README.md
In clepadellec/ClustersAnalysis: Analyses and interpretation of clustering
- Introduction
- Import ClustersAnalysis from Github (using
devtools)
- Univariate Analysis for qualitatives
variariables
- Univariate Analysis for quantitatives
variables
- Multivariate Analysis
- Let’s practice on your own
dataset
Introduction
This is a demonstration of using the R package ClustersAnalysis. You
will see how to analyze classes according to one or more variables. The
group variable must be of the type factor or character and the
exploratory variables can be quantitative or qualitative. In this
demonstration we are going to use natives dataset from R such as “iris”,
“infert” or “esoph”.
Short Descriptions of datasets
Iris :
The data set consists of 50 samples from each of three species of Iris
(Iris setosa, Iris virginica and Iris versicolor). Four features were
measured from each sample: the length and the width of the sepals and
petals, in centimeters. Based on the combination of these four features,
Fisher developed a linear discriminant model to distinguish the species
from each other.
summary(iris)
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100
## 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300
## Median :5.800 Median :3.000 Median :4.350 Median :1.300
## Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199
## 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800
## Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500
## Species
## setosa :50
## versicolor:50
## virginica :50
##
##
##
Infert :
This is a matched case-control study dating from before the availability
of conditional logistic regression.
summary(infert)
## education age parity induced
## 0-5yrs : 12 Min. :21.00 Min. :1.000 Min. :0.0000
## 6-11yrs:120 1st Qu.:28.00 1st Qu.:1.000 1st Qu.:0.0000
## 12+ yrs:116 Median :31.00 Median :2.000 Median :0.0000
## Mean :31.50 Mean :2.093 Mean :0.5726
## 3rd Qu.:35.25 3rd Qu.:3.000 3rd Qu.:1.0000
## Max. :44.00 Max. :6.000 Max. :2.0000
## case spontaneous stratum pooled.stratum
## Min. :0.0000 Min. :0.0000 Min. : 1.00 Min. : 1.00
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:21.00 1st Qu.:19.00
## Median :0.0000 Median :0.0000 Median :42.00 Median :36.00
## Mean :0.3347 Mean :0.5766 Mean :41.87 Mean :33.58
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:62.25 3rd Qu.:48.25
## Max. :1.0000 Max. :2.0000 Max. :83.00 Max. :63.00
Esoph :
Data from a case-control study of (o)esophageal cancer in
Ille-et-Vilaine, France. This is a data frame with records for 88
age/alcohol/tobacco combinations.
summary(esoph)
## agegp alcgp tobgp ncases ncontrols
## 25-34:15 0-39g/day:23 0-9g/day:24 Min. : 0.000 Min. : 1.00
## 35-44:15 40-79 :23 10-19 :24 1st Qu.: 0.000 1st Qu.: 3.00
## 45-54:16 80-119 :21 20-29 :20 Median : 1.000 Median : 6.00
## 55-64:16 120+ :21 30+ :20 Mean : 2.273 Mean :11.08
## 65-74:15 3rd Qu.: 4.000 3rd Qu.:14.00
## 75+ :11 Max. :17.000 Max. :60.00
CO2 :
The CO2 data frame has 84 rows and 5 columns of data from an experiment
on the cold tolerance of the grass species Echinochloa crus-galli.
summary(CO2)
## Plant Type Treatment conc uptake
## Qn1 : 7 Quebec :42 nonchilled:42 Min. : 95 Min. : 7.70
## Qn2 : 7 Mississippi:42 chilled :42 1st Qu.: 175 1st Qu.:17.90
## Qn3 : 7 Median : 350 Median :28.30
## Qc1 : 7 Mean : 435 Mean :27.21
## Qc3 : 7 3rd Qu.: 675 3rd Qu.:37.12
## Qc2 : 7 Max. :1000 Max. :45.50
## (Other):42
Import ClustersAnalysis from Github (using devtools)
Please download the latest R version (>4.0) before running the code
below.
#Use the below line to install devtools if necessary
#install.packages("devtools")
#library(devtools)
#install package from github or download the folder and open it with R
#Use the below line to install ClustersAnalysis if necessary
#devtools::install_github("clepadellec/ClustersAnalysis")
#load package
library(ClustersAnalysis)
How to access to help
You can juste use the fonction help(function name) to see all the
documentation about your function.
help("u_plot_size_effect")
Univariate Analysis for qualitatives variariables
To begin we will try to understand, for each qualitative explanatory
variable, if it affects the group variable. It’s necessary to create an
object of univariate type. You can use the constructor
Univariate_object.
#Creation of univariate object using esoph dataframe and "agegp" (first column) as the group variable
u_esoph<-Univariate_object(esoph,1)
#detail of attributes associated with the object
print(u_esoph)
## $ind.qual
## agegp alcgp tobgp ncases ncontrols
## TRUE TRUE TRUE FALSE FALSE
##
## $ind.quan
## agegp alcgp tobgp ncases ncontrols
## FALSE FALSE FALSE TRUE TRUE
##
## $df
## agegp alcgp tobgp ncases ncontrols
## 1 25-34 0-39g/day 0-9g/day 0 40
## 2 25-34 0-39g/day 10-19 0 10
## 3 25-34 0-39g/day 20-29 0 6
## 4 25-34 0-39g/day 30+ 0 5
## 5 25-34 40-79 0-9g/day 0 27
## 6 25-34 40-79 10-19 0 7
## 7 25-34 40-79 20-29 0 4
## 8 25-34 40-79 30+ 0 7
## 9 25-34 80-119 0-9g/day 0 2
## 10 25-34 80-119 10-19 0 1
## 11 25-34 80-119 30+ 0 2
## 12 25-34 120+ 0-9g/day 0 1
## 13 25-34 120+ 10-19 1 1
## 14 25-34 120+ 20-29 0 1
## 15 25-34 120+ 30+ 0 2
## 16 35-44 0-39g/day 0-9g/day 0 60
## 17 35-44 0-39g/day 10-19 1 14
## 18 35-44 0-39g/day 20-29 0 7
## 19 35-44 0-39g/day 30+ 0 8
## 20 35-44 40-79 0-9g/day 0 35
## 21 35-44 40-79 10-19 3 23
## 22 35-44 40-79 20-29 1 14
## 23 35-44 40-79 30+ 0 8
## 24 35-44 80-119 0-9g/day 0 11
## 25 35-44 80-119 10-19 0 6
## 26 35-44 80-119 20-29 0 2
## 27 35-44 80-119 30+ 0 1
## 28 35-44 120+ 0-9g/day 2 3
## 29 35-44 120+ 10-19 0 3
## 30 35-44 120+ 20-29 2 4
## 31 45-54 0-39g/day 0-9g/day 1 46
## 32 45-54 0-39g/day 10-19 0 18
## 33 45-54 0-39g/day 20-29 0 10
## 34 45-54 0-39g/day 30+ 0 4
## 35 45-54 40-79 0-9g/day 6 38
## 36 45-54 40-79 10-19 4 21
## 37 45-54 40-79 20-29 5 15
## 38 45-54 40-79 30+ 5 7
## 39 45-54 80-119 0-9g/day 3 16
## 40 45-54 80-119 10-19 6 14
## 41 45-54 80-119 20-29 1 5
## 42 45-54 80-119 30+ 2 4
## 43 45-54 120+ 0-9g/day 4 4
## 44 45-54 120+ 10-19 3 4
## 45 45-54 120+ 20-29 2 3
## 46 45-54 120+ 30+ 4 4
## 47 55-64 0-39g/day 0-9g/day 2 49
## 48 55-64 0-39g/day 10-19 3 22
## 49 55-64 0-39g/day 20-29 3 12
## 50 55-64 0-39g/day 30+ 4 6
## 51 55-64 40-79 0-9g/day 9 40
## 52 55-64 40-79 10-19 6 21
## 53 55-64 40-79 20-29 4 17
## 54 55-64 40-79 30+ 3 6
## 55 55-64 80-119 0-9g/day 9 18
## 56 55-64 80-119 10-19 8 15
## 57 55-64 80-119 20-29 3 6
## 58 55-64 80-119 30+ 4 4
## 59 55-64 120+ 0-9g/day 5 10
## 60 55-64 120+ 10-19 6 7
## 61 55-64 120+ 20-29 2 3
## 62 55-64 120+ 30+ 5 6
## 63 65-74 0-39g/day 0-9g/day 5 48
## 64 65-74 0-39g/day 10-19 4 14
## 65 65-74 0-39g/day 20-29 2 7
## 66 65-74 0-39g/day 30+ 0 2
## 67 65-74 40-79 0-9g/day 17 34
## 68 65-74 40-79 10-19 3 10
## 69 65-74 40-79 20-29 5 9
## 70 65-74 80-119 0-9g/day 6 13
## 71 65-74 80-119 10-19 4 12
## 72 65-74 80-119 20-29 2 3
## 73 65-74 80-119 30+ 1 1
## 74 65-74 120+ 0-9g/day 3 4
## 75 65-74 120+ 10-19 1 2
## 76 65-74 120+ 20-29 1 1
## 77 65-74 120+ 30+ 1 1
## 78 75+ 0-39g/day 0-9g/day 1 18
## 79 75+ 0-39g/day 10-19 2 6
## 80 75+ 0-39g/day 30+ 1 3
## 81 75+ 40-79 0-9g/day 2 5
## 82 75+ 40-79 10-19 1 3
## 83 75+ 40-79 20-29 0 3
## 84 75+ 40-79 30+ 1 1
## 85 75+ 80-119 0-9g/day 1 1
## 86 75+ 80-119 10-19 1 1
## 87 75+ 120+ 0-9g/day 2 2
## 88 75+ 120+ 10-19 1 1
##
## $group
## [1] 1
##
## $name_group
## [1] "agegp"
##
## $lst_quali
## [1] "agegp" "alcgp" "tobgp"
##
## $lst_quanti
## [1] "ncases" "ncontrols"
##
## $multiple_var
## [1] TRUE
Contingency table and size effect
The first thing we can do is to create a contingency table between the
explanatory variable and the group variable and then visualize
lines/columns profils. In our case the explanatory variable is “tobgp”
which is the tobacco consumption (gm/day). To do this you can use the
u_desc_profils
#use interact=TRUE to show an interactive graphique with widgets like zoom, comparisons...
ClustersAnalysis::u_desc_profils(u_esoph,3,interact=FALSE)
## [1] "Tableau de contingence : "
##
## 0-9g/day 10-19 20-29 30+
## 25-34 4 4 3 4
## 35-44 4 4 4 3
## 45-54 4 4 4 4
## 55-64 4 4 4 4
## 65-74 4 4 4 3
## 75+ 4 4 1 2
## [1] "Profils lignes : "
##
## 0-9g/day 10-19 20-29 30+ Total
## 25-34 26.7 26.7 20.0 26.7 100.0
## 35-44 26.7 26.7 26.7 20.0 100.0
## 45-54 25.0 25.0 25.0 25.0 100.0
## 55-64 25.0 25.0 25.0 25.0 100.0
## 65-74 26.7 26.7 26.7 20.0 100.0
## 75+ 36.4 36.4 9.1 18.2 100.0
## Ensemble 27.3 27.3 22.7 22.7 100.0
## [1] "Profils colonnes : "
##
## 0-9g/day 10-19 20-29 30+ Ensemble
## 25-34 16.67 16.67 15.00 20.00 17.05
## 35-44 16.67 16.67 20.00 15.00 17.05
## 45-54 16.67 16.67 20.00 20.00 18.18
## 55-64 16.67 16.67 20.00 20.00 18.18
## 65-74 16.67 16.67 20.00 15.00 17.05
## 75+ 16.67 16.67 5.00 10.00 12.50
## Total 100.00 100.00 100.00 100.00 100.00
The
distributions don’t show any particular phenomena. The most represented
classes are the 35-44 and 55-64 years. Then we can see that there are
more than a half that smokes less than 20 g/days. The only fact that we
can see is that the 75+ people are close to 75% to don’t smoke a lot.
Now we are going to see in details if there is a size effect between
these two variables. To do this we can use u_desc_size_effect
which return the test statistic vt (comparison between proportions).
Then we can also use u_plot_size_effect which create a mosaic
plot.
u_desc_size_effect(u_esoph,3)
##
## 0-9g/day 10-19 20-29 30+ Sum
## 25-34 4 4 3 4 15
## 35-44 4 4 4 3 15
## 45-54 4 4 4 4 16
## 55-64 4 4 4 4 16
## 65-74 4 4 4 3 15
## 75+ 4 4 1 2 11
## Sum 24 24 20 20 88
##
## 0-9g/day 10-19 20-29 30+
## 25-34 -0.1291915 -0.1291915 -0.6565969 0.9484178
## 35-44 -0.1291915 -0.1291915 0.9484178 -0.6565969
## 45-54 -0.5038193 -0.5038193 0.5690195 0.5690195
## 55-64 -0.5038193 -0.5038193 0.5690195 0.5690195
## 65-74 -0.1291915 -0.1291915 0.9484178 -0.6565969
## 75+ 1.6158165 1.6158165 -2.7373833 -0.9124611
#use intecract=TRUE to show an interactive graphique with widgets like zoom, comparisons...
u_plot_size_effect(u_esoph,3,interact=FALSE)
## Warning: Ignoring unknown aesthetics: width
If we
refer to the results we can see that the biggest “vt” values are for 75+
peoples who smokes 0-9g/day or 10-19 g/day. So this is for these two
combinations that one can most easily conclude that there is an
over-representation. We can use the mosaic plot to confirm our comment.
You can do the sames analyses for the variable “tobgp”.
Chisq test
We can now use u_chisq_test_all which is use to calculate the
p-avlue for a chisq test between the group variable and each
qualitatives variables.
u_chisq_test_all(u_esoph)
## var.groupement var.explicative p.value.chisq.test interpretation
## 1 agegp alcgp 0.999997088517426 non significatif
## 2 agegp tobgp 0.999902175028874 non significatif
## intensité(v cramer)
## 1 <NA>
## 2 <NA>
Here we can see that the p-avlues are very high which mean that we
accept the null hypothesis and the variables are independant. Because of
this, it’s useless to calculate v-cramer.
If you want to see significant results you can run the code below, the
aim is to predict the sexe according to many qualitatives attributs. We
can see that for each chisq.test, we can conclude that the sex depends
on the attributs. But the attributs which has the most influence is
“qualif”.
#install.packages("questionr")
#library(questionr)
# data(hdv2003)
# d<- hdv2003[,3:8]
# u_chisq_test_all(Univariate_object(d,1))
Correspondence analysis
To better visualize if some groups are close to a particular modality we
can use correspondence analysis. The u_afc_plot function return a
biplot to visualize our results.
u_afc_plot((Univariate_object(esoph,1)),3)
In our case the principal information that we can see is that the 25-34
peoples are quite close to 30+g/day. It’s a new information that we
didn’t have before.
Univariate Analysis for quantitatives variables
Now we are going to use the famous iris dataset. The aim si to
understand how the Species can be described.
#Creation of univariate object with the "Species" as group variable
u_iris <-Univariate_object(iris,5)
Means comparisons (using student test)
To begin we are going to search for each group and each explanatory
variable if the fact to belong to a species or not have an influence on
the length and the width of Petal/Sepal. To do this we use
u_ttest_all, this function for each group, separates the group
variable into two modalities : target modality or others modality. Then
we verify normality hypothesis and if it’s possible we use a student
test to define if it’s significative or not.
u_ttest_all(u_iris)
## Sepal.Length Sepal.Width Petal.Length
## setosa "significatif" "significatif" "significatif"
## versicolor "non significatif" "significatif" "significatif"
## virginica "significatif" "non significatif" "significatif"
## Petal.Width
## setosa "significatif"
## versicolor "non significatif"
## virginica "significatif"
Here we can see that each group have one or many significatives
variables which mean that the fact to belong to setosa,versicolor or
virginica have an influence on the attributs.
Fisher Test on correlation
The aim is to established if there is correlation between group variable
and an other quantitative variable.
u_fisher_test_all(u_iris)
## Eta2 Test_value p_value
## Sepal.Length 0.6187057 119.26450 0
## Sepal.Width 0.4007828 49.16004 0
## Petal.Length 0.9413717 1180.16118 0
## Petal.Width 0.9288829 960.00715 0
Here we can see that each variable has a p-value lower than 0.05 which
mean that there is a link between the group variable and quantitatives
data. Moreover we can see that “eta2” which are the correlation values
are quite high.
Multivariate Analysis
In this section, we characterize the group variable by using several
qualitative or quantitative explanatory variables. If the data contains
categorical variables, we encode it to numbers by using one-hot
encoding. This is an intermediate step of the functions in our package,
therefore our functions can take as input a qualitative data,
quantitative data or mixed data.
To begin we compute the proportion between inter-class inertia and total
inertia. It’s necessary to create an object of multivariate type as
Univariate Analysis part. You can use the constructor
Multivariate_object.
#Creation of multivariate object in case of quantitative data using iris dataframe and
# "Species" (fifth column) as the group variable
m_iris<-multivariate_object(iris,5)
#Creation of multivariate object in case of mixed data using iris dataframe and
# "Type" (second column) as the group variable
m_CO2<-multivariate_object(data.frame(CO2),2)
#detail of attributes associated with the object
#print(m_iris)
#print(m_CO2)
Proportion between inter-class inertia and total inertia (R square)
Starting with the quantitative case in Iris data, we have a high R
square (0.87) which results a clear categorization of three types of the
Iris flower by four explanatory variables.
#quantitative data
m_R2_multivariate(m_iris)
## [1] 0.8689444
Turning to mixed data, we encode qualitative explanatory variables to
numbers by using one-hot encoding. Also, we rescale quantitative
explanatory ones (rescale = TRUE). R square is not high in this case.
#mixed data
m_R2_multivariate(m_CO2, rescale = TRUE)
## [1] 0.125534
Internal measures
Two internal measures are investigated in this section in order to
evaluate the goodness of a clustering structure without respect to
external information including Silhouette index and Davies Boulin index.
Silhouette index
Silhouette coefficient of Iris data is high for all three species
(setorsa, versicolor and virginica), which unifies results of R square
in the previous part. In other words, these four explanatory variables
clearly categorize three types of flowers mentioned above. Moreover,
silhouette coefficient of setosa is extremely higher than that of two
types rest. This results provide that setosa is separated to the rest,
which can be observed by graphic “ACP and Silhouette” representing
individuals in the factorial plan in which different shapes represent
variables groups, at the meanwhile, distinguish colors represent
silhouette coefficients.
m_silhouette_ind(m_iris)
## [1] 0.846469167 0.807398624 0.822366948 0.796876817 0.842846154
## [6] 0.736507297 0.814515322 0.847356179 0.742514780 0.817476712
## [11] 0.794022278 0.828702784 0.802439759 0.737078463 0.689960878
## [16] 0.628999725 0.766148464 0.844448086 0.692395962 0.812505487
## [21] 0.773274497 0.818253227 0.785451525 0.784113653 0.764467842
## [26] 0.789153491 0.825818819 0.834753090 0.836562949 0.809910370
## [31] 0.806887667 0.789361476 0.752791405 0.710627128 0.821092541
## [36] 0.825165104 0.784801580 0.835250278 0.759758982 0.843495197
## [41] 0.843051188 0.625304380 0.778506146 0.791253901 0.734990902
## [46] 0.801610336 0.805121738 0.811665590 0.809962469 0.845574752
## [51] 0.063715563 0.340711283 -0.064281513 0.561473318 0.305000462
## [56] 0.530022415 0.200545585 0.308661268 0.319555176 0.543435800
## [61] 0.406053695 0.550061016 0.537256657 0.385789403 0.571311879
## [66] 0.321608094 0.472621711 0.605407613 0.372686019 0.603296093
## [71] 0.147370132 0.583675548 0.154964703 0.424476170 0.485144208
## [76] 0.371265559 0.103724987 -0.181429615 0.475130100 0.556363272
## [81] 0.583818539 0.574789098 0.617045132 0.012110302 0.452127963
## [86] 0.342655400 0.148502744 0.439260455 0.584909351 0.589378605
## [91] 0.544467525 0.430746508 0.616053311 0.337310169 0.596447444
## [96] 0.586870976 0.596975798 0.536457716 0.196223138 0.612465204
## [101] 0.486842095 0.044986135 0.532358573 0.420690626 0.536542484
## [106] 0.462715960 -0.374840516 0.479717476 0.437605428 0.484479316
## [111] 0.313233908 0.346347201 0.511927944 -0.040778258 0.186761261
## [116] 0.433115124 0.438175908 0.416637998 0.419567558 -0.180048546
## [121] 0.539110752 -0.110879955 0.436867338 -0.010490659 0.526019728
## [126] 0.491425863 -0.127795281 -0.052646866 0.487318513 0.439510070
## [131] 0.479010718 0.399922091 0.492761852 0.006878731 0.193836006
## [136] 0.466476643 0.462003014 0.420618071 -0.171385023 0.482116062
## [141] 0.531199096 0.388712742 0.044986135 0.548803450 0.520693164
## [146] 0.429514550 0.099807524 0.374300521 0.399617217 0.053972269
m_silhouette_plot(m_iris, interact = FALSE)
m_sil_pca_plot(m_iris, interact = FALSE)
In
contrast, Silhouette coefficient of CO2 data is low for the origin of
the plant (Quebec and Mississippi) unifying results of R square above.
m_silhouette_ind(m_CO2,rescale = TRUE)
## [1] -0.159919623 0.066971709 0.146283669 0.184470793 0.154969542
## [6] 0.184290085 0.130544554 -0.181591734 0.002721663 0.172098782
## [11] 0.225199097 0.217370250 0.204897674 0.163850659 -0.160316617
## [16] 0.096165825 0.206199936 0.229594240 0.235183107 0.222602347
## [21] 0.170555900 -0.178507102 -0.043239194 0.084318803 0.161092495
## [26] 0.124293406 0.150166578 0.129226510 -0.214066767 0.016210988
## [31] 0.158493623 0.211020134 0.209711652 0.177363430 0.158317525
## [36] -0.170452547 -0.102886050 0.192413471 0.150254799 0.211555843
## [41] 0.199002673 0.151591438 0.216267449 0.172864134 0.080751622
## [46] 0.010898985 -0.004475726 -0.034332808 -0.071670134 0.209264611
## [51] 0.136795082 -0.006122365 -0.026153013 -0.035538285 -0.007876043
## [56] -0.018762679 0.214833437 0.172732242 0.090197689 0.057550088
## [61] 0.048638632 0.051055364 0.032253641 0.231109208 0.225640474
## [66] 0.207878011 0.208524105 0.200849948 0.145043203 0.101659398
## [71] 0.241968570 0.249421768 0.258063487 0.263358912 0.263849005
## [76] 0.235467591 0.165995611 0.230160459 0.196237304 0.211542206
## [81] 0.221761240 0.221204490 0.190379759 0.122687023
m_silhouette_plot(m_CO2,rescale = TRUE, interact = FALSE)
m_sil_pca_plot(m_CO2, rescale=TRUE,interact = FALSE)
m_sil_pca_plot(m_CO2, rescale=TRUE,interact = FALSE, i=1,j=3)
m_sil_pca_plot(m_CO2, rescale=TRUE,interact = FALSE, i=2,j=3)
Davies Bouldin index
A good Davies Bouldin index is indicated at a low value. Based on the
result analyzing, Davies Bouldin index of Iris data is low for all three
flower species, which is consistent with results mentioned above.
Specifically, Davies Bouldin index of setosa is seriously low, it,
therefore, distinguishes to versicolor and virginica.
m_DB_index(m_iris)
## Indice de Davies Bouldin
## setosa 0.2853079
## versicolor 0.9151115
## virginica 0.9151115
Davies Bouldin index of the origin of the plants (CO2 data) are high
(4.55), therefore, is consistent with results of R square and Silhouette
coefficient.
m_DB_index(m_CO2, rescale = TRUE)
## Indice de Davies Bouldin
## Mississippi 4.546164
## Quebec 4.546164
External measure
Two external measures in this section are investigated in order to
comparing two partitions including Rand index and Ajusted Rand index.
Rand index
We establish an artificial partition from k-mean algorithm and we
compute the Rand index between variables group and artificial partition.
Rand index of Iris data is very high (0.83), hence, this partition and
variables group are similar. Further, Rand index of CO2 data is equal
0.49, thus, Ajusted Rand index is examined.
m_kmean_rand_index(m_iris)
## [1] 0.8322148
m_kmean_rand_index(m_CO2, rescale=TRUE)
## [1] 0.4939759
Ajusted Rand index
Based on the results of Ajusted Rand index of Iris data, we could
strongly confirm that artificial partition and variables group are
strongly similar. Furthermore, Ajusted Rand index of CO2 data is low,
resulting that there is no similar of two partitions.
m_kmean_rand_ajusted(m_iris)
## [1] 0.6201352
m_kmean_rand_ajusted(m_CO2, rescale = TRUE)
## [1] -0.01219512
Comparison between kmean clustering and variable group
This graphic illustrates individuals on the factorial plan in which
different shapes represent variables groups, at the meanwhile,
distinguish colors represent artificial partitions.
m_kmean_clustering_plot(m_iris, interact = FALSE)
m_kmean_clustering_plot(m_iris, interact = FALSE, i=1,j=3)
m_kmean_clustering_plot(m_iris, interact = FALSE,i=2,j=3)
m_kmean_clustering_plot(m_CO2, rescale=TRUE, interact = FALSE)
m_kmean_clustering_plot(m_CO2, rescale=TRUE, interact = FALSE, i=1,j=3)
m_kmean_clustering_plot(m_CO2, rescale=TRUE, interact = FALSE, i=2,j=3)
Test value for clustering
Data analyzing allows us to several conclusions. First, Petal.Length
shows the most effective characterization on Setosa and virginica.
Second, Sepal.Width characterizes most powerful to versicolor.
m_test.value(m_iris)
## setosa pvalue
## Petal.Length -11.263787 1.980605e-29
## Petal.Width -10.831410 2.443627e-27
## Sepal.Length -8.757174 2.002060e-18
## Sepal.Width 7.364799 1.774136e-13
m_test.value(m_iris,i=2)
## versicolor pvalue
## Sepal.Width -5.7090437 1.136127e-08
## Petal.Length 2.4627269 1.378849e-02
## Petal.Width 1.4391384 1.501113e-01
## Sepal.Length 0.9691459 3.324724e-01
m_test.value(m_iris,i=3)
## virginica pvalue
## Petal.Length 8.801060 0.000000e+00
## Petal.Width 9.392272 0.000000e+00
## Sepal.Length 7.788028 6.883383e-15
## Sepal.Width -1.655755 9.777142e-02
Multiple component analysis
This function used to detect and represent underlying structures in a
qualitative data set.
m_acm_plot(multivariate_object(CO2[,1:3],1))
Here we can see that the fours groups are very distinct and if we look
at the data it’s normal. On this dataset this function is a little bit
useless because it return logical facts.
Let’s practice on your own dataset
Now that you have seen how the package works, it is up to you to use it
on your own data. Remember to use the help() function to access all
documentation and **don’t forget to use “interact=TRUE” on the plot to
see interactive plot !
clepadellec/ClustersAnalysis documentation built on Dec. 31, 2020, 10:03 p.m.
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- Introduction
- Import ClustersAnalysis from Github (using devtools)
- Univariate Analysis for qualitatives variariables
- Univariate Analysis for quantitatives variables
- Multivariate Analysis
- Let’s practice on your own dataset
Introduction
This is a demonstration of using the R package ClustersAnalysis. You will see how to analyze classes according to one or more variables. The group variable must be of the type factor or character and the exploratory variables can be quantitative or qualitative. In this demonstration we are going to use natives dataset from R such as “iris”, “infert” or “esoph”.
Short Descriptions of datasets
Iris :
The data set consists of 50 samples from each of three species of Iris (Iris setosa, Iris virginica and Iris versicolor). Four features were measured from each sample: the length and the width of the sepals and petals, in centimeters. Based on the combination of these four features, Fisher developed a linear discriminant model to distinguish the species from each other.
summary(iris)
## Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min. :4.300 Min. :2.000 Min. :1.000 Min. :0.100
## 1st Qu.:5.100 1st Qu.:2.800 1st Qu.:1.600 1st Qu.:0.300
## Median :5.800 Median :3.000 Median :4.350 Median :1.300
## Mean :5.843 Mean :3.057 Mean :3.758 Mean :1.199
## 3rd Qu.:6.400 3rd Qu.:3.300 3rd Qu.:5.100 3rd Qu.:1.800
## Max. :7.900 Max. :4.400 Max. :6.900 Max. :2.500
## Species
## setosa :50
## versicolor:50
## virginica :50
##
##
##
Infert :
This is a matched case-control study dating from before the availability of conditional logistic regression.
summary(infert)
## education age parity induced
## 0-5yrs : 12 Min. :21.00 Min. :1.000 Min. :0.0000
## 6-11yrs:120 1st Qu.:28.00 1st Qu.:1.000 1st Qu.:0.0000
## 12+ yrs:116 Median :31.00 Median :2.000 Median :0.0000
## Mean :31.50 Mean :2.093 Mean :0.5726
## 3rd Qu.:35.25 3rd Qu.:3.000 3rd Qu.:1.0000
## Max. :44.00 Max. :6.000 Max. :2.0000
## case spontaneous stratum pooled.stratum
## Min. :0.0000 Min. :0.0000 Min. : 1.00 Min. : 1.00
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:21.00 1st Qu.:19.00
## Median :0.0000 Median :0.0000 Median :42.00 Median :36.00
## Mean :0.3347 Mean :0.5766 Mean :41.87 Mean :33.58
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:62.25 3rd Qu.:48.25
## Max. :1.0000 Max. :2.0000 Max. :83.00 Max. :63.00
Esoph :
Data from a case-control study of (o)esophageal cancer in Ille-et-Vilaine, France. This is a data frame with records for 88 age/alcohol/tobacco combinations.
summary(esoph)
## agegp alcgp tobgp ncases ncontrols
## 25-34:15 0-39g/day:23 0-9g/day:24 Min. : 0.000 Min. : 1.00
## 35-44:15 40-79 :23 10-19 :24 1st Qu.: 0.000 1st Qu.: 3.00
## 45-54:16 80-119 :21 20-29 :20 Median : 1.000 Median : 6.00
## 55-64:16 120+ :21 30+ :20 Mean : 2.273 Mean :11.08
## 65-74:15 3rd Qu.: 4.000 3rd Qu.:14.00
## 75+ :11 Max. :17.000 Max. :60.00
CO2 :
The CO2 data frame has 84 rows and 5 columns of data from an experiment on the cold tolerance of the grass species Echinochloa crus-galli.
summary(CO2)
## Plant Type Treatment conc uptake
## Qn1 : 7 Quebec :42 nonchilled:42 Min. : 95 Min. : 7.70
## Qn2 : 7 Mississippi:42 chilled :42 1st Qu.: 175 1st Qu.:17.90
## Qn3 : 7 Median : 350 Median :28.30
## Qc1 : 7 Mean : 435 Mean :27.21
## Qc3 : 7 3rd Qu.: 675 3rd Qu.:37.12
## Qc2 : 7 Max. :1000 Max. :45.50
## (Other):42
Import ClustersAnalysis from Github (using devtools)
Please download the latest R version (>4.0) before running the code below.
#Use the below line to install devtools if necessary
#install.packages("devtools")
#library(devtools)
#install package from github or download the folder and open it with R
#Use the below line to install ClustersAnalysis if necessary
#devtools::install_github("clepadellec/ClustersAnalysis")
#load package
library(ClustersAnalysis)
How to access to help
You can juste use the fonction help(function name) to see all the documentation about your function.
help("u_plot_size_effect")
Univariate Analysis for qualitatives variariables
To begin we will try to understand, for each qualitative explanatory variable, if it affects the group variable. It’s necessary to create an object of univariate type. You can use the constructor Univariate_object.
#Creation of univariate object using esoph dataframe and "agegp" (first column) as the group variable
u_esoph<-Univariate_object(esoph,1)
#detail of attributes associated with the object
print(u_esoph)
## $ind.qual
## agegp alcgp tobgp ncases ncontrols
## TRUE TRUE TRUE FALSE FALSE
##
## $ind.quan
## agegp alcgp tobgp ncases ncontrols
## FALSE FALSE FALSE TRUE TRUE
##
## $df
## agegp alcgp tobgp ncases ncontrols
## 1 25-34 0-39g/day 0-9g/day 0 40
## 2 25-34 0-39g/day 10-19 0 10
## 3 25-34 0-39g/day 20-29 0 6
## 4 25-34 0-39g/day 30+ 0 5
## 5 25-34 40-79 0-9g/day 0 27
## 6 25-34 40-79 10-19 0 7
## 7 25-34 40-79 20-29 0 4
## 8 25-34 40-79 30+ 0 7
## 9 25-34 80-119 0-9g/day 0 2
## 10 25-34 80-119 10-19 0 1
## 11 25-34 80-119 30+ 0 2
## 12 25-34 120+ 0-9g/day 0 1
## 13 25-34 120+ 10-19 1 1
## 14 25-34 120+ 20-29 0 1
## 15 25-34 120+ 30+ 0 2
## 16 35-44 0-39g/day 0-9g/day 0 60
## 17 35-44 0-39g/day 10-19 1 14
## 18 35-44 0-39g/day 20-29 0 7
## 19 35-44 0-39g/day 30+ 0 8
## 20 35-44 40-79 0-9g/day 0 35
## 21 35-44 40-79 10-19 3 23
## 22 35-44 40-79 20-29 1 14
## 23 35-44 40-79 30+ 0 8
## 24 35-44 80-119 0-9g/day 0 11
## 25 35-44 80-119 10-19 0 6
## 26 35-44 80-119 20-29 0 2
## 27 35-44 80-119 30+ 0 1
## 28 35-44 120+ 0-9g/day 2 3
## 29 35-44 120+ 10-19 0 3
## 30 35-44 120+ 20-29 2 4
## 31 45-54 0-39g/day 0-9g/day 1 46
## 32 45-54 0-39g/day 10-19 0 18
## 33 45-54 0-39g/day 20-29 0 10
## 34 45-54 0-39g/day 30+ 0 4
## 35 45-54 40-79 0-9g/day 6 38
## 36 45-54 40-79 10-19 4 21
## 37 45-54 40-79 20-29 5 15
## 38 45-54 40-79 30+ 5 7
## 39 45-54 80-119 0-9g/day 3 16
## 40 45-54 80-119 10-19 6 14
## 41 45-54 80-119 20-29 1 5
## 42 45-54 80-119 30+ 2 4
## 43 45-54 120+ 0-9g/day 4 4
## 44 45-54 120+ 10-19 3 4
## 45 45-54 120+ 20-29 2 3
## 46 45-54 120+ 30+ 4 4
## 47 55-64 0-39g/day 0-9g/day 2 49
## 48 55-64 0-39g/day 10-19 3 22
## 49 55-64 0-39g/day 20-29 3 12
## 50 55-64 0-39g/day 30+ 4 6
## 51 55-64 40-79 0-9g/day 9 40
## 52 55-64 40-79 10-19 6 21
## 53 55-64 40-79 20-29 4 17
## 54 55-64 40-79 30+ 3 6
## 55 55-64 80-119 0-9g/day 9 18
## 56 55-64 80-119 10-19 8 15
## 57 55-64 80-119 20-29 3 6
## 58 55-64 80-119 30+ 4 4
## 59 55-64 120+ 0-9g/day 5 10
## 60 55-64 120+ 10-19 6 7
## 61 55-64 120+ 20-29 2 3
## 62 55-64 120+ 30+ 5 6
## 63 65-74 0-39g/day 0-9g/day 5 48
## 64 65-74 0-39g/day 10-19 4 14
## 65 65-74 0-39g/day 20-29 2 7
## 66 65-74 0-39g/day 30+ 0 2
## 67 65-74 40-79 0-9g/day 17 34
## 68 65-74 40-79 10-19 3 10
## 69 65-74 40-79 20-29 5 9
## 70 65-74 80-119 0-9g/day 6 13
## 71 65-74 80-119 10-19 4 12
## 72 65-74 80-119 20-29 2 3
## 73 65-74 80-119 30+ 1 1
## 74 65-74 120+ 0-9g/day 3 4
## 75 65-74 120+ 10-19 1 2
## 76 65-74 120+ 20-29 1 1
## 77 65-74 120+ 30+ 1 1
## 78 75+ 0-39g/day 0-9g/day 1 18
## 79 75+ 0-39g/day 10-19 2 6
## 80 75+ 0-39g/day 30+ 1 3
## 81 75+ 40-79 0-9g/day 2 5
## 82 75+ 40-79 10-19 1 3
## 83 75+ 40-79 20-29 0 3
## 84 75+ 40-79 30+ 1 1
## 85 75+ 80-119 0-9g/day 1 1
## 86 75+ 80-119 10-19 1 1
## 87 75+ 120+ 0-9g/day 2 2
## 88 75+ 120+ 10-19 1 1
##
## $group
## [1] 1
##
## $name_group
## [1] "agegp"
##
## $lst_quali
## [1] "agegp" "alcgp" "tobgp"
##
## $lst_quanti
## [1] "ncases" "ncontrols"
##
## $multiple_var
## [1] TRUE
Contingency table and size effect
The first thing we can do is to create a contingency table between the explanatory variable and the group variable and then visualize lines/columns profils. In our case the explanatory variable is “tobgp” which is the tobacco consumption (gm/day). To do this you can use the u_desc_profils
#use interact=TRUE to show an interactive graphique with widgets like zoom, comparisons...
ClustersAnalysis::u_desc_profils(u_esoph,3,interact=FALSE)
## [1] "Tableau de contingence : "
##
## 0-9g/day 10-19 20-29 30+
## 25-34 4 4 3 4
## 35-44 4 4 4 3
## 45-54 4 4 4 4
## 55-64 4 4 4 4
## 65-74 4 4 4 3
## 75+ 4 4 1 2
## [1] "Profils lignes : "
##
## 0-9g/day 10-19 20-29 30+ Total
## 25-34 26.7 26.7 20.0 26.7 100.0
## 35-44 26.7 26.7 26.7 20.0 100.0
## 45-54 25.0 25.0 25.0 25.0 100.0
## 55-64 25.0 25.0 25.0 25.0 100.0
## 65-74 26.7 26.7 26.7 20.0 100.0
## 75+ 36.4 36.4 9.1 18.2 100.0
## Ensemble 27.3 27.3 22.7 22.7 100.0
## [1] "Profils colonnes : "
##
## 0-9g/day 10-19 20-29 30+ Ensemble
## 25-34 16.67 16.67 15.00 20.00 17.05
## 35-44 16.67 16.67 20.00 15.00 17.05
## 45-54 16.67 16.67 20.00 20.00 18.18
## 55-64 16.67 16.67 20.00 20.00 18.18
## 65-74 16.67 16.67 20.00 15.00 17.05
## 75+ 16.67 16.67 5.00 10.00 12.50
## Total 100.00 100.00 100.00 100.00 100.00
The
distributions don’t show any particular phenomena. The most represented
classes are the 35-44 and 55-64 years. Then we can see that there are
more than a half that smokes less than 20 g/days. The only fact that we
can see is that the 75+ people are close to 75% to don’t smoke a lot.
Now we are going to see in details if there is a size effect between these two variables. To do this we can use u_desc_size_effect which return the test statistic vt (comparison between proportions). Then we can also use u_plot_size_effect which create a mosaic plot.
u_desc_size_effect(u_esoph,3)
##
## 0-9g/day 10-19 20-29 30+ Sum
## 25-34 4 4 3 4 15
## 35-44 4 4 4 3 15
## 45-54 4 4 4 4 16
## 55-64 4 4 4 4 16
## 65-74 4 4 4 3 15
## 75+ 4 4 1 2 11
## Sum 24 24 20 20 88
##
## 0-9g/day 10-19 20-29 30+
## 25-34 -0.1291915 -0.1291915 -0.6565969 0.9484178
## 35-44 -0.1291915 -0.1291915 0.9484178 -0.6565969
## 45-54 -0.5038193 -0.5038193 0.5690195 0.5690195
## 55-64 -0.5038193 -0.5038193 0.5690195 0.5690195
## 65-74 -0.1291915 -0.1291915 0.9484178 -0.6565969
## 75+ 1.6158165 1.6158165 -2.7373833 -0.9124611
#use intecract=TRUE to show an interactive graphique with widgets like zoom, comparisons...
u_plot_size_effect(u_esoph,3,interact=FALSE)
## Warning: Ignoring unknown aesthetics: width
If we
refer to the results we can see that the biggest “vt” values are for 75+
peoples who smokes 0-9g/day or 10-19 g/day. So this is for these two
combinations that one can most easily conclude that there is an
over-representation. We can use the mosaic plot to confirm our comment.
You can do the sames analyses for the variable “tobgp”.
Chisq test
We can now use u_chisq_test_all which is use to calculate the p-avlue for a chisq test between the group variable and each qualitatives variables.
u_chisq_test_all(u_esoph)
## var.groupement var.explicative p.value.chisq.test interpretation
## 1 agegp alcgp 0.999997088517426 non significatif
## 2 agegp tobgp 0.999902175028874 non significatif
## intensité(v cramer)
## 1 <NA>
## 2 <NA>
Here we can see that the p-avlues are very high which mean that we accept the null hypothesis and the variables are independant. Because of this, it’s useless to calculate v-cramer.
If you want to see significant results you can run the code below, the aim is to predict the sexe according to many qualitatives attributs. We can see that for each chisq.test, we can conclude that the sex depends on the attributs. But the attributs which has the most influence is “qualif”.
#install.packages("questionr")
#library(questionr)
# data(hdv2003)
# d<- hdv2003[,3:8]
# u_chisq_test_all(Univariate_object(d,1))
Correspondence analysis
To better visualize if some groups are close to a particular modality we can use correspondence analysis. The u_afc_plot function return a biplot to visualize our results.
u_afc_plot((Univariate_object(esoph,1)),3)
In our case the principal information that we can see is that the 25-34 peoples are quite close to 30+g/day. It’s a new information that we didn’t have before.
Univariate Analysis for quantitatives variables
Now we are going to use the famous iris dataset. The aim si to understand how the Species can be described.
#Creation of univariate object with the "Species" as group variable
u_iris <-Univariate_object(iris,5)
Means comparisons (using student test)
To begin we are going to search for each group and each explanatory variable if the fact to belong to a species or not have an influence on the length and the width of Petal/Sepal. To do this we use u_ttest_all, this function for each group, separates the group variable into two modalities : target modality or others modality. Then we verify normality hypothesis and if it’s possible we use a student test to define if it’s significative or not.
u_ttest_all(u_iris)
## Sepal.Length Sepal.Width Petal.Length
## setosa "significatif" "significatif" "significatif"
## versicolor "non significatif" "significatif" "significatif"
## virginica "significatif" "non significatif" "significatif"
## Petal.Width
## setosa "significatif"
## versicolor "non significatif"
## virginica "significatif"
Here we can see that each group have one or many significatives variables which mean that the fact to belong to setosa,versicolor or virginica have an influence on the attributs.
Fisher Test on correlation
The aim is to established if there is correlation between group variable and an other quantitative variable.
u_fisher_test_all(u_iris)
## Eta2 Test_value p_value
## Sepal.Length 0.6187057 119.26450 0
## Sepal.Width 0.4007828 49.16004 0
## Petal.Length 0.9413717 1180.16118 0
## Petal.Width 0.9288829 960.00715 0
Here we can see that each variable has a p-value lower than 0.05 which mean that there is a link between the group variable and quantitatives data. Moreover we can see that “eta2” which are the correlation values are quite high.
Multivariate Analysis
In this section, we characterize the group variable by using several qualitative or quantitative explanatory variables. If the data contains categorical variables, we encode it to numbers by using one-hot encoding. This is an intermediate step of the functions in our package, therefore our functions can take as input a qualitative data, quantitative data or mixed data.
To begin we compute the proportion between inter-class inertia and total inertia. It’s necessary to create an object of multivariate type as Univariate Analysis part. You can use the constructor Multivariate_object.
#Creation of multivariate object in case of quantitative data using iris dataframe and
# "Species" (fifth column) as the group variable
m_iris<-multivariate_object(iris,5)
#Creation of multivariate object in case of mixed data using iris dataframe and
# "Type" (second column) as the group variable
m_CO2<-multivariate_object(data.frame(CO2),2)
#detail of attributes associated with the object
#print(m_iris)
#print(m_CO2)
Proportion between inter-class inertia and total inertia (R square)
Starting with the quantitative case in Iris data, we have a high R square (0.87) which results a clear categorization of three types of the Iris flower by four explanatory variables.
#quantitative data
m_R2_multivariate(m_iris)
## [1] 0.8689444
Turning to mixed data, we encode qualitative explanatory variables to numbers by using one-hot encoding. Also, we rescale quantitative explanatory ones (rescale = TRUE). R square is not high in this case.
#mixed data
m_R2_multivariate(m_CO2, rescale = TRUE)
## [1] 0.125534
Internal measures
Two internal measures are investigated in this section in order to evaluate the goodness of a clustering structure without respect to external information including Silhouette index and Davies Boulin index.
Silhouette index
Silhouette coefficient of Iris data is high for all three species (setorsa, versicolor and virginica), which unifies results of R square in the previous part. In other words, these four explanatory variables clearly categorize three types of flowers mentioned above. Moreover, silhouette coefficient of setosa is extremely higher than that of two types rest. This results provide that setosa is separated to the rest, which can be observed by graphic “ACP and Silhouette” representing individuals in the factorial plan in which different shapes represent variables groups, at the meanwhile, distinguish colors represent silhouette coefficients.
m_silhouette_ind(m_iris)
## [1] 0.846469167 0.807398624 0.822366948 0.796876817 0.842846154
## [6] 0.736507297 0.814515322 0.847356179 0.742514780 0.817476712
## [11] 0.794022278 0.828702784 0.802439759 0.737078463 0.689960878
## [16] 0.628999725 0.766148464 0.844448086 0.692395962 0.812505487
## [21] 0.773274497 0.818253227 0.785451525 0.784113653 0.764467842
## [26] 0.789153491 0.825818819 0.834753090 0.836562949 0.809910370
## [31] 0.806887667 0.789361476 0.752791405 0.710627128 0.821092541
## [36] 0.825165104 0.784801580 0.835250278 0.759758982 0.843495197
## [41] 0.843051188 0.625304380 0.778506146 0.791253901 0.734990902
## [46] 0.801610336 0.805121738 0.811665590 0.809962469 0.845574752
## [51] 0.063715563 0.340711283 -0.064281513 0.561473318 0.305000462
## [56] 0.530022415 0.200545585 0.308661268 0.319555176 0.543435800
## [61] 0.406053695 0.550061016 0.537256657 0.385789403 0.571311879
## [66] 0.321608094 0.472621711 0.605407613 0.372686019 0.603296093
## [71] 0.147370132 0.583675548 0.154964703 0.424476170 0.485144208
## [76] 0.371265559 0.103724987 -0.181429615 0.475130100 0.556363272
## [81] 0.583818539 0.574789098 0.617045132 0.012110302 0.452127963
## [86] 0.342655400 0.148502744 0.439260455 0.584909351 0.589378605
## [91] 0.544467525 0.430746508 0.616053311 0.337310169 0.596447444
## [96] 0.586870976 0.596975798 0.536457716 0.196223138 0.612465204
## [101] 0.486842095 0.044986135 0.532358573 0.420690626 0.536542484
## [106] 0.462715960 -0.374840516 0.479717476 0.437605428 0.484479316
## [111] 0.313233908 0.346347201 0.511927944 -0.040778258 0.186761261
## [116] 0.433115124 0.438175908 0.416637998 0.419567558 -0.180048546
## [121] 0.539110752 -0.110879955 0.436867338 -0.010490659 0.526019728
## [126] 0.491425863 -0.127795281 -0.052646866 0.487318513 0.439510070
## [131] 0.479010718 0.399922091 0.492761852 0.006878731 0.193836006
## [136] 0.466476643 0.462003014 0.420618071 -0.171385023 0.482116062
## [141] 0.531199096 0.388712742 0.044986135 0.548803450 0.520693164
## [146] 0.429514550 0.099807524 0.374300521 0.399617217 0.053972269
m_silhouette_plot(m_iris, interact = FALSE)
m_sil_pca_plot(m_iris, interact = FALSE)
In
contrast, Silhouette coefficient of CO2 data is low for the origin of
the plant (Quebec and Mississippi) unifying results of R square above.
m_silhouette_ind(m_CO2,rescale = TRUE)
## [1] -0.159919623 0.066971709 0.146283669 0.184470793 0.154969542
## [6] 0.184290085 0.130544554 -0.181591734 0.002721663 0.172098782
## [11] 0.225199097 0.217370250 0.204897674 0.163850659 -0.160316617
## [16] 0.096165825 0.206199936 0.229594240 0.235183107 0.222602347
## [21] 0.170555900 -0.178507102 -0.043239194 0.084318803 0.161092495
## [26] 0.124293406 0.150166578 0.129226510 -0.214066767 0.016210988
## [31] 0.158493623 0.211020134 0.209711652 0.177363430 0.158317525
## [36] -0.170452547 -0.102886050 0.192413471 0.150254799 0.211555843
## [41] 0.199002673 0.151591438 0.216267449 0.172864134 0.080751622
## [46] 0.010898985 -0.004475726 -0.034332808 -0.071670134 0.209264611
## [51] 0.136795082 -0.006122365 -0.026153013 -0.035538285 -0.007876043
## [56] -0.018762679 0.214833437 0.172732242 0.090197689 0.057550088
## [61] 0.048638632 0.051055364 0.032253641 0.231109208 0.225640474
## [66] 0.207878011 0.208524105 0.200849948 0.145043203 0.101659398
## [71] 0.241968570 0.249421768 0.258063487 0.263358912 0.263849005
## [76] 0.235467591 0.165995611 0.230160459 0.196237304 0.211542206
## [81] 0.221761240 0.221204490 0.190379759 0.122687023
m_silhouette_plot(m_CO2,rescale = TRUE, interact = FALSE)
m_sil_pca_plot(m_CO2, rescale=TRUE,interact = FALSE)
m_sil_pca_plot(m_CO2, rescale=TRUE,interact = FALSE, i=1,j=3)
m_sil_pca_plot(m_CO2, rescale=TRUE,interact = FALSE, i=2,j=3)
Davies Bouldin index
A good Davies Bouldin index is indicated at a low value. Based on the result analyzing, Davies Bouldin index of Iris data is low for all three flower species, which is consistent with results mentioned above. Specifically, Davies Bouldin index of setosa is seriously low, it, therefore, distinguishes to versicolor and virginica.
m_DB_index(m_iris)
## Indice de Davies Bouldin
## setosa 0.2853079
## versicolor 0.9151115
## virginica 0.9151115
Davies Bouldin index of the origin of the plants (CO2 data) are high (4.55), therefore, is consistent with results of R square and Silhouette coefficient.
m_DB_index(m_CO2, rescale = TRUE)
## Indice de Davies Bouldin
## Mississippi 4.546164
## Quebec 4.546164
External measure
Two external measures in this section are investigated in order to comparing two partitions including Rand index and Ajusted Rand index.
Rand index
We establish an artificial partition from k-mean algorithm and we compute the Rand index between variables group and artificial partition. Rand index of Iris data is very high (0.83), hence, this partition and variables group are similar. Further, Rand index of CO2 data is equal 0.49, thus, Ajusted Rand index is examined.
m_kmean_rand_index(m_iris)
## [1] 0.8322148
m_kmean_rand_index(m_CO2, rescale=TRUE)
## [1] 0.4939759
Ajusted Rand index
Based on the results of Ajusted Rand index of Iris data, we could strongly confirm that artificial partition and variables group are strongly similar. Furthermore, Ajusted Rand index of CO2 data is low, resulting that there is no similar of two partitions.
m_kmean_rand_ajusted(m_iris)
## [1] 0.6201352
m_kmean_rand_ajusted(m_CO2, rescale = TRUE)
## [1] -0.01219512
Comparison between kmean clustering and variable group
This graphic illustrates individuals on the factorial plan in which different shapes represent variables groups, at the meanwhile, distinguish colors represent artificial partitions.
m_kmean_clustering_plot(m_iris, interact = FALSE)
m_kmean_clustering_plot(m_iris, interact = FALSE, i=1,j=3)
m_kmean_clustering_plot(m_iris, interact = FALSE,i=2,j=3)
m_kmean_clustering_plot(m_CO2, rescale=TRUE, interact = FALSE)
m_kmean_clustering_plot(m_CO2, rescale=TRUE, interact = FALSE, i=1,j=3)
m_kmean_clustering_plot(m_CO2, rescale=TRUE, interact = FALSE, i=2,j=3)
Test value for clustering
Data analyzing allows us to several conclusions. First, Petal.Length shows the most effective characterization on Setosa and virginica. Second, Sepal.Width characterizes most powerful to versicolor.
m_test.value(m_iris)
## setosa pvalue
## Petal.Length -11.263787 1.980605e-29
## Petal.Width -10.831410 2.443627e-27
## Sepal.Length -8.757174 2.002060e-18
## Sepal.Width 7.364799 1.774136e-13
m_test.value(m_iris,i=2)
## versicolor pvalue
## Sepal.Width -5.7090437 1.136127e-08
## Petal.Length 2.4627269 1.378849e-02
## Petal.Width 1.4391384 1.501113e-01
## Sepal.Length 0.9691459 3.324724e-01
m_test.value(m_iris,i=3)
## virginica pvalue
## Petal.Length 8.801060 0.000000e+00
## Petal.Width 9.392272 0.000000e+00
## Sepal.Length 7.788028 6.883383e-15
## Sepal.Width -1.655755 9.777142e-02
Multiple component analysis
This function used to detect and represent underlying structures in a qualitative data set.
m_acm_plot(multivariate_object(CO2[,1:3],1))
Here we can see that the fours groups are very distinct and if we look at the data it’s normal. On this dataset this function is a little bit useless because it return logical facts.
Let’s practice on your own dataset
Now that you have seen how the package works, it is up to you to use it on your own data. Remember to use the help() function to access all documentation and **don’t forget to use “interact=TRUE” on the plot to see interactive plot !
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