From 22a7b9d9670ec176fb2f1022a62e82510b222cb3 Mon Sep 17 00:00:00 2001 From: jibidar Date: Wed, 15 Jan 2025 16:57:58 +0100 Subject: [PATCH] le feur --- Projet.Rmd | 332 ++++++++++++++++++------ Projet.log | 724 +++++++++++++++++++++++++++++++++++++++++++++++++++++ Projet.pdf | Bin 628520 -> 635558 bytes 3 files changed, 973 insertions(+), 83 deletions(-) create mode 100644 Projet.log diff --git a/Projet.Rmd b/Projet.Rmd index 9824b2b..95c0a1f 100644 --- a/Projet.Rmd +++ b/Projet.Rmd @@ -1,9 +1,17 @@ --- title: "Projet" output: - pdf_document: default - html_document: default + pdf_document : + toc : TRUE + toc_depth : 2 + number_section : TRUE +header-includes: + - \usepackage{dsfont} + - \usepackage{color} + - \newcommand{\1}{\mathds{1}} +--- date: "2024-12-04" + --- ```{r setup, include=FALSE} @@ -42,12 +50,10 @@ levels(T$ExpT1) -# Contenu du jeu de données : -- 3 variables qualitatives nominales représentant l'expression du gêne $$g$$ dont les modalités sont $$\{"sur","sous","non"\}$$. chaque variable correspond respectivement à la différence d'expression du gêne mesurée à la 6ème heure lors du traitement $$T \in \{T1,T2,T3\}$$ en moyenne, sur les réplicats $$\{R1,R2\}$$ +# Contenu du jeu de données : +$$\text{3 variables qualitatives nominales représentant l'expression du gêne } g \text{ dont les modalités sont } \{"sur","sous","non"\}. \\ \text{ Chaque variable correspond respectivement à la différence d'expression du gêne mesurée à la 6ème heure lors du traitement }\\ T \in \{T1,T2,T3\} \text{ en moyenne, sur les réplicats } \{R1,R2\}$$ -- $$3*6 + 3*6 = 36$$ variables quantitatives continues représentant les effets des traitements sur l'expression des gênes T1 T2 et T3 à 1h,2h,3h,4h,5h,6h après l'administration pour les replicats R1 et R2, par rapport à leur expression à T=0 ( sans traitement). - -- Ce jeu de données contient des relevés sur 542 individus, ici des gênes. +$$3\times6 + 3\times6 = 36 \text{ variables quantitatives continues représentant les effets des traitements sur l'expression des gênes T1 T2 et T3 à 1h,2h,3h,4h,5h,6h}\\ \text{après l'administration pour les replicats } \{R1,R2\} \text{, par rapport à leur expression à T=0 ( sans traitement).} \\ \text{Ce jeu de données contient des relevés sur 542 individus, ici des gênes.}$$ # Analyse unidimentionnelle : @@ -56,25 +62,28 @@ levels(T$ExpT1) Nous avons réalisé 3 histogrammes pour visualiser les effectifs des gènes en fonction de leur expression relative moyenne à 6h suite aux traitements T1,T2 et T3, cette moyenne est représenté par les variables qualitatives nominales ExpT1,ExpT2 et ExpT3 -```{r,fig.height=3,warning=FALSE,fig.cap="Visualualisation des expressions relative des gènes lors du traitement T1,T2 et T3"} +```{r,fig.height=3,warning=FALSE,fig.cap="\\label{fig:histo1}Visualualisation des expressions relative des gènes lors du traitement T1,T2 et T3"} g1<-ggplot(T, aes(x=T$ExpT1))+ geom_bar()+ - ylab("Effectifs")+ggtitle("Effectifs") + ylab("Effectifs") g2<-ggplot(T, aes(x=T$ExpT2))+ geom_bar()+ - ylab("Effectifs")+ggtitle("Effectifs") + ylab("Effectifs") g3<-ggplot(T, aes(x=T$ExpT3))+ geom_bar()+ - ylab("Effectifs")+ggtitle("Effectifs") + ylab("Effectifs") grid.arrange(g1,g2,g3,ncol=3) ``` +\vspace{1cm} + + ### Analyse des résultats -On remarque que les traitements T2 et T3 semblent avoir un effet assez similaire sur l'expression des gênes relevée à la 6ème heure : Une polarisation entre la sous expression et la sur expression qui se partagent presque la totalité des relevés, avec un poids légèrement superieur à 55% pour la sur-expression au détriment de la sous-expression. Cela a peut être un rapport avec le fait que T3 est une combinaison des traitement T1 et T2. +Sur la Figure \ref{fig:histo1} on remarque que les traitements T2 et T3 semblent avoir un effet assez similaire sur l'expression des gênes relevée à la 6ème heure : Une polarisation entre la sous expression et la sur expression qui se partagent presque la totalité des relevés, avec un poids légèrement superieur à 55% pour la sur-expression au détriment de la sous-expression. Cela a peut être un rapport avec le fait que T3 est une combinaison des traitement T1 et T2. T1 quant à lui se démarque grandement par une large majorité (Un peu plus de 80%), de gêne n'ayant pas changé d'expression après 6h de traitement. @@ -105,19 +114,26 @@ ggplot(T_long, aes(x = value)) + facet_wrap(~variable,scales = "free",ncol=6) + labs(title = "Histogrammes de l'expression relative des gènes aux différents relevés lors du traitement T3", x = "Valeurs", y = "Effectifs") ``` -Lors d'une analyse supplémentaire des fréquences d'expression des gènes à chaque heure et chaque traitement, nous observons bien une concordance avec l'analyse des expressions des gênes figure . En effet, les histogrammes en rapport avec le traitement 1 sont très nettement regroupés vers 0, soit une expression relative des gênes qui ne change peu. Les histogrammes pour les relevés des variables en lien avec T2 et T3 sont tout aussi similaires aux résultats précédents : La variance de l'expression relative des gênes est plus élevée et on observe bien une polarisation "sous-exprimé-"sur-exprimé" sur les relevés à 6h. Attention, ici on observe aussi que T2 et T3 n'ont pas leur effet caractéristique directement : à 2h, la distribution de l'expression des genes semble presque Gaussienne, et à 1h elle ne se distingue pas beaucoup du traitement 1 avec un regroupement sur 0. + + + +\vspace{1cm} + +Lors d'une analyse supplémentaire des fréquences d'expression des gènes à chaque heure et chaque traitement, nous observons bien une concordance avec l'analyse des expressions des gênes Figure \ref{fig:histo1}. En effet, les histogrammes en rapport avec le traitement 1 sont très nettement regroupés vers 0, soit une expression relative des gênes qui ne change peu. Les histogrammes pour les relevés des variables en lien avec T2 et T3 sont tout aussi similaires aux résultats précédents : La variance de l'expression relative des gênes est plus élevée et on observe bien une polarisation "sous-exprimé-"sur-exprimé" sur les relevés à 6h. Attention, ici on observe aussi que T2 et T3 n'ont pas leur effet caractéristique directement : à 2h, la distribution de l'expression des genes semble presque Gaussienne, et à 1h elle ne se distingue pas beaucoup du traitement 1 avec un regroupement sur 0. c.f le document RMarkdown pour les histogrammes. ## Boxplots des différentes variables quantitatives du jeu de données -```{r,fig.height=4,message=FALSE,warning=FALSE,fig.cap="Boxplots des différentes variables du jeu de données lors du réplicat R1"} +```{r,fig.height=4,message=FALSE,warning=FALSE,fig.cap="\\label{fig:boxplot1}Boxplots des différentes variables du jeu de données lors du réplicat R1"} ggplot(melt(T[1:18]),aes(x=variable,y=value))+ geom_boxplot()+ theme(axis.text.x = element_text(angle=90, vjust = 0.5, hjust = 1)) ``` -Nous avons choisi de n'inclure que le graphe portant sur le réplicat R1 car il est porteur des mêmes informations que celui sur le réplicat R2. +\vspace{1cm} + +Sur la figure \ref{fig:boxplot1} nous avons choisi de n'inclure que le graphe portant sur le réplicat R1 car il est porteur des mêmes informations que celui sur le réplicat R2. L'analyse des boxplots montre que, même sans effectuer de réduction des données, chaque variable présente une dispersion similaire, ce qui suggère qu'il n'est pas nécessaire de procéder à un centrage et à une réduction avant de réaliser l'Analyse en Composantes Principales. # Analyse bi-dimensionnelle @@ -128,7 +144,7 @@ Nous avons ensuite générés des graphes contenants des boxplots d'expression d Cela nous a permis d'identifier les changements d'expressions de chaque groupes de gènes sur, sous ou non-exprimés entre un traitement et les deux autres. Les deux réplicats ayant des résultats très similaires, pour ne pas surcharger le rapport nous avons décidé d'afficher seulement le réplicat R1. -```{r,fig.cap="Boxplots par paire de variables (qualitative,quantitative)" ,warning=FALSE} +```{r,fig.cap="\\label{fig:boxplot2}Boxplots par paire de variables (qualitative,quantitative)" ,warning=FALSE} # traitement 1 corrélation avec l'expression des genes du T1 T2 et T3 @@ -166,7 +182,12 @@ grid.arrange(p1, p3, p6, p2, p4, p5, ncol = 3) ``` +\vspace{1cm} + ### Analyse des boxplots : +Nous allons analyser les boxplots obtenus à la Figure \ref{fig:boxplot2} + + #### Traitement 1 Les genes sur-exprimés au T1 sont non-exprimé durant le T2 et T3 (Boxplots T1/ExpT2 et T1/ExpT3) . Il est difficile d'observer une catégorie de genes de T1 qui se soient sous exprimés ou sur exprimés dans T2 et T3, ceux qui n'avaient pas changés d'expression relative durant T1, se sont soit sous exprimé soit sur exprimé (Boxplots T1/ExpT2 et T1/ExpT3). @@ -179,20 +200,22 @@ On observe une légère tendance des genes s'étant sous-exprimé avec T1 à se Nous avons généré la matrice de covariance de nos données sans les variables quantitatives. Suite à cela nous avons remarqué qu'il était inutile d'afficher le réplicat R2 dans la matrice et que cela rendait le graphe moins lisible. Nous avons donc décidé de seulement afficher le graphe de la matrice de covariance avec le réplicat R1. -```{r, fig.height = 4,fig.cap="Visualisation de la matrice de covariance des variables quantitatives sur le replicat R1"} +```{r, fig.height = 4,fig.cap="\\label{fig:covplot1}Visualisation de la matrice de covariance des variables quantitatives sur le replicat R1"} cr = cor(T[c(1:18)]) corrplot(cr,method="ellipse", type="lower", bg = "lightgrey") ``` +\vspace{1cm} + ### analyse de la matrice de covariance -On observe clairement de grandes zones de de corrélation entre T2 et T3 délimitées par une correlation plus moyenne à la première heure des deux traitements sûrement dues au fait que T3 est influencé par T1 aux premières heures. +Sur la Figure \ref{fig:covplot1} on observe clairement de grandes zones de de corrélation entre T2 et T3 délimitées par une correlation plus moyenne à la première heure des deux traitements sûrement dues au fait que T3 est influencé par T1 aux premières heures. On remarque que T3 est plus fortement corrélé à T1 à 1H que T2 (qui ne l'est que légèrement), semblant indiquer que T1 s'exprime avant T2; T3 étant la combinaison des deux traitements. ## Rapport de correlation Eta2 -```{r} +```{r,echo=FALSE,results = FALSE,message=FALSE,warning=FALSE,fig.show='hide'} library(BioStatR) print("T1 vs T2") @@ -209,12 +232,14 @@ cat("Replicat 2 : ", eta2(T$T2_6H_R2, T$ExpT3), "\n") ``` - -Le calcul du rapport de correlation eta² bien notre observation de la grande similarité d'expression des genes traités avec T2 et T3 et la dissimilarité des expression des genes lorsque la plante est traitée avec T1 comparée à T2 et T3, chose normale au vu du peu de genes affectés par T1. ++ Pour la comparaison entre T1 et T2, le rapport de corrélation est de 0,187 pour le réplicat 1 et de 0,199 pour le réplicat 2. ++ Pour la comparaison entre T1 et T3, le rapport de corrélation est de 0,152 pour le réplicat 1 et de 0,142 pour le réplicat 2. ++ Pour la comparaison entre T2 et T3, le rapport de corrélation est de 0,902 pour le réplicat 1 et de 0,888 pour le réplicat 2. +Le calcul du rapport de correlation eta² confirme bien notre observation de la grande similarité d'expression des genes traités avec T2 et T3 et la dissimilarité des expression des genes lorsque la plante est traitée avec T1 comparée à T2 et T3, chose normale au vu du peu de genes affectés par T1. ## tables de contingence pour les variables qualitatives, 2 à 2 -```{r,fig.cap="tables de contingence pour les variables qualitatives, 2 à 2"} +```{r,fig.cap="\\label{fig:table1}tables de contingence pour les variables qualitatives, 2 à 2"} print("table de contingence entre T1 et T2") table(T$ExpT1,T$ExpT2) print("table de contingence entre T1 et T3") @@ -234,41 +259,58 @@ La grande valeur des effectifs partiels sur la diagonale de la table de continge L'ACP permet d'obtenir une vision synthétique des données en réduisant leur complexité tout en préservant l'information essentielle. Elle facilite l'identification des tendances et profils d'individus, ainsi que la construction de méta-variables, plus simples à interpréter, tout en évitant les redondances entre les variables. Pour faire cela, nous devons transposer la matrice de données originale qui elle décrivait les gènes (individus) en fonction des Tt sH Rr. -Nous décidons de faire directement une ACP car, comme mentionné plus tôt lors de l'analyse de la figure , nous n'avons pas besoin de centrer et réduire le jeu de données. +Nous décidons de faire directement une ACP car, comme mentionné plus tôt lors de l'analyse de la Figure \ref{fig:boxplot1}, nous n'avons pas besoin de centrer et réduire le jeu de données. -```{r, fig.width=10, fig.height=5, fig.cap="Participation des chaque valeur propre de la matrice de correlation à l'intertie totale des données"} +```{r, fig.width=10, fig.height=5, fig.cap="\\label{fig:vp1}Participation des chaque valeur propre de la matrice de correlation à l'intertie totale des données"} donnees_transposees = t(T[-c(37:39)]) res_pca<-PCA(donnees_transposees,scale.unit=FALSE,graph=FALSE) fviz_eig(res_pca) ``` -Ce graphique représente la participation de chaque valeur propre de la matrice de corrélation du jeu de données dans l'inertie totale. L'inertie totale étant la somme des valeurs propres ( qui elles sont les inerties axiale associées à l'axe de vecteur directeur le vecteur propre associé ), chaque valeur propre est donc une fraction de l'inertie totale. +\vspace{1cm} + + +La Figure \ref{fig:vp1} représente la participation de chaque valeur propre de la matrice de corrélation du jeu de données dans l'inertie totale. L'inertie totale étant la somme des valeurs propres ( qui elles sont les inerties axiale associées à l'axe de vecteur directeur le vecteur propre associé ), chaque valeur propre est donc une fraction de l'inertie totale. On voit qu'on dépasse 80% de l'inertie totale rien qu'avec les deux premieres valeurs propres, on en prend donc les vecteurs propres associés comme axes principaux de l'analyse. -```{r,fig.cap="Corrélations des variables avec les composantes principales"} -fviz_pca_ind(res_pca,label="all",title="Projection des individus sur un plan factoriel") -fviz_pca_var(res_pca,axes=c(1,2),label="none",title="Corrélations des variables avec les composantes principales") +```{r,fig.width=8,fig.cap="\\label{fig:acp1}Projection des individus dans le plan factoriel et corrélations des variables avec les composantes principales"} +plot1=fviz_pca_ind(res_pca,label="all") +plot2=fviz_pca_var(res_pca,axes=c(1,2),label="none",habillage=T$ExpT1, geom=c("point")) +plot3=fviz_pca_var(res_pca,axes=c(1,2),label="none",habillage=T$ExpT2, geom=c("point")) +plot4=fviz_pca_var(res_pca,axes=c(1,2),label="none",habillage=T$ExpT3, geom=c("point")) +grid.arrange(plot1,plot2,plot3,plot4,ncol=2) ``` -Contexte : les relevés aux heures sont décrits par les gènes ( les gènes sont considérés comme les variables). + +\vspace{1cm} + +Contexte de la figure \ref{fig:acp1} : les relevés aux heures sont décrits par les gènes ( les gènes sont considérés comme les variables). - les genes proches d'un axe sont très représentés par celui-ci - les genes dont l'angle entre eux est petit sont corrélés entre eux -## Interprétation globale du couple de graphes +## Interprétation globale du couple de graphes Figure \ref{fig:acp1} On voit que les genes se polarisent principalement sur l'axe 1 dans un sens ou l'autre. Certaines flèches sont d'une longueur presque du rayon du cercle, indiquant une participation très forte des genes dans la variance expliquée par ces dimensions. -Il n'y a pas de tendance particulière sur la direction selon l'axe 2 des flèches : Dans chaque "polarité" de fleches selon l'axe 1, il y a des fleches dont la direction est negative d'autres positive selon l'axe 2. Bien que l'on dénote une quantité plus grande de gènes corrélés positiviement à la dimension 2. +Dans chaque "polarité" de fleches selon l'axe 1, il y a des fleches dont la direction est negative d'autres positive selon l'axe 2. Bien que l'on dénote une quantité plus grande de gènes corrélés positiviement à la dimension 2. + + +Gràce à l'habillage des graphes des variables (gènes) à l'aide des variables qualitatives, on remarque que les gènes se polarisent sur la dimension 1 du côté des valeurs negatives les gènes s'étant sous-exprimés à 6h en moyenne sur le traitement T2 et du côté des valeurs positives, ceux qui étaient sur-exprimés. +Pour la dimension 2, on observe les heures de relevés de traitement s'étaler selon cet axe, on suppose alors que les gènes corrélés à l'axe 2 très positivement s'exprime tôt, et inversement pour ceux qui s'expriment aux environs des 6h. Le traitement 1 est entièrement groupé sur des valeurs très negatives de l'axe 1. On remarque dans ce groupement la présence des T2 et T3 à la première heure de relevés d'expression des gènes. Pour le traitement 2 et 3, on les retrouves formant 2 groupements, 1 en haut à droite du graphe contenant les relevés à 2 et 3h puis un groupement s'étalant sur la droite du graphe du centre jusqu'en bas contenant les relevés à partir de 4h. +On en déduit alors que les gènes étant impliqués dans le traitement 1 s'expriment à vitesse moyenne, ni rapidement ni lentement mais qu'ils se sont sous-exprimés dans le traitement T2. +De plus, on observe que T2 et T3 visent durant la première heure les gènes qui vont se sous-exprimer et se déplacent petit-à-petit sur le graphe pour toucher les gènes qui vont se sur-exprimer. + ## Clustering + L'objectif du clustering est de regrouper des individus (ici, les Tt_sH_Rr) en groupes homogènes selon leurs similarités, sans connaissance préalable des catégories. Cela permet d’identifier des profils ou des comportements communs, facilitant l’interprétation des données et la mise en évidence de structures sous-jacentes. @@ -278,8 +320,11 @@ Pour le dendogramme, nous avons utilisé la mesure d'agrégation de Ward car il ### Clustering k-means + On commence par afficher l'inertie intra classe en fonction du nombre de classe pour le clustering avec k-means, le but étant de la minimiser tout en gardant un nombre de classes raisonnable. -```{r,fig.cap="Visualisation de l'inertie intra-classe en fonction du nombre de classes demandées pour le clustering"} + + +```{r,fig.width=5,fig.cap="\\label{fig:intra1}Visualisation de l'inertie intra-classe en fonction du nombre de classes demandées pour le clustering"} #centrage et réduction des données s = donnees_transposees set.seed(1234) @@ -302,10 +347,14 @@ ggplot(df,aes(x=K,y=Iintra))+ -On dénote un coude dans la courbe d'inertie intraclasse aux alentours de 4 clusters. +\vspace{1cm} -À présent on va afficher l'évolution de l'indicateur Silouhette en fonction du nombre de classe ainsi que l'évolution de l'indice de Calinski-Harabasz en fonction du nombre de classe. -```{r,fig.cap="Visualisation du critère de Silhouette et de Calinski-Harabasz en fonction du nombre de classes demandées pour le clustering",fig.width=5} +Sur la Figure \ref{fig:intra1} on dénote un coude dans la courbe d'inertie intraclasse aux alentours de 4 clusters. + +À présent on va afficher sur la Figure \ref{fig:sil1} l'évolution de l'indicateur Silouhette en fonction du nombre de classe ainsi que l'évolution de l'indice de Calinski-Harabasz en fonction du nombre de classe. + + +```{r,fig.cap="\\label{fig:sil1}Visualisation du critère de Silhouette et de Calinski-Harabasz en fonction du nombre de classes demandées pour le clustering",fig.width=5} set.seed(1234) Silhou<-NULL for (k in 2:Kmax){ @@ -336,29 +385,29 @@ grid.arrange(p11,p12,ncol=2) ``` +\vspace{1cm} -Silhouette et l'indice de Calinski-Harabasz ont un pic à 2, mais cela est normal sachant que Silhouette et l'indice de Calinski-Harabasz ont tendance à sous-estimer le nombre de clusters. +Sur la Figure \ref{fig:sil1} Silhouette et l'indice de Calinski-Harabasz ont un pic à 2, mais cela est normal sachant que Silhouette et l'indice de Calinski-Harabasz ont tendance à sous-estimer le nombre de clusters. ### visualisation du clustering -```{r,fig.cap="Visualisation des clusters générés par la méthode kmeans dnas le plan factoriel 1,2"} +```{r,fig.cap="\\label{fig:clust1}Visualisation des clusters générés par la méthode kmeans dans le plan factoriel 1,2",echo=FALSE,message=FALSE} set.seed(1234) #graphes des clusters res_kmeans = kmeans(s,4) p11 = fviz_cluster(res_kmeans,data=donnees_transposees, ellipse.type="norm",labelsize=8, - geom=c("point"))+ggtitle("Visualisation des clusters générés par la méthode kmeans dnas le plan factoriel 1,2") + geom=c("point")) # on choisis 2 clusters aux<-silhouette(reskmeanscl[,4-1], daisy(s)) -p12 = fviz_silhouette(aux)+ - theme(plot.title = element_text(size =9)) +p12 = fviz_silhouette(aux) #graphes des clusters res_kmeans = kmeans(s,2) p21 = fviz_cluster(res_kmeans,data=donnees_transposees, ellipse.type="norm",labelsize=8, - geom=c("point"))+ggtitle("Visualisation des clusters générés par la méthode kmeans dnas le plan factoriel 1,2") + geom=c("point")) # on choisis 2 clusters @@ -370,14 +419,16 @@ grid.arrange(p11,p12,p21,p22,ncol=2) ``` +\vspace{1cm} -Après comparaison, on choisit 2 classes car cela nous semble plus optimal que 4. +Après comparaison sur la Figure \ref{fig:clust1}, on choisit 2 classes car cela nous semble plus optimal que 4. ### clustering CAH À présent on va afficher l'évolution de l'indice de Calinski-Harabasz en fonction du nombre de classes utilisées pour découper le dendogramme. -```{r, fig.width=5, fig.cap="Visualisation du critère de Calinski-Harabasz en fonction du nombre de classes demandées pour le clustering"} + +```{r, fig.width=5, fig.cap="\\label{fig:cah1}Visualisation du critère de Calinski-Harabasz en fonction du nombre de classes demandées pour le clustering"} set.seed(1234) dx<-dist(donnees_transposees) @@ -396,17 +447,22 @@ ggplot(daux,aes(x=NbClust,y=CH))+ ``` +\vspace{1cm} -On choisit alors de prendre 2 classes par observation du maximum du graphe. -```{r, fig.width=5, fig.cap="Dendogramme du clustering de l'ACP des variables Tt en tant qu'individus, obtenu par méthode CAH"} +En regardant la Figure \ref{fig:cah1}, on choisit alors de prendre 2 classes par observation du maximum du graphe. + +```{r, fig.width=5, warning=FALSE, fig.cap="\\label{fig:dend1}Dendogramme du clustering de l'ACP des variables Tt en tant qu'individus, obtenu par méthode CAH"} set.seed(1234) ClustCH<-cutree(hward,k=2) -fviz_dend(hward,k=2,show_labels=FALSE)+ggtitle("Dendogramme du clustering de l'ACP des variables Tt en tant qu'individus, obtenu par méthode CAH") -fviz_pca_ind(res_pca, habillage = as.factor(ClustCH), geom = c("point")) +plot1=fviz_dend(hward,k=2,show_labels=FALSE) +plot2=fviz_pca_ind(res_pca, habillage = as.factor(ClustCH), geom = c("point")) +grid.arrange(plot1,plot2,ncol=2) ``` +\vspace{1cm} + ### Comparaison des clusterings A 2 classes nous obtenons une classification qui ne change pas entre chaque méthode. Nous décidons donc qu'il s'agit donc d'un bon choix de nombre de classes. @@ -414,7 +470,7 @@ A 2 classes nous obtenons une classification qui ne change pas entre chaque mét La classification obtenue est en accord avec les observations faites lors de l'ACP, on y retrouve plus ou moins les mêmes groupements : celui majoritarement composé des relevés de T1 avec une majorité de gènes sans changement d'expression relative et celui composé des relevés de T2 et T3. -```{r,fig.width=5} +```{r,fig.width=5,fig.cap="\\label{fig:chord1}Diagramme mettant en valeur l'exacte correspondance des classes entre les deux clusterings"} # kmeans et CAH clust1f = paste("CLkm-",res_kmeans$cluster, sep="") clust2f = paste("CLCAH-", cutree(hward,2), sep="") @@ -422,12 +478,17 @@ chordDiagram(table(clust1f,clust2f)) ``` +\vspace{1cm} -# ANALYSE DES GENES + +Sur la Figure \ref{fig:chord1} nous observons que les 2 clustering nous donne les même cluster peuplés des mêmes gènes. + + +# Analyse des gènes ## Generation de dataExpMoy -Nous construisons le jeu de données DataExpMoy contenant la moyenne des expressions sur les réplicats de chaque gène, pour chaque traitement et chaque heure. DataExpMoy est donc une matrice de taille 542× 18. +Nous construisons le jeu de données DataExpMoy contenant la moyenne des expressions sur les réplicats de chaque gène, pour chaque traitement et chaque heure. DataExpMoy est donc une matrice de taille 542×18. ```{r,echo=FALSE,results = FALSE,message=FALSE,warning=FALSE,fig.show='hide'} # Liste des traitements, heures et réplicats @@ -463,10 +524,15 @@ head(DataExpMoy) ``` +\vspace{1cm} + ## ACP de DataExpMoy -A partir d'ici, nous avons centré et réduit les données car cela donnait des résultats sensiblement plus exploitables au niveau des indicateurs pour le clustering. -```{r, fig.width=5,fig.cap="Participation de chaque valeur propre à l'inertie totale des données"} + +Pour l'ACP de DataExpMoy, nous avons centré et réduit les données car cela donnait des résultats sensiblement plus exploitables au niveau des indicateurs pour le clustering. + + +```{r, fig.width=5,fig.cap="\\label{fig:vp2}Participation de chaque valeur propre à l'inertie totale des données"} # Effectuer l'ACP res_pca2 = PCA(DataExpMoy, scale.unit = TRUE, graph = FALSE) @@ -476,9 +542,14 @@ plot1 ``` +\vspace{1cm} -On voit qu'on dépasse 80% de l'inertie totale avec les deux premières valeurs propres, on prend donc les vecteurs propres associés à ces deux valeurs propres comme composantes principales de notre ACP. -```{r, fig.width=7,fig.cap="Couple de graphes représentant la Projection des individus sur un plan factoriel (droite) et la Corrélations des variables avec les composantes principales (gauche)"} + +Sur la Figure \ref{fig:vp2} on voit qu'on dépasse 80% de l'inertie totale avec les deux premières valeurs propres, on prend donc les vecteurs propres associés à ces deux valeurs propres comme composantes principales de notre ACP. + + + +```{r, fig.width=7,fig.cap="\\label{fig:acp2}Couple de graphes représentant la Projection des individus sur un plan factoriel (droite) et la Corrélations des variables avec les composantes principales (gauche)"} plot2 = fviz_pca_ind(res_pca2, label = "point") plot3 = fviz_pca_var(res_pca2, axes = c(1, 2), label = "all") @@ -488,7 +559,13 @@ grid.arrange(plot2,plot3, ncol = 2) ``` -Il semble y avoir deux groupes principaux de gènes (individus), ce qui pourrait refléter une différenciation claire entre les niveaux d'expression sous différents traitements. + + +\vspace{1cm} + + + +En analysant la Figure \ref{fig:acp2}, il semble y apparaître deux groupes principaux de gènes (individus), ce qui pourrait refléter une différenciation claire entre les niveaux d'expression sous différents traitements. Les points plus éloignés du centre vers le haut représentent des gènes ayant des comportements plus spécifiques ou atypiques. Le premier axe (DIM 1) est fortement corrélé avec les traitements T2, T3 à des moments précis, en particulier pour les temps plus avancés (par exemple, T3 4H, T3 5H, T3 6H). Cela suggère que Dim1 reflète les différences d'expression liées à l'effet des traitements T2 au fil du temps, qui a la particularité de faire exprimer ses gènes sur les temps plus longs. Cela explique aussi la corrélation des variables de relevés de T3 à cette dimension, car T3 est un mélange de T1 et T2. @@ -500,8 +577,11 @@ Comme T3 est une combinaison des traitements T1 et T2, il semble structurer fort ### Ajout des variables qualitatives -Nous allons maintenant afficher les points dans les dimensions de l'ACP, colorés en fonction des modalités des 3 variables qualitatives ExpT1, ExpT2 et ExpT3. Cela peut nous permettre d'affiner notre interprétation des résultats de l'ACP. -```{r, fig.height=7, fig.cap="Données sous forme de points dans les dimensions de l'ACP, colorés en fonction des modalités des 3 variables qualitatives ExpT1, ExpT2 et ExpT3."} +Nous allons maintenant afficher les points dans les dimensions de l'ACP, colorés en fonction des modalités des 3 variables qualitatives ExpT1, ExpT2 et ExpT3. Cela peut nous permettre d'affiner notre interprétation des résultats de l'ACP. Cela nous a donné les graphes Figure \ref{fig:proj1} + + + +```{r, fig.height=7, fig.cap="\\label{fig:proj1}Données sous forme de points dans les dimensions de l'ACP, colorés en fonction des modalités des 3 variables qualitatives ExpT1, ExpT2 et ExpT3."} p11 = fviz_pca_ind(res_pca2,habillage=T$ExpT1,geom=c("point")) p12 = fviz_pca_ind(res_pca2,habillage=T$ExpT2,geom=c("point")) p13 = fviz_pca_ind(res_pca2,habillage=T$ExpT3,geom=c("point")) @@ -511,8 +591,11 @@ grid.arrange(p11,p12,p13) +\vspace{1cm} + + ### analyse -On observe donc 3 clusters de gènes : +Sur la Figure \ref{fig:proj1},on observe donc 3 clusters de gènes : - Les gènes étant poussés à la sur-expression par T1, affichés comme non-exprimés durant T2 et partiellement sur-exprimés avec T3 - Les gènes étant sous-exprimés (verts) durant T2 et T3, non-exprimés durant T1. - Les gènes étant sur-exprimés (bleus) durant T2 et T3, non-exprimés durant T1. @@ -521,9 +604,10 @@ On confirme donc bien notre analyse descriptive préliminaire, et nos suppositio ## Clustering + L'objectif de ce clustering est de regrouper des individus (ici, des gènes) en groupes homogènes selon leurs similarités. -```{r,fig.cap="Visualisation de l'inertie intra-classe et Silouhette en fonction du nombre de classes demandées pour le clustering",fig.width=5} +```{r,fig.cap="\\label{fig:sil2}Visualisation de l'inertie intra-classe et Silouhette en fonction du nombre de classes demandées pour le clustering",fig.width=5} #centrage et réduction des données set.seed(1234) @@ -562,23 +646,30 @@ grid.arrange(p11,p12,ncol=2) ``` -En lisant le graphe de l'inertie intra-classe, on observe le coude aux alentours de 3 classes. En observant l'indice de Silouhette, on remarque le pic recherché à 3 classes également. Les indices concordants, on en déduit que le choix optimal du nombre de classes pour le clustering est 3. + +\vspace{1cm} + +En lisant le graphe de l'inertie intra-classe (Figure \ref{fig:sil2}), on observe le coude aux alentours de 3 classes. En observant l'indice de Silouhette, on remarque le pic recherché à 3 classes également. Les indices concordants, on en déduit que le choix optimal du nombre de classes pour le clustering est 3. -```{r,fig.cap="Visualisation des clusters générés par la méthode kmeans dnas le plan factoriel 1,2",fig.width=5} +```{r,fig.cap="\\label{fig:clust2}Visualisation des clusters générés par la méthode kmeans dans le plan factoriel 1,2",fig.width=5} set.seed(1234) #graphes des clusters res_kmeans_2 = kmeans(s_2,3) fviz_cluster(res_kmeans_2,data=s_2, ellipse.type="norm",labelsize=8, - geom=c("point"))+ggtitle("Visualisation des clusters générés par la méthode kmeans dnas le plan factoriel 1,2") + geom=c("point")) ``` -```{r, fig.width=9, fig.cap="Dendogramme du clustering de l'ACP, obtenu par méthode CAH",fig.width=5} +\vspace{1cm} + + + +```{r, fig.width=9,message=FALSE,warning=FALSE, fig.cap="\\label{fig:cah2}Dendogramme du clustering de l'ACP, obtenu par méthode CAH",fig.width=5,echo=FALSE, } dx=dist(s_2) hward=hclust(dx,method = "ward.D2") @@ -587,20 +678,27 @@ fviz_dend(hward,k=3, show_labels = FALSE, palette = "npg", rect_border = "npg", - labels_track_height = 0.8)+ggtitle("Dendogramme découpé représentant le clustering obtenu par méthode CAH") + labels_track_height = 0.8) ``` +\vspace{1cm} + + ### analyse des clusterings -On remarque que les clusterings correspondent aux groupes que nous avions discernés sur la figure + +On remarque que le clustering de la figure \ref{fig:clust2} correspond aux groupes que nous avions discernés sur la Figure \ref{fig:proj2}. On en déduis donc la correlation des gènes de ces classes avec des expressions moyennes similaires dans chaque classe et distinctes entre les différentes classes. ### Evolution de l'expression des genes en fonction de leur traitement et cluster -Nous avons généré 3 graphiques, représentant l'évolution de l'expression moyenne des gènes par cluster et par traitement. Cela pourra nous permettre d'affiner nos observations sur les traitements. -```{r,fig.width=13, fig.cap="Graphiques représentant l'évolution de l'expression moyenne des gènes par cluster et par traitement"} +Nous avons généré 3 graphiques (Figure \ref{fig:evol1}) , représentant l'évolution de l'expression moyenne des gènes par cluster et par traitement. Cela pourra nous permettre d'affiner nos observations sur les traitements. + + + +```{r,fig.width=10, fig.cap="\\label{fig:evol1}Graphiques représentant l'évolution de l'expression moyenne des gènes par cluster et par traitement",warning=FALSE} DataExpMoy$GeneID <- rownames(DataExpMoy) DataExpMoy$Cluster <- as.factor(res_kmeans_2$cluster) @@ -632,7 +730,6 @@ ggplot(data_mean, aes(x = Temps, y = Expression, group = Cluster, color = Cluste geom_line(size = 1.2) + facet_wrap(~ Traitement, scales = "free_y") + labs( - title = "Évolution moyenne de l'expression génique par traitement et cluster", x = "Temps (heures)", y = "Expression génique (moyenne)" ) + @@ -642,7 +739,11 @@ ggplot(data_mean, aes(x = Temps, y = Expression, group = Cluster, color = Cluste ``` -On lis sur les graphiques de la figure <> la liaison de toutes les observations que nous avons pu faire : + +\vspace{1cm} + + +On lis sur les graphiques de la Figure \ref{fig:evol1} la liaison de toutes les observations que nous avons pu faire : On remarque sur T1 le fait que le cluster 2 correspond au peu de gènes qu'il influence et qui vont se sur-exprimer tôt dans le traitement, pour ensuite l'expression relative re-diminue. Lors du traitement 2, les gènes de ce cluster ne vont pas/peu s'exprimer et lors du traitement 3, ils vont s'exprimer de la même façon que lors du traitement 1, ce qui est logique sachant que T3 est le mélange de T2 et T1. @@ -656,7 +757,78 @@ Le cluster 1 correspond aux gènes sur-exprimés et le cluster 3 aux gènes sous ## Clustering des gènes à partir des variables ExpT1, ExpT2 et ExpT3. Comme ce sont des données qualitatives, on doit utiliser des méthodes alternatives de clustering comme les kmodes ou les kmeans mais sur les coordonnées de points projetés dans le plan d'une ACM -## generation de la matrice de données qualitatives + + + +## Approfondissement de L'ACP avec un clustering de 7 classes +Sur la figure \ref{fig:intra2}, on peut aussi remarquer un coude aux alentours de 7 classes, nous avons donc décidé de compléter notre analyse par un clustering à 7 classes dont on peut voir la projection dans le plan factoriel sur la Figure \ref{fig:clust3} et Figure \ref{fig:evol2} l'évolution de l'expression moyenne des gènes par cluster, en fonction du temps. + + + + +```{r,fig.cap="\\label{fig:clust3}Visualisation des clusters générés par la méthode kmeans dans le plan factoriel 1,2",fig.width=5} +set.seed(1234) +#graphes des clusters +res_kmeans_3 = kmeans(s_2,7) +fviz_cluster(res_kmeans_3,data=s_2, + ellipse.type="norm",labelsize=8, + geom=c("point")) + +``` + + + + + + +```{r,fig.width=10, fig.cap="\\label{fig:evol2}Graphiques représentant l'évolution de l'expression moyenne des gènes par cluster et par traitement",warning=FALSE} +set.seed(1234) + +DataExpMoy$Cluster <- as.factor(res_kmeans_3$cluster) + +data_long <- pivot_longer( + DataExpMoy, + cols = -c(Cluster, GeneID), + names_to = "Condition", + values_to = "Expression" +) + +data_long <- separate( + data_long, + col = "Condition", + into = c("Traitement", "Temps"), + sep = "_" +) + +data_long$Temps <- as.numeric(gsub("H", "", data_long$Temps)) + +data_grouped <- group_by(data_long, Cluster, Traitement, Temps) +data_mean <- summarise( + data_grouped, + Expression = mean(Expression), + .groups = "drop" +) + +ggplot(data_mean, aes(x = Temps, y = Expression, group = Cluster, color = Cluster)) + + geom_line(size = 1.2) + + facet_wrap(~ Traitement, scales = "free_y") + + labs( + x = "Temps (heures)", + y = "Expression génique (moyenne)" + ) + +``` + + + + + +### Analyse + +Avec plus de clusters, on retrouve plus de précisions dans les comportements différents, avec différentes trajectoire d'expression pour les gènes qui finissent sous-exprimés et ceux qui finissent sur exprimés dans T2 et T3, et même une classe de gènes qui se sur-exprime, se calme, puis se re-sur exprime. Il est tout de même intéressant de noter que la courbe d'expression moyenne pour les gènes sur-exprimés par T1 ne bouge pas par rapport à l'analyse sur 3 clusters, il semblerait donc que ce cluster n'ait sensiblement pas bougé. On peut confirmer les tendances vues dans la première ACP, comme le fait que T1 vise des gènes qui s'expriment à un horizon temporel moyen. + + + ```{r} MatriceExp = T[,c(37,38,39)] rownames(MatriceExp) = rownames(T) @@ -666,9 +838,12 @@ MatriceExp = as.data.frame(MatriceExp) -### PAM -Pour effectuer un clustering PAM avec des données qualitatives, nous avons généré en amont une matrice de dissimilarité grâce à la métrique de gower, pour ensuite lancer l'algorithme PAM sur cette matrice. -```{r, fig.cap="Visualisation des clusters générés par la méthode PAM"} + + + +```{r, fig.cap="Visualisation des clusters générés par la méthode PAM, dans un plan de L'acp et dans les plans originaux des données",echo=FALSE,results = FALSE,message=FALSE,warning=FALSE,fig.show='hide'} +# Pour effectuer un clustering PAM avec des données qualitatives, nous avons généré en amont une matrice de dissimilarité grâce à la métrique de gower, pour ensuite lancer l'algorithme PAM sur cette matrice. + # La distance de Gower est adaptée aux données qualitatives ds <- daisy(MatriceExp, metric = "gower") @@ -700,8 +875,7 @@ fviz_cluster( res_pam, labelsize = 8, # Taille des étiquettes geom = c("point") # Utiliser des points pour visualiser les données -) + - ggtitle("Visualisation des clusters générés par la méthode PAM") +) # Visualisation des clusters dans le plan original # Ajouter les clusters aux données d'origine @@ -711,7 +885,6 @@ data_with_clusters$cluster <- as.factor(res_pam$clustering) ggplot(data_with_clusters, aes(x = ExpT1, y = ExpT2, color = cluster)) + geom_point(size = 3) + labs( - title = "Visualisation des clusters PAM dans le plan original des données", x = "ExpT1", y = "ExpT2", color = "Cluster" @@ -720,7 +893,6 @@ ggplot(data_with_clusters, aes(x = ExpT1, y = ExpT2, color = cluster)) + ggplot(data_with_clusters, aes(x = ExpT1, y = ExpT3, color = cluster)) + geom_point(size = 3) + labs( - title = "Visualisation des clusters PAM dans le plan original des données", x = "ExpT1", y = "ExpT2", color = "Cluster" @@ -730,15 +902,9 @@ ggplot(data_with_clusters, aes(x = ExpT1, y = ExpT3, color = cluster)) + ggplot(data_with_clusters, aes(x = ExpT2, y = ExpT3, color = cluster)) + geom_point(size = 3) + labs( - title = "Visualisation des clusters PAM dans le plan original des données", x = "ExpT1", y = "ExpT2", color = "Cluster" ) + theme_minimal() ``` - - - -# TODO : -- Voir pourquoi des graphes se mettent après l'analyse d'eux-même c'est n'importe quoi \ No newline at end of file diff --git a/Projet.log b/Projet.log new file mode 100644 index 0000000..fae9a7f --- /dev/null +++ b/Projet.log @@ -0,0 +1,724 @@ +This is pdfTeX, Version 3.141592653-2.6-1.40.22 (TeX Live 2022/dev/Debian) (preloaded format=pdflatex 2024.7.25) 15 JAN 2025 16:57 +entering extended mode + restricted \write18 enabled. + %&-line parsing enabled. +**Projet.tex +(./Projet.tex +LaTeX2e <2021-11-15> patch level 1 +L3 programming layer <2022-01-21> 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