From 4369b675a9bf6721d7d6fbbca2d1a7b8dabff84e Mon Sep 17 00:00:00 2001 From: pajaskowiak Date: Wed, 15 Feb 2023 22:50:52 -0300 Subject: [PATCH] all set --- README.md | 56 +- data/dataset_1.txt | 925 ++++++++++ data/dataset_2.txt | 1863 +++++++++++++++++++++ data/dataset_3.txt | 1500 +++++++++++++++++ data/dataset_4.txt | 885 ++++++++++ plots/dataset_1.pdf | Bin 0 -> 35055 bytes plots/dataset_1.png | Bin 0 -> 26664 bytes plots/dataset_2.pdf | Bin 0 -> 42108 bytes plots/dataset_2.png | Bin 0 -> 56685 bytes plots/dataset_3.pdf | Bin 0 -> 77207 bytes plots/dataset_3.png | Bin 0 -> 37772 bytes plots/dataset_4.pdf | Bin 0 -> 32452 bytes plots/dataset_4.png | Bin 0 -> 25022 bytes src/MST_Edges.m | 52 + src/dbcv.m | 93 + src/matrix_mutual_reachability_distance.m | 23 + src/plot_clusters.m | 15 + 17 files changed, 5410 insertions(+), 2 deletions(-) create mode 100644 data/dataset_1.txt create mode 100644 data/dataset_2.txt create mode 100644 data/dataset_3.txt create mode 100644 data/dataset_4.txt create mode 100644 plots/dataset_1.pdf create mode 100644 plots/dataset_1.png create mode 100644 plots/dataset_2.pdf create mode 100644 plots/dataset_2.png create mode 100644 plots/dataset_3.pdf create mode 100644 plots/dataset_3.png create mode 100644 plots/dataset_4.pdf create mode 100644 plots/dataset_4.png create mode 100644 src/MST_Edges.m create mode 100644 src/dbcv.m create mode 100644 src/matrix_mutual_reachability_distance.m create mode 100644 src/plot_clusters.m diff --git a/README.md b/README.md index 0a36e0c..a2d4935 100644 --- a/README.md +++ b/README.md @@ -7,8 +7,60 @@ This is the source code employed to compute DBCV (Density-Based Clustering Valid You can read the paper here: https://epubs.siam.org/doi/10.1137/1.9781611973440.96 -The Matlab source code from this repository is from Davoud Moulavi and Pablo A. Jaskowiak. +The Matlab source code from this repository is from [Davoud Moulavi](https://scholar.google.com.br/citations?user=VoJmF8QAAAAJ) and [Pablo A. Jaskowiak](https://scholar.google.com.br/citations?user=by6xRbkAAAAJ). + +## Usage + +For calculating the DBCV Validation Index of a partition run dbcv.m. The output of the function is the DBCV index for the corresponding partition. Its values are within -1 and +1. DBCV is a *maximization* index, which means that higher values correspond to better partitions, according to the index. The necessary inputs are the dataset (without labels) and the partition, which correspond to a clustering solution, that is, labels. The dataset should be formatted with each line corresponding to an object, with columns corresponding to features. The partition is a 1-dimensional array with cluster assignments, in integer format. The number of labels must match the number of objects in the dataset. + +**Important note**: noise is represented by label 0 (zero). Therefore, any object with label of zero in the partition is considered as noise. By definition, singletons (clusters with a single object) will be treated as noise by the measure (please see the paper for discussion on this topic). + + +### Example: Computing DBCV on a Synthetic Dataset + +Assuming you are running Matlab and your current working directory is *src*. + +``` +%first we load the dataset +load ../data/dataset_1.txt + +%we run dbcv on the dataset (first two columns), +%passing its ground truth as partition (column 3). +val = dbcv(dataset_1(:,-3),dataset_1(:,3)) + +%val should be 0.6149. Note that this is low given +%that some noise points actually overlap the clusters. + +%we can also plot the dataset with the following +plot_clusters(dataset_1(:,1:2),dataset_1(:,3)) + +%that's all :) +``` + + +## Datasets + +In the folder *data* you can find the four synthetic datasets employed in our paper. These are shown below. Plots in PDF and PNG can be found in the folder *plots*. Please, if you use any of these datasets in a publication, cite *both* our paper and this repository. + +

+ + +

+ +

+ + +

+ + +## Other resources You can also find an implementation of DBCV in the R Package [clusterConfusion](https://github.com/pajaskowiak/clusterConfusion). -If you find any bugs or problems, please, get in touch. +## Disclaimer + +This prototype was developed for research purposes only. It was *by no means* implemented to optimize computational performance. Therefore, its computational performance should not be evaluated and/or fairly compared to that of other measures. + +## Contact + +If you find any bugs or problems, please, get in touch. You can reach me [here](https://andretta.paginas.ufsc.br/). diff --git a/data/dataset_1.txt b/data/dataset_1.txt new file mode 100644 index 0000000..07c510a --- /dev/null +++ b/data/dataset_1.txt @@ -0,0 +1,925 @@ +-0.0014755 0.99852 1 +-0.005943 0.98904 1 +0.028184 1.0181 1 +0.019204 1.0041 1 +0.033017 1.0128 1 +0.011014 0.9857 1 +0.033779 1.0033 1 +0.045243 1.0096 1 +0.02493 0.98413 1 +0.064521 1.0185 1 +0.032742 0.98149 1 +0.042959 0.98645 1 +0.049146 0.98734 1 +0.05769 0.99058 1 +0.070368 0.99792 1 +0.070434 0.99262 1 +0.09811 1.0149 1 +0.078285 0.98967 1 +0.096586 1.0025 1 +0.10724 1.0077 1 +0.083108 0.9781 1 +0.088157 0.97763 1 +0.092311 0.97624 1 +0.10984 0.98821 1 +0.12512 0.99789 1 +0.13833 1.0055 1 +0.12534 0.98686 1 +0.13543 0.99127 1 +0.13098 0.98113 1 +0.14075 0.98519 1 +0.16177 1.0005 1 +0.13901 0.97193 1 +0.14619 0.97331 1 +0.14712 0.96842 1 +0.16767 0.98311 1 +0.19442 1.004 1 +0.16394 0.96761 1 +0.1977 0.99543 1 +0.19514 0.98692 1 +0.1946 0.9804 1 +0.19852 0.97831 1 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(G.no_vertices x 3) = MST edges (a pair of vertices and the corresponding weight) +% G.MST_degrees (No x 1) = MST vertex degrees (a self-edge counts one additional degree !) + +%'COMPUTING THE MST (PRIMs Algorithm on a Complete Graph using List Search)'; + +for i=1:G.no_vertices + intree(i) = 0; + d(i) = Inf; + G.MST_parent(i) = i; +end + +d(start) = 0; +v = start; +counter = 0; + +while (counter < (G.no_vertices - 1)) + intree(v) = 1; + dist = Inf; + for w=1:G.no_vertices + if ((w~=v) && (intree(w) == 0)) + weight = G_edges_weights(v,w); + if (d(w) > weight) + d(w) = weight; + G.MST_parent(w) = v; + end + if (dist > d(w)) + dist = d(w); + next_v = w; + end + end + + end + counter = counter + 1; + G.MST_edges(counter,:) = [G.MST_parent(next_v) ; next_v ; G_edges_weights(G.MST_parent(next_v) , next_v)]; % Includes Edge into the MST + G.MST_degrees(G.MST_parent(next_v)) = G.MST_degrees(G.MST_parent(next_v)) + 1; % Increments MST vertex degree + G.MST_degrees(next_v) = G.MST_degrees(next_v) + 1; % Increments MST vertex degree + v = next_v; % Vertex included +end +Edg = G.MST_edges; +Degr = G.MST_degrees; + diff --git a/src/dbcv.m b/src/dbcv.m new file mode 100644 index 0000000..b00a1b6 --- /dev/null +++ b/src/dbcv.m @@ -0,0 +1,93 @@ +function valid = dbcv(data,partition) + +clusters = unique(partition); +dist = squareform(pdist(data)).^2; +%treating singleton clusters +for i=1:length(clusters) + if(sum(partition == clusters(i)) == 1) + partition(partition == clusters(i)) = 0; + clusters(i) = 0; + end +end + +%clusters without noise and singletons +clusters = setdiff(clusters,0); + +if (isempty(clusters) || (length(clusters) == 1)) + valid = 0; + return; +end + +data = data(partition~=0,:); + +dist = dist(partition~=0,partition~=0); + +poriginal = partition; +partition = partition(partition~=0); + + +nclusters = length(clusters); + +[nobjects nfeatures] = size(data); + +d_ucore_cl = zeros(1,nobjects); +compcl = zeros(1,nclusters); +int_edges = cell(1,nclusters); +int_node_data = cell(1,nclusters); +for i=1:nclusters + + objcl = find(partition == clusters(i)); + + nuobjcl = length(objcl); + + [d_ucore_cl(objcl) mr] = matrix_mutual_reachability_distance(nuobjcl, dist(objcl,objcl),nfeatures); % ucore distance of each object in its own cluster + + G.no_vertices = nuobjcl; + G.MST_edges = zeros(nuobjcl-1,3); + G.MST_degrees = zeros(nuobjcl,1); + G.MST_parent = zeros(nuobjcl,1); + + [Edges Degrees] = MST_Edges(G, 1,mr); + + int_node = find(Degrees~=1); + int_edg1 = find(ismember(Edges(:,1),int_node)); + int_edg2 = find(ismember(Edges(:,2),int_node)); + int_edges{i} = intersect(int_edg1,int_edg2); + + + if (~isempty(int_edges{i})) + compcl(i) = max(Edges(int_edges{i},3)); + else + compcl(i) = max(Edges(:,3)); + end + int_node_data{i} = objcl(int_node); + if isempty(int_node_data{i}) + int_node_data{i} = objcl; + end +end + +sep_point = zeros(nobjects,nobjects); +for i=1:(nobjects-1) + for j=i:nobjects + sep_point(i,j) = max([dist(i,j) d_ucore_cl(i) d_ucore_cl(j)]); + sep_point(j,i) = sep_point(i,j); + end +end + +valid = 0; +sepcl = Inf(nclusters,1); +for i=1:nclusters + other_cls = setdiff(clusters,clusters(i)); + + sep = zeros(1,length(other_cls)); + for j=1:length(other_cls) + sep(j) = min(min(sep_point(int_node_data{i},int_node_data{clusters==other_cls(j)}))); + end + sepcl(i) = min(sep); + dbcvcl = (sepcl(i) - compcl(i)) / max(compcl(i),sepcl(i)); + valid = valid + (dbcvcl * sum(partition == clusters(i))); +end + +valid = valid / length(poriginal); + +end diff --git a/src/matrix_mutual_reachability_distance.m b/src/matrix_mutual_reachability_distance.m new file mode 100644 index 0000000..7d839fb --- /dev/null +++ b/src/matrix_mutual_reachability_distance.m @@ -0,0 +1,23 @@ +function [d_ucore G_edges_weights] = matrix_mutual_reachability_distance(MinPts, G_edges_weights,d) + +No = size(G_edges_weights,1); + +K_NN_Dist = G_edges_weights.^(-1*d); +K_NN_Dist(K_NN_Dist == Inf) = 0; + +%original +d_ucore = sum(K_NN_Dist); + +d_ucore = d_ucore / (No - 1); +d_ucore = (1./d_ucore).^(1/(1*d)); +d_ucore(d_ucore == Inf) = 0; + +for i = 1:No + for j=1:MinPts + G_edges_weights(i,j) = max([d_ucore(i) d_ucore(j) G_edges_weights(i,j)]); + G_edges_weights(j,i) = G_edges_weights(i,j); + end +end + +end + diff --git a/src/plot_clusters.m b/src/plot_clusters.m new file mode 100644 index 0000000..90085e5 --- /dev/null +++ b/src/plot_clusters.m @@ -0,0 +1,15 @@ +function plot_clusters(data,labels) + +color = {'b','g','r','c','m','y'}; +point = {'x','o','*','s','d','v','^','>','<','p','h'}; + +for i=1:size(data,1) + if ((labels(i) == -1) || sum(labels == labels(i)) == 1 ) + plot(data(i,1),data(i,2),'k+','MarkerSize',6); + else + plot(data(i,1),data(i,2),strcat(color{mod(labels(i),length(color))+1},point{mod(labels(i),length(point))+1}),'MarkerSize',9); + end + hold on; +end + +end