

See compare_partitions() for more details.

@@ -562,17 +703,21 @@

Notes

-

See genieclust.compare_partitions.compare_partitions for more details.

+

See compare_partitions() for more details.

genieclust.compare_partitions.normalize_confusion_matrix(C)
-

Applies pivoting to a given confusion matrix

+

Permutes the rows and columns of a confusion matrix +so that the sum of the elements +on the main diagonal is the largest possible (by solving +the maximal assignment problem)

Parameters
-
Cndarray

A c_contiguous confusion matrix (contingency table).

+
Cndarray

A confusion matrix (contingency table), +whose row count is not greater than the column count

@@ -588,13 +733,15 @@
genieclust.compare_partitions.confusion_matrix

Determines the confusion matrix

+
genieclust.compare_partitions.normalized_confusion_matrix

Determines the confusion matrix and permutes the rows and columns so that the sum of the elements of the main diagonal is the largest possible

+
+
genieclust.compare_partitions.normalizing_permutation

The underlying function to determine the ordering permutation of the columns

+

Notes

-

This function permutes the columns of C so as to relocate the largest -elements in each row onto the main diagonal.

-

It may come in handy whenever C summarises the results generated -by clustering algorithms, where actual label values do not matter +

This function comes in handy when C summarises the results generated +by clustering algorithms, where the actual label values do not matter (e.g., (1, 2, 0) can be remapped to (0, 2, 1) with no change in meaning).

Examples

>>> x = np.r_[1, 2, 1, 2, 2, 2, 3, 1, 2, 1, 2, 1, 2, 2]
@@ -614,9 +761,8 @@
 
 
-genieclust.compare_partitions.normalized_accuracy()
-

genieclust.compare_partitions.normalized accuracy(x, y)

-

Normalised accuracy

+genieclust.compare_partitions.normalized_accuracy(x, y) +

Normalised accuracy

Parameters
@@ -639,21 +785,28 @@
genieclust.compare_partitions.compare_partitions2

Computes multiple similarity scores based on two label vectors

+
genieclust.compare_partitions.normalized_confusion_matrix

Determines the confusion matrix and permutes the rows and columns so that the sum of the elements of the main diagonal is the largest possible

+

Notes

-

See genieclust.compare_partitions.compare_partitions for more details.

+

See compare_partitions() for more details.

genieclust.compare_partitions.normalized_confusion_matrix(x, y)
-

Computes the confusion matrix for two label vectors and applies pivoting

+

Computes the confusion matrix for two label vectors and +permutes its rows and columns so that the sum of the elements +of the main diagonal is the largest possible (by solving +the maximal assignment problem)

Parameters
x, yarray_like

Two vectors of “small” integers of identical lengths.

+
use_sumbool

Whether the pivoting should be based on

+
Returns
@@ -668,7 +821,7 @@

See also

-
genieclust.compare_partitions.normalize_confusion_matrix

Applies pivoting

+
genieclust.compare_partitions.normalizing_permutation

The underlying function to determine the ordering permutation of the columns

genieclust.compare_partitions.confusion_matrix

Determines the confusion matrix

@@ -714,7 +867,60 @@

Notes

-

See genieclust.compare_partitions.compare_partitions for more details.

+

See compare_partitions() for more details.

+
+ +
+
+genieclust.compare_partitions.normalizing_permutation(C)
+

Determines the permutation of columns of a confusion matrix +so that the sum of the elements on the main diagonal is the largest +possible (by solving the maximal assignment problem)

+
+
Parameters
+
+
Cndarray

A confusion matrix (contingency table), +whose row count is not greater than the column count

+
+
+
+
Returns
+
+
ndarray

A vector of indexes

+
+
+
+
+
+

See also

+
+
genieclust.compare_partitions.confusion_matrix

Determines the confusion matrix

+
+
genieclust.compare_partitions.normalized_confusion_matrix

Determines the confusion matrix and permutes the rows and columns so that the sum of the elements of the main diagonal is the largest possible

+
+
+
+

Notes

+

This function comes in handy when C summarises the results generated +by clustering algorithms, where the actual label values do not matter +(e.g., (1, 2, 0) can be remapped to (0, 2, 1) with no change in meaning).

+

Examples

+
>>> x = np.r_[1, 2, 1, 2, 2, 2, 3, 1, 2, 1, 2, 1, 2, 2]
+>>> y = np.r_[3, 3, 3, 3, 2, 2, 3, 1, 2, 3, 2, 3, 2, 2]
+>>> C = genieclust.compare_partitions.confusion_matrix(x, y)
+>>> C
+array([[1, 0, 4],
+       [0, 6, 2],
+       [0, 0, 1]])
+>>> I = genieclust.compare_partitions.normalizing_permutation(C)
+>>> I
+array([2, 1, 0])
+>>> C[:, I]
+array([[4, 0, 1],
+       [2, 6, 0],
+       [1, 0, 0]])
+
+
@@ -727,6 +933,9 @@
x, yarray_like

Two vectors of “small” integers of identical lengths, representing two partitions of the same set.

+
simplifiedbool

Whether to assume E=1 in the definition of the index, +i.e., use Eq. (20) instead of (18); see [1].

+
Returns
@@ -743,10 +952,20 @@
genieclust.compare_partitions.compare_partitions2

Computes multiple similarity scores based on two label vectors

+
genieclust.compare_partitions.normalized_confusion_matrix

Determines the confusion matrix and permutes the rows and columns so that the sum of the elements of the main diagonal is the largest possible

+

Notes

-

See genieclust.compare_partitions.compare_partitions for more details.

+

See compare_partitions() for more details.

+

References

+
+
1
+

Rezaei M., Franti P., Set matching measures for external cluster validity, +IEEE Transactions on Knowledge and Data Mining 28(8), 2016, +2173-2186. https://doi.org/10.1109/TKDE.2016.2551240.

+
+
@@ -778,7 +997,7 @@

Notes

-

See genieclust.compare_partitions.compare_partitions for more details.

+

See compare_partitions() for more details.

@@ -787,23 +1006,31 @@ -
@@ -818,12 +1045,7 @@ jQuery(function () { SphinxRtdTheme.Navigation.enable(true); }); - - - - - - + \ No newline at end of file diff --git a/docs/genieclust_genie.html b/docs/genieclust_genie.html index 58d3bc1d..e6d94c38 100644 --- a/docs/genieclust_genie.html +++ b/docs/genieclust_genie.html @@ -2,13 +2,20 @@ + + - genieclust.Genie — genieclust + genieclust.Genie — Python and R Package genieclust + + + + + @@ -49,7 +56,7 @@ - + @@ -64,25 +71,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
@@ -575,23 +632,31 @@

genieclust.Genie +
+
-

© Copyright 2018–2022, Marek Gagolewski. - Last updated on 2022-08-09T17:56:16+1000. -

-
+

+ Copyright © 2018–2022 by Marek Gagolewski. Some rights reserved. Licensed under CC BY-NC-ND 4.0. - Built with Sphinx using a - theme - provided by Read the Docs. - + Built with Sphinx + and a customised rtd + theme. + + Last updated on 2022-09-05T12:45:35+1000. + + + + This site will never display any ads: it is a non-profit project. + It does not collect any data. + +

+

@@ -606,12 +671,7 @@

genieclust.Genie + + - genieclust.inequity — genieclust + genieclust.inequity — Python and R Package genieclust + + + + + @@ -64,25 +71,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
@@ -411,23 +468,31 @@
-
@@ -442,12 +507,7 @@ jQuery(function () { SphinxRtdTheme.Navigation.enable(true); }); - - - - - - + \ No newline at end of file diff --git a/docs/genieclust_internal.html b/docs/genieclust_internal.html index 8569a4c9..bc2c76e5 100644 --- a/docs/genieclust_internal.html +++ b/docs/genieclust_internal.html @@ -2,13 +2,20 @@ + + - genieclust.internal — genieclust + genieclust.internal — Python and R Package genieclust + + + + + @@ -64,25 +71,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
@@ -505,23 +562,31 @@
-
@@ -536,12 +601,7 @@ jQuery(function () { SphinxRtdTheme.Navigation.enable(true); }); - - - - - - + \ No newline at end of file diff --git a/docs/genieclust_plots-1.pdf b/docs/genieclust_plots-1.pdf index e0b709de3525e5614ff5bc70db958298380ec7f4..37782fe9211fb57575bd09b70bd126769e3496b6 100644 GIT binary patch delta 22 ecmbR4INfo>QCUt)15-mI6H{ZO&F5rKG64WtmQCUt414~15Q!_*3&F5rKG64Wt^#_dr diff --git a/docs/genieclust_plots-2.pdf b/docs/genieclust_plots-2.pdf index 3c455295831d442ab46461dbbfa3c47716a6f420..8cc4d95873eb5413036bcb9585c7b60b659f2f99 100644 GIT binary patch delta 22 dcmX?@a4=!RJ#9`)15-mI6H{ZO&Cj)?SO8~_2loH~ delta 22 dcmX?@a4=!RJ#9`414~15Q!_*3&Cj)?SO9122mk;8 diff --git a/docs/genieclust_plots-3.pdf b/docs/genieclust_plots-3.pdf index f714aef7274c2d725b1c2f0afc46dbb633b7b22c..b892058a150b7def73783015003cb2aca4c3ffaa 100644 GIT binary patch delta 22 dcmZ2%vDjimr6i}NfvKU9iK(&C<|fI7OaN0*2EqUU delta 22 dcmZ2%vDjimr6i|?fu*6jshOei<|fI7OaN1@2Fm~d diff --git a/docs/genieclust_plots-4.pdf b/docs/genieclust_plots-4.pdf index ce7b5e8856aded0413e5a7cc00db51712372fc93..bd949e3ed957abf4f2bcc8957988b300356f3aeb 100644 GIT binary patch delta 21 dcmZ4Ny4ZEYQ+W + + - genieclust.plots — genieclust + genieclust.plots — Python and R Package genieclust + + + + + @@ -62,25 +69,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
@@ -186,7 +243,7 @@

Various plotting functions

-genieclust.plots.plot_scatter(X, y=None, labels=None, **kwargs)
+genieclust.plots.plot_scatter(X, y=None, labels=None, axis=None, title=None, xlabel=None, ylabel=None, xlim=None, ylim=None, **kwargs)

Draws a scatter plot

Parameters
@@ -200,6 +257,9 @@
labelsNone or array_like

A vector of n integer labels that correspond to each point in X, that gives its plot style.

+
axis, title, xlabel, ylabel, xlim, ylimNone or object

If not None, values passed to matplotlib.pyplot.axis, +matplotlib.pyplot.title, etc.

+
**kwargsCollection properties

Further arguments to matplotlib.pyplot.scatter.

@@ -319,23 +379,31 @@
-
@@ -350,12 +418,7 @@ jQuery(function () { SphinxRtdTheme.Navigation.enable(true); }); - - - - - - + \ No newline at end of file diff --git a/docs/genieclust_tools.html b/docs/genieclust_tools.html index d6252abf..09beb727 100644 --- a/docs/genieclust_tools.html +++ b/docs/genieclust_tools.html @@ -2,13 +2,20 @@ + + - genieclust.tools — genieclust + genieclust.tools — Python and R Package genieclust + + + + + @@ -64,25 +71,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
@@ -185,7 +242,7 @@

genieclust.tools

-

Functions a person might find useful, but not necessarily

+

Functions one might find useful, but not necessarily

genieclust.tools.argkmin(x, k)
@@ -300,10 +357,6 @@
genieclust.tools.cummin

Cumulative minimum

-
numpy.cumsum

Cumulative sum

-
-
numpy.cumprod

Cumulative product

-

Examples

@@ -338,10 +391,6 @@
genieclust.tools.cummax

Cumulative maximum

-
numpy.cumsum

Cumulative sum

-
-
numpy.cumprod

Cumulative product

-

Examples

@@ -357,23 +406,31 @@ -
@@ -388,12 +445,7 @@ jQuery(function () { SphinxRtdTheme.Navigation.enable(true); }); - - - - - - + \ No newline at end of file diff --git a/docs/genindex.html b/docs/genindex.html index 8c976662..557f6b1e 100644 --- a/docs/genindex.html +++ b/docs/genindex.html @@ -2,12 +2,19 @@ + + - Index — genieclust + Index — Python and R Package genieclust + + + + + @@ -59,25 +66,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
- +
@@ -98,6 +111,10 @@

Examples and Tutorials

    @@ -117,11 +134,7 @@

See Also

Appendix

@@ -154,13 +167,49 @@ @@ -332,12 +426,7 @@

Examples + + - emst_mlpack: Euclidean Minimum Spanning Tree — genieclust + emst_mlpack: Euclidean Minimum Spanning Tree — Python and R Package genieclust + + + + + @@ -47,8 +54,8 @@ - - + + @@ -62,25 +69,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
- +
@@ -101,6 +114,10 @@

Examples and Tutorials

+ + + +
@@ -236,8 +293,8 @@

Author(s)

References

-

March W.B., Ram P., Gray A.G., Fast Euclidean Minimum Spanning Tree: Algorithm, Analysis, and Applications, Proc. ACM SIGKDD’10 (2010) 603-611, https://mlpack.org/papers/emst.pdf.

-

Curtin R.R., Edel M., Lozhnikov M., Mentekidis Y., Ghaisas S., Zhang S., mlpack 3: A fast, flexible machine learning library, Journal of Open Source Software 3(26), 726, 2018.

+

March W.B., Ram P., Gray A.G., Fast Euclidean Minimum Spanning Tree: Algorithm, Analysis, and Applications, Proc. ACM SIGKDD’10, 2010, 603-611, https://mlpack.org/papers/emst.pdf.

+

Curtin R.R., Edel M., Lozhnikov M., Mentekidis Y., Ghaisas S., Zhang S., mlpack 3: A fast, flexible machine learning library, Journal of Open Source Software 3(26), 2018, 726.

See Also

@@ -250,23 +307,31 @@

See Also - - +
+
-

© Copyright 2018–2022, Marek Gagolewski. - Last updated on 2022-08-09T17:56:16+1000. -

-
+

+ Copyright © 2018–2022 by Marek Gagolewski. Some rights reserved. Licensed under CC BY-NC-ND 4.0. - Built with Sphinx using a - theme - provided by Read the Docs. - + Built with Sphinx + and a customised rtd + theme. + + Last updated on 2022-09-05T12:45:35+1000. + + + + This site will never display any ads: it is a non-profit project. + It does not collect any data. + +

+

@@ -281,12 +346,7 @@

See Also + + - gclust: The Genie++ Hierarchical Clustering Algorithm — genieclust + gclust: Hierarchical Clustering Algorithm Genie — Python and R Package genieclust + + + + + @@ -49,7 +56,7 @@ - + @@ -64,25 +71,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
- +
@@ -103,6 +116,10 @@

Examples and Tutorials

-
-

gclust: The Genie++ Hierarchical Clustering Algorithm

+
+

gclust: Hierarchical Clustering Algorithm Genie

Description

-

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 single linkage, it consumes the edges of the MST in 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_v1.

+

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., 2015). 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.

@@ -307,7 +364,7 @@

Arguments

Details

-

Note that as in the case of all the distance-based methods, the standardisation of the input features is definitely worth giving a try.

+

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). Departures from ultrametricity are corrected by applying height = rev(cummin(rev(height))).

@@ -361,23 +418,31 @@

Examples +
+
-

© Copyright 2018–2022, Marek Gagolewski. - Last updated on 2022-08-09T17:56:16+1000. -

-
+

+ Copyright © 2018–2022 by Marek Gagolewski. Some rights reserved. Licensed under CC BY-NC-ND 4.0. - Built with Sphinx using a - theme - provided by Read the Docs. - + Built with Sphinx + and a customised rtd + theme. + + Last updated on 2022-09-05T12:45:35+1000. + + + + This site will never display any ads: it is a non-profit project. + It does not collect any data. + +

+

@@ -392,12 +457,7 @@

Examples + + - genieclust-package: The Genie++ Hierarchical Clustering Algorithm (with Extras) — genieclust + genieclust-package: The Genie Hierarchical Clustering Algorithm (with Extras) — Python and R Package genieclust + + + + + @@ -48,7 +55,7 @@ - + @@ -62,25 +69,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
- +
@@ -101,6 +114,10 @@

Examples and Tutorials

-

genieclust-package: The Genie++ Hierarchical Clustering Algorithm (with Extras)

+

genieclust-package: The Genie Hierarchical Clustering Algorithm (with Extras)

Description

See genie() for more details.

@@ -207,23 +264,31 @@

See Also - +
+
-

© Copyright 2018–2022, Marek Gagolewski. - Last updated on 2022-08-09T17:56:16+1000. -

-
+

+ Copyright © 2018–2022 by Marek Gagolewski. Some rights reserved. Licensed under CC BY-NC-ND 4.0. - Built with Sphinx using a - theme - provided by Read the Docs. - + Built with Sphinx + and a customised rtd + theme. + + Last updated on 2022-09-05T12:45:35+1000. + + + + This site will never display any ads: it is a non-profit project. + It does not collect any data. + +

+

@@ -238,12 +303,7 @@

See Also + + - inequity: Inequity (Inequality) Measures — genieclust + inequity: Inequity (Inequality) Measures — Python and R Package genieclust + + + + + @@ -50,7 +57,7 @@ - + @@ -64,25 +71,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
- +
@@ -103,6 +116,10 @@

Examples and Tutorials

@@ -267,9 +324,9 @@

Author(s)

References

-

Bonferroni C., Elementi di Statistica Generale, Libreria Seber, Firenze, 1930.

-

Gagolewski M., Bartoszuk M., Cena A., Genie: A new, fast, and outlier-resistant hierarchical clustering algorithm, Information Sciences 363, 2016, pp. 8-23. doi:10.1016/j.ins.2016.05.003

-

Gini C., Variabilita e Mutabilita, Tipografia di Paolo Cuppini, Bologna, 1912.

+

Bonferroni C., Elementi di Statistica Generale, Libreria Seber, Firenze, 1930.

+

Gagolewski M., Bartoszuk M., Cena A., Genie: A new, fast, and outlier-resistant hierarchical clustering algorithm, Information Sciences 363, 2016, pp. 8-23. doi:10.1016/j.ins.2016.05.003

+

Gini C., Variabilita e Mutabilita, Tipografia di Paolo Cuppini, Bologna, 1912.

See Also

@@ -278,13 +335,13 @@

See Also

Examples

-
gini_index(c(2, 2, 2, 2, 2))  # no inequality
+
gini_index(c(2, 2, 2, 2, 2))   # no inequality
 ## [1] 0
-gini_index(c(0, 0, 10, 0, 0)) # one has it all
+gini_index(c(0, 0, 10, 0, 0))  # one has it all
 ## [1] 1
-gini_index(c(7, 0, 3, 0, 0))  # give to the poor, take away from the rich
+gini_index(c(7, 0, 3, 0, 0))   # give to the poor, take away from the rich
 ## [1] 0.85
-gini_index(c(6, 0, 3, 1, 0))  # (a.k.a. Pigou-Dalton principle)
+gini_index(c(6, 0, 3, 1, 0))   # (a.k.a. Pigou-Dalton principle)
 ## [1] 0.75
 bonferroni_index(c(2, 2, 2, 2, 2))
 ## [1] 0
@@ -311,23 +368,31 @@ 

Examples - +
+
-

© Copyright 2018–2022, Marek Gagolewski. - Last updated on 2022-08-09T17:56:16+1000. -

-
+

+ Copyright © 2018–2022 by Marek Gagolewski. Some rights reserved. Licensed under CC BY-NC-ND 4.0. - Built with Sphinx using a - theme - provided by Read the Docs. - + Built with Sphinx + and a customised rtd + theme. + + Last updated on 2022-09-05T12:45:35+1000. + + + + This site will never display any ads: it is a non-profit project. + It does not collect any data. + +

+

@@ -342,12 +407,7 @@

Examples + + - mst: Minimum Spanning Tree of the Pairwise Distance Graph — genieclust + mst: Minimum Spanning Tree of the Pairwise Distance Graph — Python and R Package genieclust + + + + + @@ -64,25 +71,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
- +
@@ -103,6 +116,10 @@

Examples and Tutorials

@@ -230,22 +287,22 @@

Arguments

d

-

either 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.

+

either 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

...

-

further arguments passed to or from other methods.

+

further arguments passed to or from other methods

distance

-

metric used to compute the linkage, one of: "euclidean" (synonym: "l2"), "manhattan" (a.k.a. "l1" and "cityblock"), "cosine".

+

metric used to compute the linkage, one of: "euclidean" (synonym: "l2"), "manhattan" (a.k.a. "l1" and "cityblock"), "cosine"

M

-

smoothing factor; M = 1 gives the selected distance; otherwise, the mutual reachability distance is used.

+

smoothing factor; M = 1 gives the selected distance; otherwise, the mutual reachability distance is used

cast_float32

-

logical; whether to compute the distances using 32-bit instead of 64-bit precision floating-point arithmetic (up to 2x faster).

+

logical; whether to compute the distances using 32-bit instead of 64-bit precision floating-point arithmetic (up to 2x faster)

verbose

-

logical; whether to print diagnostic messages and progress information.

+

logical; whether to print diagnostic messages and progress information

@@ -270,10 +327,10 @@

Author(s)

References

-

V. Jarnik, O jistem problemu minimalnim, Prace Moravske Prirodovedecke Spolecnosti 6 (1930) 57-63.

-

Olson C.F., Parallel algorithms for hierarchical clustering, Parallel Comput. 21 (1995) 1313-1325.

-

Prim R., Shortest connection networks and some generalisations, Bell Syst. Tech. J. 36 (1957) 1389-1401.

-

Campello R., Moulavi D., Zimek A., Sander J., Hierarchical density estimates for data clustering, visualization, and outlier detection, ACM Transactions on Knowledge Discovery from Data 10(1) (2015) 5:1-5:51.

+

Jarnik V., O jistem problemu minimalnim, Prace Moravske Prirodovedecke Spolecnosti 6, 1930, 57-63.

+

Olson C.F., Parallel algorithms for hierarchical clustering, Parallel Comput. 21, 1995, 1313-1325.

+

Prim R., Shortest connection networks and some generalisations, Bell Syst. Tech. J. 36, 1957, 1389-1401.

+

Campello R., Moulavi D., Zimek A., Sander J., Hierarchical density estimates for data clustering, visualization, and outlier detection, ACM Transactions on Knowledge Discovery from Data 10(1), 2015, 5:1-5:51.

See Also

@@ -296,23 +353,31 @@

Examples - +
+
-

© Copyright 2018–2022, Marek Gagolewski. - Last updated on 2022-08-09T17:56:16+1000. -

-
+

+ Copyright © 2018–2022 by Marek Gagolewski. Some rights reserved. Licensed under CC BY-NC-ND 4.0. - Built with Sphinx using a - theme - provided by Read the Docs. - + Built with Sphinx + and a customised rtd + theme. + + Last updated on 2022-09-05T12:45:35+1000. + + + + This site will never display any ads: it is a non-profit project. + It does not collect any data. + +

+

@@ -327,12 +392,7 @@

Examples + + - Search — genieclust + Search — Python and R Package genieclust + + + + + @@ -62,25 +69,31 @@ - genieclust + genieclust +
+ Python and R Package
v1.1.0 +
+ +
- +
@@ -101,6 +114,10 @@

Examples and Tutorials

    @@ -120,11 +137,7 @@

See Also

Appendix

@@ -157,13 +170,49 @@

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