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# Statistical-Learning-Project
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# Exam
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The exam consists in two assignments, one on the first part(regression, tree, neural nets) and the second part (unsupervised learning). For both you must prepare a writing report using one or more techniques and comparing their performance on one or more data set chosen by the student. A brief oral presentation of the reports will be asked.
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Each report must contain:
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- short **abstract**: what are your going to present in the report
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- **statement** of the problem/**goal** of the analysis and description of the **data set**(s)
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- list of three to five **findings/keypoints**
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- the analysis with **wise** commentary
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- (optional) theoretical background of the used methods
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- **conclusions**(should include the findings/keypoints)
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- the **Appendix**, containing all the R code
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Notice:
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- The **paper length** is irrelevant provided that the content is correct.
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- **No R code in the main text**. The R code must be confined to the appendix
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- The report should be prepared in **PDF** only
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---
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title: "Statistical Learning Project"
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output:
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html_document:
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df_print: paged
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toc: true
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toc_float:
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collapsed: false
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smooth_scroll: false
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pdf_document:
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keep_tex: yes
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latex_engine: xelatex
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toc: true
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---
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\ \
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<strong > Author: Andrea Ierardi </strong >
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\ \
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<strong > Repository </strong > : Code [link](https://github.com/Andreaierardi/Statistical-Learning-Project)
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\ \
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### Assignment
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The exam consists in two assignments, one on the first part(regression, tree, neural nets) and the second part (unsupervised learning). For both you must prepare a writing report using one or more techniques and comparing their performance on one or more data set chosen by the student.
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\ \
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# Libraries
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```{r}
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library(knitr)
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library(ggplot2)
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library(plotly)
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library(tidyr)
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library(dplyr)
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library(png)
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library(ggpubr)
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library(tidyverse)
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library(caTools)
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library(caret)
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library(tree)
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library(MASS)
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library(randomForest)
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library(ranger)
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library(tuneRanger)
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library(keras)
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library(kableExtra)
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library(clustMixType)
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library(cluster)
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library(dendextend)
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library(readr)
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library(factoextra)
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library(FactoMineR)
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library(PCAmixdata)
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```
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\ \
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# Dataset
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Link of the [dataset](https://www.kaggle.com/dgomonov/new-york-city-airbnb-open-data)
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```{r}
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ds = read.csv("AB_NYC_2019.csv")
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```
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\ \
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# Data Inspection
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```{r}
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head(ds)
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summary(ds)
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```
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```{r}
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cat("Shape of the dataset:" ,dim(ds))
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```
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```{r}
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img <- readPNG("map.png")
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map_ds = ggplot() + background_image(img)+ geom_point(data = ds, aes(y=latitude,x = longitude, color = price))
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map_ds
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```
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\ \
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# Data cleaning
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\ \
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## Check for NA and NULL values
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```{r}
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apply(ds,2,function(x) sum(is.na(x)))
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```
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\ \
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## Variable selection
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```{r}
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dataset = ds %>% dplyr::select(neighbourhood_group,latitude, longitude, room_type,price)
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head(dataset)
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```
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\ \
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## Variable scaling
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```{r}
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scale_data = function(df)
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{
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df = df %>%filter( price >= 15 & price <= 500)
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numerical = c("price")
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numerical2 = c("latitude","longitude")
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categorical = c("room_type", "neighbourhood_group")
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for( cat in categorical )
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{
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df[cat] = factor(df[[cat]],
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level = unique(df[[cat]]),
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labels = c(1:length(unique(df[[cat]])) ))
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}
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df[numerical] = as.numeric(scale(df[numerical]))
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df2 = df
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df2[numerical2] = as.numeric(scale(df2[numerical2]))
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df3 = list()
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df3$df2 = df2
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df3$df = df
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return(df3)
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}
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dataframe = scale_data(dataset)
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dataset = dataframe$df
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data = dataframe$df2
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head(dataset)
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summary(dataset)
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```
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\ \
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## Data visualisation after the scaling
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```{r}
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mappa = ggplot() + background_image(img)+ geom_point(data = dataset, aes(y=latitude,x = longitude, color = price))
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mappa
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```
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\ \
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# Data split
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## Split data in subsets for each neighbourhood_group and room_type
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```{r}
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neighbourhoods = unique(dataset$neighbourhood_group)
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rooms = unique(dataset$room_type)
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clust_data = vector("list")
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lis_n = vector("list")
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for (n in neighbourhoods)
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{
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tmp = dataset %>%filter( neighbourhood_group == n)
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lis_n[[n]] = tmp[-1]
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tmp2 = data %>%filter( neighbourhood_group == n)
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clust_data[[n]] = tmp2[-1]
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clust_data[[n]]$room_type = factor(clust_data[[n]]$room_type , level = unique(clust_data[[n]]$room_type) , labels= unique(ds$room_type))
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}
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lis_r_n= vector("list")
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for (n in neighbourhoods)
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{
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for(r in rooms)
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{
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tmp = dataset %>%
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filter( room_type == r & neighbourhood_group == n)
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lis_r_n[[paste0("n",n,"-","r",r)]]= tmp[-1][-3]
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tmp2 = data %>%
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filter( room_type == r & neighbourhood_group == n)
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clust_data[[paste0("n",n,"-","r",r)]]= tmp2[-1][-3]
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}
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}
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data$neighbourhood_group = factor(data$neighbourhood_group , level = unique(data$neighbourhood_group ) , labels= unique(ds$neighbourhood_group))
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data$room_type = factor(data$room_type , level = unique(data$room_type ) , labels= unique(ds$room_type))
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clust_data[["all"]] = data
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```
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\ \
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## Split in train and test for each subset
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```{r}
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trains = vector("list")
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tests = vector("list")
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datas = vector("list")
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for (i in names(lis_n))
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{
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sample = sample.split(lis_n[[i]], SplitRatio = .75)
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train = subset(lis_n[[i]], sample == TRUE)
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test = subset(lis_n[[i]], sample == FALSE)
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trains[[i]]= train
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tests[[i]] = test
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datas[[i]] = lis_n[[i]]
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}
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for (i in names(lis_r_n))
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{
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sample = sample.split(lis_r_n[[i]], SplitRatio = .75)
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train = subset(lis_r_n[[i]], sample == TRUE)
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test = subset(lis_r_n[[i]], sample == FALSE)
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trains[[i]]= train
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tests[[i]] = test
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datas[[i]] = lis_r_n[[i]]
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}
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sample = sample.split(dataset, SplitRatio = .75)
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train = subset(dataset, sample == TRUE)
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test = subset(dataset, sample == FALSE)
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trains[["all"]] = train
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tests[["all"]] = test
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datas[["all"]] = dataset
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```
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\ \
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# MODELS TRAIN
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\ \
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```{r}
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model_lis = vector("list")
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```
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\ \
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## LINEAR REGRESSION
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```{r}
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lin_reg = vector("list")
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for (sub in names(trains))
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{
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lin_reg[[sub]]$fit =lm.fit = lm(price~., data = trains[[sub]])
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lin_reg[[sub]]$summary = summary(lm.fit)
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lin_reg[[sub]]$pred = pr.lm = predict(lm.fit,tests[[sub]])
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lin_reg[[sub]]$MSE = sum((pr.lm - tests[[sub]]$price)^2)/nrow(tests[[sub]])
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print(paste0("========== ",sub, " =========="))
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print(summary(lm.fit))
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cat("\n\n")
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}
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lin_reg$name = "Linear Regression"
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model_lis$linear_regression= lin_reg
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```
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\ \
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## DECISION TREE
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```{r}
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dec_tree = vector("list")
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for (sub in names(trains))
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{
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dec_tree[[sub]]$fit = tree_res=tree(price~., data = trains[[sub]])
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dec_tree[[sub]]$summary = sum = summary(tree_res)
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print(paste0("========== ",sub, " =========="))
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print(sum)
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if(sum$size > 1 )
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{
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plot(tree_res)
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text(tree_res,pretty=0)
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title(paste0("Tree of: ",sub))
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}
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else
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{
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cat("Not possible to plot tree: ", sub)
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}
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dec_tree[[sub]]$pred = pred = predict(tree_res,tests[[sub]])
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dec_tree[[sub]]$MSE = mse = sum((pred - tests[[sub]]$price)^2)/nrow(tests[[sub]])
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print(mse)
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cat("\n\n")
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}
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dec_tree$name = "Decision Tree"
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model_lis$decision_tree = dec_tree
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```
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\ \
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## RANDOM FOREST
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```{r}
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rf = vector("list")
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for (sub in names(trains))
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{
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rf[[sub]]$fit = res = randomForest( price ~ . , data=trains[[sub]])
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rf[[sub]]$pred = predt = predict(res,tests[[sub]])
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print(paste0("========== ",sub, " =========="))
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print(res)
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rf[[sub]]$MSE = mse = sum((predt - tests[[sub]]$price)^2)/nrow(tests[[sub]])
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print(paste0("MSE: ",mse))
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cat("\n\n")
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}
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rf$name = "Random Forest"
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model_lis$random_forest = rf
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```
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\ \
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## RANGER RANDOM FOREST
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```{r}
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ranger_rf = vector("list")
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for (sub in names(trains))
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{
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print(paste0("========== ",sub, " =========="))
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ranger_rf[[sub]]$fit = res = ranger( price~ ., data = trains[[sub]], write.forest = TRUE, classification = F)
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ranger_rf[[sub]]$pred = predt = predict(res,tests[[sub]])
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ranger_rf[[sub]]$MSE = mse = sum((predt$predictions - tests[[sub]]$price)^2)/nrow(tests[[sub]])
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print(res)
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print(paste0("MSE: ",mse))
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cat("\n\n")
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}
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ranger_rf$name = "Ranger Random Forest"
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model_lis$ranger = ranger_rf
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```
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\ \
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## NEURAL NETWORKS
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```{r}
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build_model <- function(dimension) {
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model <- keras::keras_model_sequential() %>%
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layer_dense(units = 32, activation = "relu",
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input_shape = dimension) %>%
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layer_dense(units = 16, activation = "relu") %>%
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layer_dense(units = 1,activation="linear")
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model %>% compile(
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loss = "mse",
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optimizer = optimizer_rmsprop(),
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metrics = list("mean_absolute_error")
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)
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return(model)
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}
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print_dot_callback <- callback_lambda(
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on_epoch_end = function(epoch, logs) {
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if (epoch %% 1 == 0)
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cat(".")
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}
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)
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nn = vector("list")
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for (sub in names(trains))
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{
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d = trains[[sub]]
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d2 = tests[[sub]]
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len = length(d)
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len2 = length(d2)
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if(!is.null(d$room_type))
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{
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d$room_type = keras::to_categorical(d$room_type)
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d2$room_type = keras::to_categorical(d2$room_type)
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}
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if(!is.null(d$neighbourhood_group))
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{
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d$neighbourhood_group = keras::to_categorical(d$neighbourhood_group)
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d2$neighbourhood_group = keras::to_categorical(d2$neighbourhood_group)
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}
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target = as.vector(d$price)
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features = as.matrix(as_tibble(d[-len]))
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target_test = as.vector(d2$price)
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features_test = as.matrix(as_tibble(d2[-len]))
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nn[[sub]]$epochs = epochs = 30
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nn[[sub]]$model = model = build_model(dim(features)[2])
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nn[[sub]]$summary = model %>% summary()
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nn[[sub]]$history = hist = model %>% fit(
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x = features,
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y = target,
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epochs = epochs,
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validation_split = 0.2,
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verbose = 0,
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callbacks = list(print_dot_callback)
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)
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eva = model %>% evaluate(features_test,target_test, verbose = 0)
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nn[[sub]]$mae = eva[1]
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nn[[sub]]$loss = eva[2]
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nn[[sub]]$pred = pred = model %>% predict(features_test)
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nn[[sub]]$MSE = sum((pred - target_test)^2)/length(target_test)
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}
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nn$name = "Neural Networks"
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model_lis$neural_networks = nn
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```
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\ \
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## NN plots
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```{r}
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for (sub in names(nn))
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{
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if(sub != "name")
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{
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m = nn[[sub]]
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hist = m$history
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print(paste0("========== ",sub, " =========="))
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str = paste0("MAE: ",round(m$mae,3)," --- Loss: ",round(m$loss,3))
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p = plot(hist, y ~ x) + theme_bw(base_size = 12) +ggtitle(paste0("NN of: ",sub))+ labs(caption= str)
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print(p)
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plot(p)
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cat("MAE: ",m$mae)
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cat("\nLoss: ",m$loss,"\n\n")
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}
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}
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```
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\ \
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# Comparison between the models
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\ \
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```{r}
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conc = c()
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for (n in unique(ds$neighbourhood_group))
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{
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conc = c(conc,n)
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}
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for (n in unique(ds$neighbourhood_group))
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{
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for(r in unique(ds$room_type))
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{
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conc = c(conc, paste(n,"-",r))
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}
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}
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conc = c(conc,"All")
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n = names(nn)
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cols = vector("list")
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cols[["Subset"]] = conc
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for( m in model_lis)
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{
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col = c()
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for( nam in n)
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{
|
||||
|
||||
if( nam != "name")
|
||||
{
|
||||
col = c(col,m[[nam]]$MSE)
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
cols[[m$name]] = col
|
||||
|
||||
}
|
||||
|
||||
|
||||
mse_df = as.data.frame(cols)
|
||||
best = c()
|
||||
for (i in 1:length(cols$Subset))
|
||||
{
|
||||
m = min(mse_df[i,2:6])
|
||||
col = which(mse_df[i,1:6 ] == m)
|
||||
nam = names(mse_df)[col]
|
||||
best = c(best, nam)
|
||||
}
|
||||
mse_df$Best = best
|
||||
#kableExtra::kable(mse_df)%>%
|
||||
# kable_styling(bootstrap_options = "striped", full_width = F,font_size = 20) %>%
|
||||
## row_spec(0, bold = T, color = "white", background = "#D7261E")%>%
|
||||
## column_spec(1, bold = T, border_right = T,color = "white", background = "#191970")%>%
|
||||
# column_spec(2:6,extra_css="text-align:Center")
|
||||
|
||||
mse_df
|
||||
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\ \
|
||||
|
||||
|
||||
\ \
|
||||
|
||||
# Clustering and Groups
|
||||
|
||||
\ \
|
||||
|
||||
## Clustering for Mixed type of data
|
||||
|
||||
|
||||
|
||||
```{r}
|
||||
|
||||
|
||||
clust_num = 5
|
||||
|
||||
get_clusters = function(dts, num, dim_plot,name)
|
||||
{
|
||||
l = list()
|
||||
if(is.null(dts$room_type))
|
||||
{
|
||||
l$cl = kmeans(dts,num)
|
||||
}
|
||||
else
|
||||
{
|
||||
l$cl = kproto(dts,num)
|
||||
|
||||
}
|
||||
|
||||
clust = list()
|
||||
|
||||
for (i in 1:num)
|
||||
{
|
||||
indexes = l$cl$cluster == i
|
||||
clust[[i]] = dts[indexes,]
|
||||
}
|
||||
|
||||
min_lat = dim_plot[1]
|
||||
max_lat = dim_plot[2]
|
||||
min_long = dim_plot[3]
|
||||
max_long= dim_plot[4]
|
||||
|
||||
|
||||
myplot= ggplot() + background_image(img)+ xlab('Longitude') + ylab('Latitude')+ theme(plot.margin = unit(c(1,1,1,1),"cm"),legend.title = element_text(colour="blue", size=10, face="bold")) + xlim(min_long, max_long) + ylim(min_lat,max_lat) +ggtitle(paste0("Clusters of ", name ))
|
||||
|
||||
|
||||
count = 1
|
||||
l$clust_plot = vector("list")
|
||||
for(el in clust)
|
||||
{
|
||||
myplot = myplot+ geom_point(data = el, aes(y = latitude, x = longitude),color= count)
|
||||
|
||||
p =ggplot()+ background_image(img)+geom_point(data = el, aes(y = latitude, x = longitude),color= count) + xlim(min_long, max_long) + ylim(min_lat,max_lat) + ggtitle(paste0("Cluster: ", count," of ", name ))
|
||||
|
||||
l$clust_plot[[as.character(count)]] = p
|
||||
|
||||
l$summary[[as.character(count)]] = summary(el)
|
||||
|
||||
count= count+1
|
||||
}
|
||||
l$myplot = myplot
|
||||
return(l)
|
||||
}
|
||||
|
||||
get_all_cluster = function(clust_data, clust_num, dim)
|
||||
{
|
||||
lis = vector("list")
|
||||
plots = vector("list")
|
||||
|
||||
cnt= 1
|
||||
for(sub in names(clust_data))
|
||||
{
|
||||
|
||||
lis[[sub]] = get_clusters(clust_data[[sub]], clust_num, dim, sub)
|
||||
plots[[cnt]] = lis[[sub]]$myplot
|
||||
cnt = cnt+1
|
||||
|
||||
}
|
||||
lis[["all_plots"]]= plots
|
||||
return(lis)
|
||||
}
|
||||
|
||||
borders = c(min(clust_data$all$latitude) ,max(clust_data$all$latitude), min(clust_data$all$longitude), max(clust_data$all$longitude))
|
||||
all_cluster = get_all_cluster(clust_data,5, borders)
|
||||
|
||||
|
||||
|
||||
```
|
||||
|
||||
```{r}
|
||||
|
||||
|
||||
multiplots <- function(plotlist, file=NULL,cols = 2, layout = NULL) {
|
||||
require(grid)
|
||||
|
||||
plots <- c(plotlist)
|
||||
|
||||
numPlots = length(plots)
|
||||
|
||||
if (is.null(layout)) {
|
||||
layout <- matrix(seq(1, cols * ceiling(numPlots/cols)),
|
||||
ncol = cols, nrow = ceiling(numPlots/cols),byrow =T)
|
||||
}
|
||||
|
||||
if (numPlots == 1) {
|
||||
print(plots[[1]])
|
||||
|
||||
} else {
|
||||
grid.newpage()
|
||||
pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))
|
||||
|
||||
for (i in 1:numPlots) {
|
||||
matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))
|
||||
|
||||
print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row,
|
||||
layout.pos.col = matchidx$col))
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
all_cluster$all_plots[[21]]
|
||||
|
||||
all_cluster$all$summary
|
||||
```
|
||||
|
||||
```{r}
|
||||
multiplots(all_cluster$all_plot[1:5], cols=3)
|
||||
```
|
||||
|
||||
```{r}
|
||||
|
||||
multiplots(all_cluster$all_plot[6:11], cols=3)
|
||||
|
||||
|
||||
```
|
||||
|
||||
```{r}
|
||||
|
||||
multiplots(all_cluster$all_plot[12:17], cols=3)
|
||||
|
||||
|
||||
```
|
||||
|
||||
|
||||
```{r}
|
||||
|
||||
multiplots(all_cluster$all_plot[c(18:20,22,23)], cols=3)
|
||||
|
||||
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\ \
|
||||
|
||||
## Hierarchical Cluster Analysis
|
||||
|
||||
```{r}
|
||||
|
||||
agg = aggregate(price ~neighbourhood_group+room_type, clust_data$all , mean)
|
||||
|
||||
|
||||
name_hc = c()
|
||||
for (n1 in substr(unique(agg$neighbourhood_group),1,5))
|
||||
{
|
||||
for(n2 in substr(unique(agg$room_type),1,3))
|
||||
{
|
||||
name_hc = c(name_hc, paste0(n1,"/",n2))
|
||||
}
|
||||
}
|
||||
rownames(agg) = name_hc
|
||||
|
||||
agg
|
||||
gower <- daisy(agg, metric = "gower")
|
||||
hc1 <- hclust(gower, method = "complete" )
|
||||
|
||||
plot(hc1, cex = 0.6, hang = -1)
|
||||
|
||||
|
||||
```
|
||||
|
||||
```{r}
|
||||
avg_dend_obj <- as.dendrogram(hc1)
|
||||
avg_col_dend <- color_branches(avg_dend_obj, h = 0.6)
|
||||
plot(avg_col_dend)
|
||||
|
||||
|
||||
|
||||
```
|
||||
|
||||
|
||||
|
||||
```{r}
|
||||
agg = aggregate(price ~neighbourhood_group, clust_data$all , mean)
|
||||
agg
|
||||
|
||||
rownames(agg) = c("Brooklyn","Manhattan",
|
||||
"Queens","Staten Island", "Bronx")
|
||||
agg$neighbourhood_group = NULL
|
||||
gower <- daisy(agg, metric = "gower")
|
||||
hc1 <- hclust(gower, method = "complete" )
|
||||
|
||||
plot(hc1, cex = 0.6, hang = -1)
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
```
|
||||
|
||||
|
||||
\ \
|
||||
|
||||
# Principal Component Analysis
|
||||
|
||||
|
||||
\ \
|
||||
|
||||
## PCAmixdata
|
||||
|
||||
|
||||
```{r}
|
||||
|
||||
## Split mixed dataset into quantitative and qualitative variables
|
||||
#split <- splitmix(dataset[1:5])
|
||||
|
||||
split = splitmix(clust_data$all)
|
||||
## PCA
|
||||
res.pcamix <- PCAmix(X.quanti=split$X.quanti,
|
||||
X.quali=split$X.quali,
|
||||
rename.level=TRUE)
|
||||
|
||||
res.pcamix
|
||||
|
||||
|
||||
```
|
||||
|
||||
```{r}
|
||||
|
||||
## Inspect principal components
|
||||
res.pcamix$eig
|
||||
|
||||
|
||||
```
|
||||
|
||||
```{r}
|
||||
|
||||
res.pcamix$quanti.cor
|
||||
res.pcamix$quali.eta2
|
||||
|
||||
```
|
||||
|
||||
|
||||
\ \
|
||||
|
||||
|
||||
## Factor Analysis of Mixed Data (FAMD)
|
||||
|
||||
|
||||
FAMD (base, ncp = 5, sup.var = NULL, ind.sup = NULL, graph = TRUE)
|
||||
- base : a data frame with n rows (individuals) and p columns (variables).
|
||||
- ncp: the number of dimensions kept in the results (by default 5)
|
||||
- sup.var: a vector indicating the indexes of the supplementary variables.
|
||||
- ind.sup: a vector indicating the indexes of the supplementary individuals.
|
||||
- graph : a logical value. If TRUE a graph is displayed.
|
||||
|
||||
```{r}
|
||||
|
||||
res.famd <- FAMD(clust_data$all, graph = F, ncp = 5)
|
||||
print(res.famd)
|
||||
```
|
||||
|
||||
|
||||
```{r}
|
||||
eig.val <- get_eigenvalue(res.famd)
|
||||
head(eig.val)
|
||||
|
||||
fviz_screeplot(res.famd)
|
||||
|
||||
```
|
||||
|
||||
|
||||
```{r}
|
||||
quanti.var <- get_famd_var(res.famd, "quanti.var")
|
||||
quanti.var
|
||||
fviz_famd_var(res.famd, "quanti.var", col.var = "contrib",
|
||||
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
|
||||
repel = TRUE)
|
||||
```
|
||||
```{r}
|
||||
quali.var <- get_famd_var(res.famd, "quali.var")
|
||||
quali.var
|
||||
fviz_famd_var(res.famd, "quali.var", col.var = "contrib",
|
||||
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07")
|
||||
)
|
||||
```
|
||||
|
||||
|
||||
|
||||
```{r}
|
||||
var <- get_famd_var(res.famd)
|
||||
var
|
||||
```
|
||||
|
||||
```{r}
|
||||
# Coordinates of variables
|
||||
head(var$coord)
|
||||
# Cos2: quality of representation on the factore map
|
||||
head(var$cos2)
|
||||
# Contributions to the dimensions
|
||||
head(var$contrib)
|
||||
```
|
||||
|
||||
```{r}
|
||||
# Plot of variables
|
||||
|
||||
fviz_famd_var(res.famd, repel = TRUE)
|
||||
# Contribution to the first dimension
|
||||
fviz_contrib(res.famd, "var", axes = 1)
|
||||
# Contribution to the second dimension
|
||||
fviz_contrib(res.famd, "var", axes = 2)
|
||||
# Contribution to the third dimension
|
||||
fviz_contrib(res.famd, "var", axes = 3)
|
||||
# Contribution to the forth dimension
|
||||
fviz_contrib(res.famd, "var", axes = 4)
|
||||
# Contribution to the fifth dimension
|
||||
fviz_contrib(res.famd, "var", axes = 5)
|
||||
```
|
||||
Binary file not shown.
Loading…
Reference in New Issue