YC_Investment_Clustering
Szymon Karkoszka
2023-02-28
Introduction
Y Combinator is one of the most renowned startup accelerators in the world. Since its founding in 2005, Y Combinator has invested in more than 2,000 startups, including outsanding names such as Airbnb, Dropbox, Coinbase or Reddit. The Y Combinator investment dataset, which contains information on startups that received funding from Y Combinator between 2005 and 2019, provides a valuable resource for exploring trends and patterns in startup funding.
In this project, we will explore the Y Combinator investment dataset and apply several data mining techniques to gain insights into the characteristics of successful Y Combinator startups. We will focus on three main techniques: clustering, dimension reduction, and association rules.
First, we will use clustering techniques to group startups based on their categories and total amount of money raised, with the goal of identifying groups of companies with similar funding patterns and business focuses.
Next, we will explore dimension reduction techniques to identify important features that contribute to the success of Y Combinator startups. This will allow us to gain a better understanding of the factors that are associated with successful startups.
Finally, we will apply association rule mining techniques to identify relationships between different features of the Y Combinator investment dataset, such as the relationship between the funding amount and the type of industry.
Overall, the aim of this project is to provide a comprehensive analysis of the Y Combinator investment dataset and to gain insights into the characteristics of successful Y Combinator startups. By applying these data mining techniques, we hope to provide valuable insights for entrepreneurs, investors, and anyone interested in the startup ecosystem.
Loading packages
To do the analysis, the following packages will be needed.
packages <- c("tidyverse", "readr", "corrplot", "ggplot2", "GGally",
"patchwork", "tibble", "patchwork", "gridExtra", "RColorBrewer",
"factoextra", "labdsv", "maptools", "psych", "ClusterR",
"readxl", "cluster", "flexclust", "fpc", "clustertend",
"ggthemes", "plotly", "stringr", "missMDA", "ade4", "smacof",
"Rtsne", "psy", "scales", "kableExtra", "pdp", "jpeg", "dplyr")
# Load packages if not already loaded
for (package in packages) {
if (!require(package, character.only = TRUE)) {
install.packages(package)
library(package, character.only = TRUE)
}
}The dataset contains information on startups that received funding from Y Combinator between 2005 and 2019. It includes data on over 2,000 startups, including information on the startup’s name, category, funding stage, funding type, funding amount, pre-money valuation, post-money valuation, and more.
Some key features of the dataset include:
Funding amount: The total amount of money that the startup received from Y Combinator. Funding stage: The stage of funding that the startup received (e.g., ). Category: The category or industry that the startup operates in (e.g., healthcare, e-commerce, education). Funding type: The type of funding that the startup received (e.g., seed, series A, series B). Pre-money valuation: The estimated value of the company before receiving funding.
#upload the dataset
data <- read.csv("YC.csv")
#present column names
colnames(data)## [1] "Name"
## [2] "Transaction.Name"
## [3] "Funding.Type"
## [4] "Money.Raised.Currency..in.USD."
## [5] "Announced.Date"
## [6] "Funding.Stage"
## [7] "Pre.Money.Valuation.Currency..in.USD."
## [8] "Description"
## [9] "Categories"
## [10] "Location"
## [11] "Website"
## [12] "Revenue.Range"
## [13] "Total.Funding.Amount.Currency..in.USD."
## [14] "Funding.Status"
## [15] "Number.of.Funding.Rounds"
## [16] "Lead.Investors"
## [17] "Investor.Names"
## [18] "Number.of.Investors"
## [19] "Number.of.Partner.Investors"head(data)## Name Transaction.Name Funding.Type
## 1 Copia Seed Round - Copia Seed
## 2 Suiteness Series A - Suiteness Series A
## 3 Astranis Seed Round - Astranis Seed
## 4 Shield Bio Seed Round - Shield Bio Seed
## 5 Platzi Seed Round - Platzi Seed
## 6 Kisan Network Seed Round - Kisan Network Seed
## Money.Raised.Currency..in.USD. Announced.Date Funding.Stage
## 1 3100000 2016-03-22 Seed
## 2 5000000 2016-12-14 Early Stage Venture
## 3 120000 2016-03-22 Seed
## 4 4100000 2017-02-23 Seed
## 5 NA 2014-12-01 Seed
## 6 NA 2016-06-01 Seed
## Pre.Money.Valuation.Currency..in.USD.
## 1 NA
## 2 NA
## 3 NA
## 4 NA
## 5 NA
## 6 NA
## Description
## 1 Copia is the next-generation technology platform for food waste management.
## 2 Suiteness is a free-to-join hotel booking website connecting hotel rooms and suites.
## 3 Astranis is building small, low-cost telecommunications satellites.
## 4 Shield Bio - using ultra-fast sequencing to prevent antibiotic resistance
## 5 Platzi is an effective online education platform that offers classes on marketing, learn coding, business, and design.
## 6 Kisan Network is an online marketplace for Indian agriculture.
## Categories
## 1 Analytics, Communities, Enterprise, Enterprise Software, Marketplace, SaaS, Sharing Economy, Sustainability, Waste Management
## 2 Family, Hospitality, Hotel, Leisure, Reservations, Travel
## 3 Aerospace, Internet, Telecommunications
## 4 Biotechnology, Genetics, Health Care, Health Diagnostics
## 5 Education, Edutainment, Recruiting, Training
## 6 Agriculture, AgTech, E-Commerce, Mobile
## Location
## 1 San Francisco, California, United States, North America
## 2 Oakland, California, United States, North America
## 3 San Francisco, California, United States, North America
## 4 San Jose, California, United States, North America
## 5 Mountain View, California, United States, North America
## 6 Gurgaon, Haryana, India, Asia
## Website Revenue.Range
## 1 https://www.GoCopia.com/ $1M to $10M
## 2 https://www.suiteness.com $1M to $10M
## 3 http://www.astranis.com/ $1M to $10M
## 4 http://shieldbio.com
## 5 https://platzi.com Less than $1M
## 6 http://www.kisannetwork.com
## Total.Funding.Amount.Currency..in.USD. Funding.Status
## 1 4580000 Seed
## 2 6000000 Early Stage Venture
## 3 13619998 Early Stage Venture
## 4 12100000 Early Stage Venture
## 5 16428315 Early Stage Venture
## 6 38300 Seed
## Number.of.Funding.Rounds Lead.Investors
## 1 2 Structure Capital
## 2 3 Bullpen Capital, Global Founders Capital
## 3 7
## 4 2 Andreessen Horowitz
## 5 5
## 6 3
## Investor.Names
## 1 8VC, Alps Investing Holdings LLC, Chivas Venture, Cynthia Ringo, David Pottruck, Emerson Collective, Eucalyptus Burlingame LLC, Jahan Ali, Jillian Manus, John Solomon, Jordan Kretchmer, Ken Tam, Lutetilla LLC, Lynett Capital, Maples Burlingame LLC, Mitchell Kapor, Moment Ventures, Nurzhas Makishev, Riggs Capital Partners, Steve Case, Structure Capital, Toyota USA, Y Combinator
## 2 AltaIR Capital, Bullpen Capital, David Hauser, FundersClub, Global Founders Capital, HVF Labs, Jared Ablon, Kima Ventures, MetaProp NYC, Muhsen Syed, Rocket Internet, Roland Tanner, SciFi VC, Scott Banister, Tilo Bonow, Y Combinator
## 3 ACE & Company, Fifty Years, Jaan Tallinn, Lars Rasmussen, Refactor Capital, S2 Capital, Samvit Ramadurgam, Wei Guo, Y Combinator
## 4 Andreessen Horowitz, Friále, Josh Buckley, Refactor Capital, SGH CAPITAL, Soma Capital, Y Combinator
## 5 500 Startups, Amasia, BoomStartup, Deepak Desai, Elies Campo, FundersClub, GE32 Capital, Graph Ventures, Josh Jones, Mind the Seed - MTS Fund, TA Ventures, Thomas Floracks, Y Combinator, Zillionize Angel
## 6 FundersClub, Venture Highway, Y Combinator
## Number.of.Investors Number.of.Partner.Investors
## 1 23 10
## 2 16 2
## 3 9 NA
## 4 7 6
## 5 14 NA
## 6 3 NAFirst, let’s dive into the data
#Funding ype
table(data$`Funding.Type`)##
## Angel Convertible Note Corporate Round
## 30 10 1
## Debt Financing Funding Round Grant
## 2 11 8
## Pre-Seed Product Crowdfunding Seed
## 37 1 2188
## Series A Series B Series C
## 155 61 27
## Series D Series E Series F
## 5 3 2
## Venture - Series Unknown
## 44#money.Raised
options(scipen = 999)
summary(data$`Money.Raised.Currency..in.USD.`, na.rm = TRUE)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 6000 120000 150000 5408455 2000000 1000000000 706#Announced data
str(data$`Announced.Date`)## chr [1:2585] "2016-03-22" "2016-12-14" "2016-03-22" "2017-02-23" ...#founding stage
table(data$`Funding.Stage`)##
## Early Stage Venture Late Stage Venture Seed
## 77 216 37 2255#Premoney Valuation
summary(data$`Pre.Money.Valuation.Currency..in.USD.`)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 399603 11684720 350000000 925282590 1150000000 7700000000 2538Deep Dive into the data
Let’s first summerise how many comapnies was found per year.
library(ggplot2)
# Convert the Announced.Date column to a date format
data$Announced.Date <- as.Date(data$Announced.Date, format = "%Y-%m-%d")
# Count the number of startups announced per year
startup_count_per_year <- table(format(data$Announced.Date, "%Y"))
print(startup_count_per_year)##
## 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
## 10 18 37 45 49 69 113 173 126 259 231 294 339 371 451# create bar plot
ggplot(data = data.frame(Year = names(startup_count_per_year), Count = as.numeric(startup_count_per_year)),
aes(x = Year, y = Count, fill = Year)) +
geom_col() +
scale_fill_viridis_d() +
ggtitle("Number of Startups Announced per Year") +
xlab("Year") +
ylab("Count") +
theme_minimal()
Becasue YC is a seed investor we would like to focus on Seed rounds. To do this, let’s create a new data set.
Seed_data <- data [data$Funding.Type == "Seed", ]Becasue we would like to analysis only Companies which raised money. We will just omit the companies without data about raised money.
Raised_Money<- Seed_data [complete.cases(c(Seed_data$`Money.Raised.Currency..in.USD.`)),]I would like to first divide the location for 4 separate columns -> City, State, Country, Continent.
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.0 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ lubridate 1.9.2 ✔ tibble 3.1.8
## ✔ purrr 1.0.1 ✔ tidyr 1.3.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errorsRaised_Money <- Raised_Money %>%
separate(Location, into = c("City", "State", "Country", "Continent"), sep = ", ", remove = FALSE)## Warning: Expected 4 pieces. Missing pieces filled with `NA` in 12 rows [129, 206, 230,
## 492, 774, 781, 785, 965, 1021, 1022, 1060, 1153].library(ggplot2)
library(dplyr)
data_location <-Raised_Money
data_location %>%
group_by(Location) %>%
summarize(Total_Money_Raised = sum(Money.Raised.Currency..in.USD.)) %>%
top_n(10) %>%
mutate(Location = factor(Location, levels = rev(Location))) %>%
ggplot(aes(x = Location, y = log(Total_Money_Raised), fill = Location)) +
geom_col() +
scale_y_continuous(labels = scales::comma_format()) +
labs(x = "Location", y = "Total Money Raised (log scale)", fill = "Location") +
theme_bw()## Selecting by Total_Money_Raised
library(ggplot2)
library(dplyr)
# select the columns of interest
df_loc_sum <- Raised_Money %>%
group_by(Location) %>%
summarise(Total_Money_Raised = sum(Money.Raised.Currency..in.USD.)) %>%
ungroup() %>%
filter(Location != "") %>% # remove any rows with empty Location
top_n(10) # keep only the top 10 locations by Total_Money_Raised## Selecting by Total_Money_Raised# create a customized color palette
my_colors <- c("#3366cc", "#dc3912", "#ff9900", "#109618", "#990099",
"#0099c6", "#dd4477", "#66aa00", "#b82e2e", "#316395")
# create the bar chart
ggplot(df_loc_sum, aes(x = reorder(Location, Total_Money_Raised), y = Total_Money_Raised, fill = Location)) +
geom_bar(stat = "identity") +
scale_fill_manual(values = my_colors) +
labs(title = "Total Money Raised by Top 10 Locations",
x = "Location",
y = "Total Money Raised (in USD)",
fill = "") +
theme(plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 45, hjust = 1),
legend.position = "none")
library(ggplot2)
library(dplyr)
# select the columns of interest
df_loc_sum <- Raised_Money %>%
separate(Location, into = c("City", "State", "Country", "Continent"), sep = ", ") %>%
group_by(Continent, Country) %>%
summarise(Total_Money_Raised = sum(Money.Raised.Currency..in.USD.)) %>%
filter(!is.na(Country)) # remove any rows with missing Country## Warning: Expected 4 pieces. Missing pieces filled with `NA` in 12 rows [129, 206, 230,
## 492, 774, 781, 785, 965, 1021, 1022, 1060, 1153].## `summarise()` has grouped output by 'Continent'. You can override using the
## `.groups` argument.# select the top 5 countries for Europe only
europe_data <- df_loc_sum %>%
group_by(Continent) %>%
filter(Continent == "Europe") %>%
slice_max(Total_Money_Raised, n = 5) %>%
ungroup()
# create a customized color palette
my_colors <- c("#3366cc", "#dc3912", "#ff9900", "#109618", "#990099",
"#0099c6", "#dd4477", "#66aa00", "#b82e2e", "#316395",
"#ff0000", "#00ff00", "#0000ff", "#ffff00", "#ff00ff")
# create the bar chart
ggplot(europe_data, aes(x = reorder(Country, Total_Money_Raised), y = Total_Money_Raised, fill = Country)) +
geom_bar(stat = "identity") +
scale_fill_manual(values = my_colors) +
labs(title = "Total Money Raised by Top 10 Countries in Europe",
x = "Country",
y = "Total Money Raised (in USD)",
fill = "") +
theme(plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 45, hjust = 1),
legend.position = "none")
Total Money Raised by Top 10 Countries in Asia + Oceania
# select the top 5 countries for Asia + Oceania only
asia_oceania_data <- df_loc_sum %>%
filter(Continent %in% c("Asia", "Oceania")) %>%
group_by(Continent, Country) %>%
summarise(Total_Money_Raised = sum(Total_Money_Raised)) %>%
slice_max(Total_Money_Raised, n = 10) %>%
ungroup()## `summarise()` has grouped output by 'Continent'. You can override using the
## `.groups` argument.# create a customized color palette
my_colors <- c("#3366cc", "#dc3912", "#ff9900", "#109618", "#990099",
"#0099c6", "#dd4477", "#66aa00", "#b82e2e", "#316395",
"#ff0000", "#00ff00", "#0000ff", "#ffff00", "#ff00ff")
# create the bar chart
ggplot(asia_oceania_data, aes(x = reorder(Country, Total_Money_Raised), y = Total_Money_Raised, fill = Country)) +
geom_bar(stat = "identity") +
scale_fill_manual(values = my_colors) +
labs(title = "Total Money Raised by Top 10 Countries in Asia and Oceania",
x = "Country",
y = "Total Money Raised (in USD)",
fill = "") +
theme(plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 45, hjust = 1),
legend.position = "none")
Total Money Raised by Top 6 Countries in Africa
# select the top 6 countries for Africa only
Africa_data <- df_loc_sum %>%
group_by(Continent) %>%
filter(Continent == "Africa") %>%
slice_max(Total_Money_Raised, n = 6) %>%
ungroup()
# create a customized color palette
my_colors <- c("#3366cc", "#dc3912", "#ff9900", "#109618", "#990099",
"#0099c6", "#dd4477", "#66aa00", "#b82e2e", "#316395",
"#ff0000", "#00ff00", "#0000ff", "#ffff00", "#ff00ff")
# create the bar chart
ggplot(Africa_data, aes(x = reorder(Country, Total_Money_Raised), y = Total_Money_Raised, fill = Country)) +
geom_bar(stat = "identity") +
scale_fill_manual(values = my_colors) +
labs(title = "Total Money Raised by Top 6 Countries in Africa",
x = "Country",
y = "Total Money Raised (in USD)",
fill = "") +
theme(plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 45, hjust = 1),
legend.position = "none")
Total Money Raised by Top 3 Countries in South America
# select the top 3 countries for North America only
North_America_data <- df_loc_sum %>%
group_by(Continent) %>%
filter(Continent == "North America") %>%
slice_max(Total_Money_Raised, n = 3) %>%
ungroup()
# create a customized color palette
my_colors <- c("#3366cc", "#dc3912", "#ff9900", "#109618", "#990099",
"#0099c6", "#dd4477", "#66aa00", "#b82e2e", "#316395",
"#ff0000", "#00ff00", "#0000ff", "#ffff00", "#ff00ff")
# create the bar chart
ggplot(North_America_data, aes(x = reorder(Country, Total_Money_Raised), y = Total_Money_Raised, fill = Country)) +
geom_bar(stat = "identity") +
scale_fill_manual(values = my_colors) +
labs(title = "Total Money Raised by Top 3 Countries in North America",
x = "Country",
y = "Total Money Raised (in USD)",
fill = "") +
theme(plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 45, hjust = 1),
legend.position = "none")
South America
Total Money Raised by Top 7 Countries in South America
# select the top 7 countries for South America only
South_America_data <- df_loc_sum %>%
group_by(Continent) %>%
filter(Continent == "South America") %>%
slice_max(Total_Money_Raised, n = 7) %>%
ungroup()
# create a customized color palette
my_colors <- c("#3366cc", "#dc3912", "#ff9900", "#109618", "#990099",
"#0099c6", "#dd4477", "#66aa00", "#b82e2e", "#316395",
"#ff0000", "#00ff00", "#0000ff", "#ffff00", "#ff00ff")
# create the bar chart
ggplot(South_America_data, aes(x = reorder(Country, Total_Money_Raised), y = Total_Money_Raised, fill = Country)) +
geom_bar(stat = "identity") +
scale_fill_manual(values = my_colors) +
labs(title = "Total Money Raised by Top 7 Countries in South America",
x = "Country",
y = "Total Money Raised (in USD)",
fill = "") +
theme(plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 45, hjust = 1),
legend.position = "none")
Total money raised by Continent
Continents_data <- df_loc_sum %>%
arrange(Total_Money_Raised)
ggplot(Continents_data, aes(x = reorder(Continent, Total_Money_Raised), y = Total_Money_Raised, fill = Continent)) +
geom_bar(stat = "identity") +
scale_fill_manual(values = my_colors) +
labs(title = "Total Money Raised by Continents",
x = "Continent",
y = "Total Money Raised (in USD)",
fill = "") +
theme(plot.title = element_text(hjust = 0.5),
axis.text.x = element_text(angle = 45, hjust = 1),
legend.position = "none")
Normalised the data
# Load the dataset
Clustering_Raised_Total <- data.frame(Money = Raised_Money$Money.Raised.Currency..in.USD., Total_Funding = Raised_Money$Total.Funding.Amount.Currency..in.USD.)
# Define function to remove outliers using Tukey method
remove_outliers <- function(x, na.rm = TRUE, k = 1.5) {
qnt <- quantile(x, probs = c(0.25, 0.75), na.rm = na.rm)
H <- k * IQR(x, na.rm = na.rm)
x[x < (qnt[1] - H)] <- NA
x[x > (qnt[2] + H)] <- NA
x
}
# Remove outliers from both columns using Tukey method
Clustering_Raised_Total$Money <- remove_outliers(Clustering_Raised_Total$Money)
Clustering_Raised_Total$Total_Funding <- remove_outliers(Clustering_Raised_Total$Total_Funding)
# Remove rows with NAs
Clustering_Raised_Total <- na.omit(Clustering_Raised_Total)
Clustering_Norm <- as.data.frame(scale(Clustering_Raised_Total))
# Original data
ggplot(Clustering_Raised_Total, aes(x=Money, y=Total_Funding)) +
geom_point() +
labs(title="Original data") +
theme_bw()
# Normalized data
ggplot(Clustering_Norm, aes(x=Money, y=Total_Funding)) +
geom_point() +
labs(title="Normalized data") +
theme_bw()
library(cluster)
library(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(flexclust)## Ładowanie wymaganego pakietu: grid## Ładowanie wymaganego pakietu: lattice## Ładowanie wymaganego pakietu: modeltools## Ładowanie wymaganego pakietu: stats4library(fpc)
library(clustertend)## Package `clustertend` is deprecated. Use package `hopkins` instead.library(ClusterR)
library(psych)##
## Dołączanie pakietu: 'psych'## Następujące obiekty zostały zakryte z 'package:ggplot2':
##
## %+%, alphalibrary(ggplot2)
library(reshape2)##
## Dołączanie pakietu: 'reshape2'## Następujący obiekt został zakryty z 'package:tidyr':
##
## smithslibrary(gridExtra)##
## Dołączanie pakietu: 'gridExtra'## Następujący obiekt został zakryty z 'package:dplyr':
##
## combinebss <- numeric()
wss <- numeric()
# Run the algorithm for different values of k
set.seed(1234)
for(i in 1:10){
# For each k, calculate Money and Total_Funding
bss[i] <- kmeans(Clustering_Norm, centers=i)$betweenss
wss[i] <- kmeans(Clustering_Norm, centers=i)$tot.withinss
}
# Between-cluster sum of squares vs Choice of k
p3 <- qplot(1:10, bss, geom=c("point", "line"),
xlab="Number of clusters", ylab="Between-cluster sum of squares") +
scale_x_continuous(breaks=seq(0, 10, 1)) +
theme_bw()## Warning: `qplot()` was deprecated in ggplot2 3.4.0.# Total within-cluster sum of squares vs Choice of k
p4 <- qplot(1:10, wss, geom=c("point", "line"),
xlab="Number of clusters", ylab="Total within-cluster sum of squares") +
scale_x_continuous(breaks=seq(0, 10, 1)) +
theme_bw()
# Subplot
grid.arrange(p3, p4, ncol=2)
# Load required libraries
library(cluster)
library(factoextra)
# Standardize the data
Clustering_Raised_Total_norm <- scale(Clustering_Raised_Total)
# Perform clara clustering with k=3
set.seed(1234)
clara_flex <- eclust(Clustering_Raised_Total_norm, "clara", k=3) 
# Summarize the clustering results
summary(clara_flex)## Object of class 'clara' from call:
## fun_clust(x = x, k = k)
## Medoids:
## Money Total_Funding
## 21 -0.4470283 -0.59542725
## 121 -0.4470283 2.13854972
## 648 2.3943258 -0.01217883
## Objective function: 0.4062792
## Numerical information per cluster:
## size max_diss av_diss isolation
## [1,] 901 1.682892 0.2268980 0.6155473
## [2,] 133 2.947831 0.9189793 1.0782210
## [3,] 174 4.023056 0.9432529 1.3869745
## Average silhouette width per cluster:
## [1] 0.8496122 0.4545784 0.4903966
## Average silhouette width of best sample: 0.7543779
##
## Best sample:
## [1] 19 21 61 121 177 272 307 310 335 361 387 475 508 522 549
## [16] 586 598 612 648 672 682 693 723 807 848 903 1001 1038 1172 1187
## [31] 1210 1220 1237 1246 1247 1306 1318 1340 1356 1361 1369 1455 1465 1466 1496
## [46] 1522
## Clustering vector:
## 6 11 12 16 18 19 20 21 22 23 24 30 34 36 37 39
## 1 2 3 3 1 3 3 1 1 1 1 3 1 1 1 1
## 41 43 45 46 48 49 51 52 53 55 56 57 58 60 61 62
## 2 2 1 1 1 3 3 1 1 2 2 3 3 1 3 3
## 63 66 67 68 73 75 76 77 81 82 84 88 89 90 93 94
## 2 3 1 2 1 2 1 2 3 3 1 2 1 2 1 1
## 95 96 97 98 100 101 103 105 107 108 109 110 113 114 115 116
## 2 2 1 1 1 1 1 1 1 2 3 2 3 1 1 1
## 118 119 120 121 122 123 125 127 128 129 130 131 132 133 134 135
## 2 1 1 2 1 3 2 3 2 1 3 2 2 1 1 2
## 137 138 139 141 143 144 145 146 147 148 149 150 151 152 153 154
## 1 1 1 1 1 1 2 1 2 3 3 1 1 2 1 1
## 155 157 158 159 160 161 164 165 166 167 168 170 171 173 174 176
## 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 3
## 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192
## 1 1 1 3 1 1 2 1 1 1 1 1 2 1 1 3
## 193 194 195 196 197 198 199 200 201 202 203 204 206 207 208 209
## 1 1 1 1 3 1 1 2 1 1 1 1 1 3 1 1
## 212 213 214 215 217 218 219 221 222 223 224 225 226 228 229 230
## 3 3 1 1 3 1 2 3 1 2 1 2 1 1 3 1
## 231 232 234 235 236 237 238 239 240 242 243 244 245 246 247 248
## 1 1 1 2 2 2 2 1 1 1 1 3 1 1 1 3
## 249 250 251 253 254 255 256 258 259 260 261 263 265 266 267 268
## 1 3 1 1 1 1 1 1 2 3 1 1 1 1 1 2
## 269 270 272 273 274 275 276 277 278 279 281 282 283 284 285 286
## 1 1 1 2 1 3 1 1 3 1 1 3 1 2 1 3
## 287 288 289 290 291 293 294 295 296 297 298 299 300 301 302 303
## 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1
## 304 305 306 307 308 309 310 311 312 313 314 315 316 318 319 320
## 2 1 1 1 1 3 1 1 3 1 1 1 1 1 1 3
## 321 323 324 326 327 329 330 331 332 333 335 336 337 338 339 340
## 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1
## 343 344 345 346 347 349 351 352 353 354 356 357 358 359 360 361
## 1 1 2 2 1 1 3 1 3 1 2 1 1 1 3 1
## 362 363 364 365 366 367 369 370 371 374 375 376 377 378 380 381
## 1 1 1 1 1 1 3 1 1 1 2 2 3 2 1 3
## 382 384 386 387 388 389 390 391 392 393 394 396 397 398 399 400
## 1 1 1 2 1 1 1 2 1 1 2 1 1 3 1 3
## 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416
## 1 2 1 1 1 1 3 2 1 1 1 2 1 3 1 1
## 417 418 419 420 421 422 423 425 426 427 428 429 430 432 433 434
## 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1
## 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 451
## 1 2 1 1 1 3 1 1 1 1 1 1 1 1 2 2
## 453 454 455 456 460 461 462 463 464 465 466 467 468 469 470 471
## 2 1 1 1 1 1 1 2 1 1 2 1 2 1 2 3
## 472 473 474 475 476 477 479 480 481 482 483 484 485 487 488 489
## 2 1 1 1 2 1 1 3 1 1 1 1 1 1 1 3
## 490 492 493 494 495 498 499 500 501 502 503 504 505 506 507 508
## 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
## 509 510 511 512 513 514 515 516 517 519 520 521 522 523 524 525
## 1 1 3 1 1 1 3 1 1 1 2 1 1 1 1 1
## 528 529 530 532 533 534 536 537 538 540 541 543 544 545 546 547
## 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1
## 548 549 550 551 552 553 555 557 558 559 560 561 562 564 565 566
## 2 1 1 1 1 1 1 3 1 1 1 1 1 3 1 3
## 567 568 573 575 577 578 579 580 581 582 583 584 586 588 589 590
## 1 1 1 1 1 1 3 2 1 1 1 3 1 1 1 2
## 591 592 594 595 596 597 598 599 600 601 602 604 605 606 607 609
## 1 1 2 2 3 1 1 2 1 2 1 2 1 1 1 3
## 610 611 612 614 616 617 618 619 620 621 622 623 625 626 627 628
## 2 1 1 3 2 1 1 1 1 1 1 1 2 1 3 1
## 629 631 632 634 638 639 641 642 644 646 647 648 649 650 653 654
## 1 1 2 3 3 3 2 2 3 1 1 3 3 2 3 3
## 656 658 660 662 663 664 667 668 669 672 674 675 678 680 681 682
## 1 2 2 1 1 2 1 1 1 1 3 1 1 1 3 1
## 683 684 686 688 689 690 691 693 694 695 696 697 698 700 702 703
## 3 3 3 1 1 2 3 1 1 1 2 3 1 2 1 2
## 704 706 707 708 709 710 711 712 713 714 715 718 720 721 722 723
## 3 1 1 3 1 1 1 3 3 1 3 3 1 3 1 3
## 724 725 726 727 728 730 731 734 735 736 738 740 741 743 744 746
## 1 1 1 1 1 1 1 1 1 3 1 3 1 1 1 1
## 747 748 750 753 755 758 759 761 763 764 765 766 768 770 771 773
## 3 1 1 1 2 1 2 1 1 1 1 1 3 3 1 1
## 774 779 780 781 783 785 786 787 788 790 791 795 797 798 800 801
## 1 1 1 1 2 1 2 1 1 1 1 1 3 1 1 1
## 804 806 807 808 810 812 813 814 815 816 817 821 822 823 825 826
## 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 827 828 831 832 834 835 836 838 840 841 844 845 846 848 850 851
## 1 2 3 3 2 2 3 1 3 1 1 3 1 2 1 3
## 852 853 854 855 856 857 861 863 865 866 867 869 871 876 881 883
## 1 1 1 2 1 1 3 1 2 1 1 3 1 3 3 3
## 884 885 892 896 903 904 911 912 913 916 917 918 919 920 921 922
## 3 3 1 3 1 3 3 1 3 3 3 3 3 1 3 1
## 924 927 928 929 930 931 933 934 935 936 937 938 939 940 941 942
## 3 3 3 1 1 3 1 1 3 1 1 1 3 1 3 1
## 943 944 945 946 949 950 951 952 953 954 955 956 957 958 959 960
## 1 2 3 1 1 1 3 1 1 1 1 1 1 1 1 1
## 961 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 978 979 980 981 982 983 984 985 986 987 988 989 991 992 993 995
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1
## 996 997 999 1001 1003 1004 1005 1007 1008 1009 1010 1011 1012 1013 1014 1015
## 1 1 3 1 1 1 3 1 3 1 3 3 1 1 1 1
## 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079
## 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1
## 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1098 1099 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114
## 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1
## 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1128 1129 1130 1131 1132
## 1 1 1 1 1 1 1 1 1 1 1 3 1 2 3 1
## 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1164 1165
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1198 1199
## 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1
## 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215
## 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1
## 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1227 1228 1232 1233 1236 1237
## 1 1 1 1 1 1 1 2 1 1 1 2 3 1 1 1
## 1238 1239 1240 1242 1243 1244 1245 1246 1247 1248 1251 1252 1253 1254 1255 1256
## 1 1 3 1 3 1 1 1 1 1 1 1 1 1 3 3
## 1260 1261 1262 1263 1265 1266 1267 1268 1269 1270 1271 1272 1274 1275 1276 1277
## 1 1 3 1 1 1 1 1 1 1 1 1 2 1 1 1
## 1278 1279 1282 1283 1284 1285 1286 1288 1289 1290 1291 1292 1293 1294 1295 1296
## 3 1 1 3 1 3 2 1 1 1 1 2 3 1 1 1
## 1297 1298 1299 1301 1302 1304 1306 1307 1308 1310 1311 1312 1313 1314 1316 1317
## 3 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
## 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1330 1331 1332 1333 1334
## 3 1 1 1 1 3 1 1 1 1 1 2 2 1 1 1
## 1336 1337 1338 1339 1340 1341 1342 1344 1345 1346 1347 1348 1349 1350 1351 1352
## 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1
## 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1367 1369 1370 1372 1374 1375
## 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 3
## 1376 1377 1378 1379 1380 1381 1382 1383 1385 1386 1387 1388 1389 1390 1391 1392
## 1 1 1 1 3 1 2 1 1 3 3 2 1 1 3 1
## 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1408 1409
## 1 1 1 2 1 3 1 1 1 1 1 1 1 1 1 1
## 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1425 1426
## 1 2 1 2 1 1 2 1 2 1 1 2 1 1 1 1
## 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442
## 1 1 1 3 1 1 1 1 1 3 1 2 1 3 1 1
## 1443 1444 1446 1447 1448 1451 1452 1454 1455 1457 1459 1460 1461 1463 1464 1465
## 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481
## 2 3 1 1 1 1 1 1 2 3 1 1 2 1 3 1
## 1483 1484 1486 1487 1489 1491 1492 1493 1494 1496 1498 1499 1502 1503 1504 1505
## 1 1 2 1 1 1 1 3 1 1 1 1 1 1 2 3
## 1506 1507 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523
## 1 1 1 1 1 3 1 2 1 3 1 1 1 1 1 2
## 1524 1525 1526 1527 1528 1530 1532 1533
## 3 3 1 1 1 1 1 1
##
## Silhouette plot information for best sample:
## cluster neighbor sil_width
## 6 1 2 0.921242423
## 18 1 2 0.921242423
## 21 1 2 0.921242423
## 24 1 2 0.921242423
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## 931 3 1 0.677254281
## 1505 3 1 0.677254281
## 836 3 1 0.677021979
## 123 3 1 0.675173696
## 360 3 1 0.675173696
## 840 3 1 0.675173696
## 918 3 1 0.675173696
## 1386 3 1 0.672768086
## 30 3 1 0.672086408
## 149 3 1 0.670549420
## 49 3 1 0.669728121
## 634 3 1 0.667992768
## 916 3 1 0.667190559
## 896 3 1 0.667093458
## 398 3 1 0.666890069
## 489 3 1 0.666890069
## 1131 3 1 0.666890069
## 217 3 1 0.666623448
## 312 3 1 0.666623448
## 648 3 1 0.665509272
## 158 3 1 0.664845251
## 192 3 1 0.664845251
## 1278 3 1 0.664845251
## 81 3 1 0.662099347
## 480 3 1 0.662099347
## 1011 3 1 0.662099347
## 884 3 1 0.661234827
## 681 3 1 0.660293290
## 197 3 1 0.656224452
## 1517 3 1 0.653793954
## 1297 3 1 0.652955712
## 82 3 1 0.651674305
## 1128 3 1 0.648524988
## 130 3 1 0.648029236
## 614 3 1 0.646589806
## 861 3 1 0.646419135
## 883 3 1 0.644778776
## 1008 3 1 0.644778776
## 924 3 1 0.643658448
## 515 3 1 0.643609384
## 1240 3 1 0.643257729
## 740 3 1 0.642493470
## 1232 3 1 0.638721573
## 691 3 1 0.638020895
## 941 3 1 0.638020895
## 1436 3 1 0.635101862
## 1283 3 1 0.634854638
## 951 3 1 0.631637961
## 885 3 1 0.630921176
## 400 3 1 0.630147000
## 229 3 1 0.629126476
## 113 3 1 0.629029050
## 250 3 1 0.629029050
## 917 3 1 0.629029050
## 1370 3 1 0.629029050
## 1005 3 1 0.628192199
## 713 3 1 0.618766140
## 704 3 1 0.617918579
## 1525 3 1 0.615788545
## 913 3 1 0.613400312
## 715 3 1 0.608877858
## 911 3 1 0.608054650
## 207 3 1 0.606720890
## 440 3 1 0.606720890
## 945 3 1 0.606720890
## 1369 3 1 0.606720890
## 993 3 1 0.599978122
## 999 3 1 0.599978122
## 1285 3 1 0.599978122
## 1323 3 1 0.599978122
## 1375 3 1 0.599978122
## 1010 3 1 0.593667744
## 1524 3 1 0.591129741
## 127 3 2 0.579445106
## 609 3 2 0.552402023
## 1318 3 1 0.548341341
## 381 3 1 0.542520967
## 723 3 1 0.540917854
## 736 3 1 0.540917854
## 845 3 1 0.540917854
## 566 3 1 0.506383423
## 596 3 1 0.506383423
## 286 3 1 0.505333019
## 644 3 1 0.500067918
## 176 3 2 0.496948133
## 544 3 2 0.493264279
## 1387 3 1 0.479589580
## 260 3 1 0.474038597
## 935 3 2 0.471179431
## 927 3 1 0.470911777
## 1480 3 1 0.470911777
## 712 3 1 0.462240852
## 1255 3 1 0.462240852
## 1391 3 1 0.455007065
## 244 3 1 0.449288551
## 58 3 2 0.425312549
## 530 3 1 0.420281305
## 1475 3 2 0.415641637
## 649 3 1 0.413598817
## 1467 3 1 0.391113765
## 290 3 1 0.387000992
## 275 3 2 0.383840360
## 248 3 2 0.379201444
## 653 3 2 0.369786569
## 1430 3 1 0.368346352
## 109 3 1 0.358275617
## 471 3 1 0.358275617
## 806 3 1 0.322428850
## 557 3 2 0.322375320
## 282 3 1 0.321927843
## 320 3 1 0.321927843
## 51 3 2 0.279228012
## 1293 3 1 0.272888608
## 353 3 2 0.249683581
## 697 3 1 0.247056713
## 832 3 2 0.241100385
## 876 3 1 0.237745040
## 1256 3 1 0.223464684
## 66 3 1 0.220151949
## 407 3 1 0.218551841
## 718 3 2 0.202721533
## 62 3 1 0.190405851
## 747 3 2 0.174079562
## 1380 3 1 0.159334685
## 564 3 1 0.151212069
## 770 3 2 0.149252124
## 639 3 2 0.137520154
## 869 3 2 0.135243260
## 212 3 2 0.126102548
## 180 3 2 0.124830609
## 683 3 1 0.120773937
## 1398 3 2 0.119018615
## 797 3 1 0.109144202
## 1198 3 2 0.102683383
## 16 3 2 0.085827647
## 638 3 2 0.085827647
## 674 3 1 0.079030300
## 654 3 1 0.074361079
## 148 3 2 0.066013410
## 1513 3 1 0.064579384
## 928 3 1 0.059468025
## 708 3 1 0.051644627
## 369 3 1 0.048745865
## 511 3 1 0.048745865
## 627 3 1 0.048745865
## 686 3 1 0.048745865
## 851 3 1 0.048745865
## 1243 3 1 0.048745865
## 1493 3 1 0.048745865
## 221 3 1 -0.002925266
##
## 1035 dissimilarities, summarized :
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.1813 0.6511 1.2836 2.5109 4.4639
## Metric : euclidean
## Number of objects : 46
##
## Available components:
## [1] "sample" "medoids" "i.med" "clustering" "objective"
## [6] "clusinfo" "diss" "call" "silinfo" "data"
## [11] "clust_plot" "nbclust"# Visualize the clustering results
fviz_cluster(clara_flex)
# Visualize the silhouette plot
fviz_silhouette(clara_flex)## cluster size ave.sil.width
## 1 1 901 0.85
## 2 2 133 0.45
## 3 3 174 0.49
library(factoextra)
get_clust_tendency(Clustering_Raised_Total_norm, 2, graph=TRUE, gradient=list(low="blue", high="white"), seed=1234)## $hopkins_stat
## [1] 0.989801
##
## $plot
f1 <- fviz_nbclust(Clustering_Raised_Total_norm, FUNcluster = kmeans, method = "silhouette") +
ggtitle("Optimal number of clusters \n K-means")
f2 <- fviz_nbclust(Clustering_Raised_Total_norm, FUNcluster = cluster::pam, method = "silhouette") +
ggtitle("Optimal number of clusters \n PAM")
grid.arrange(f1, f2, ncol=2)
km3 <- eclust(Clustering_Raised_Total_norm, k=3 , FUNcluster="kmeans", hc_metric="euclidean", graph=F)
c2 <- fviz_cluster(km3, data=Clustering_Raised_Total_norm, elipse.type="convex", geom=c("point")) + ggtitle("K-means with 3 clusters")
s2 <- fviz_silhouette(km3)## cluster size ave.sil.width
## 1 1 174 0.49
## 2 2 122 0.50
## 3 3 912 0.84grid.arrange(c2, s2, ncol=2)
Money_Q1 <- quantile(Raised_Money$Money.Raised.Currency..in.USD., 0.25)
Money_Q3 <- quantile(Raised_Money$Money.Raised.Currency..in.USD., 0.75)
Money_IQR <- Money_Q3 - Money_Q1
Money_lower <- Money_Q1 - 1.5 * Money_IQR
Money_upper <- Money_Q3 + 1.5 * Money_IQR
Total_Q1 <- quantile(Raised_Money$Total.Funding.Amount.Currency..in.USD., 0.25)
Total_Q3 <- quantile(Raised_Money$Total.Funding.Amount.Currency..in.USD., 0.75)
Total_IQR <- Total_Q3 - Total_Q1
Total_lower <- Total_Q1 - 1.5 * Total_IQR
Total_upper <- Total_Q3 + 1.5 * Total_IQR
# Remove outliers
Raised_Money_Out_of_Outliers <- subset(Raised_Money,
Raised_Money$Money.Raised.Currency..in.USD. >= Money_lower &
Raised_Money$Money.Raised.Currency..in.USD. <= Money_upper &
Raised_Money$Total.Funding.Amount.Currency..in.USD. >= Total_lower &
Raised_Money$Total.Funding.Amount.Currency..in.USD. <= Total_upper)
table(Raised_Money_Out_of_Outliers$Country, km3$cluster)##
## 1 2 3
## Argentina 1 0 1
## Australia 0 0 4
## Bangladesh 0 0 1
## Brazil 0 0 1
## Canada 11 2 35
## Chile 0 0 1
## China 2 0 8
## Colombia 1 1 4
## Czech Republic 0 0 1
## Denmark 1 1 2
## Ecuador 0 0 1
## Egypt 0 0 3
## Estonia 0 1 0
## Finland 0 0 1
## France 0 0 9
## Germany 1 0 3
## Ghana 0 0 1
## Hong Kong 0 0 3
## Iceland 0 0 1
## India 3 3 22
## Indonesia 2 1 4
## Iraq 0 0 1
## Ireland 1 0 0
## Israel 0 0 3
## Malaysia 0 1 0
## Mexico 1 1 5
## Morocco 0 0 1
## Nigeria 2 2 7
## Panama 0 0 1
## Peru 0 0 2
## Poland 0 0 1
## Puerto Rico 0 0 1
## Singapore 1 2 6
## Slovenia 0 0 2
## South Africa 0 0 1
## South Korea 0 0 1
## Sweden 0 0 1
## Switzerland 0 0 1
## Tanzania 0 0 1
## United Kingdom 3 4 24
## United States 144 103 734
## Uruguay 0 0 1table(Raised_Money_Out_of_Outliers$Continent, km3$cluster)##
## 1 2 3
## Africa 2 2 14
## Asia 8 7 49
## Europe 6 6 46
## North America 156 106 776
## Oceania 0 0 4
## South America 2 1 11Raised_Money_Out_of_Outliers$Year <- format(as.Date(Raised_Money_Out_of_Outliers$Announced.Date, "%Y-%m-%d"), "%Y")
# Create a contingency table
table(Raised_Money_Out_of_Outliers$Year, km3$cluster)##
## 1 2 3
## 2005 0 0 1
## 2006 0 0 1
## 2007 0 0 11
## 2008 0 1 6
## 2009 0 4 7
## 2010 2 4 10
## 2011 7 2 9
## 2012 17 1 11
## 2013 10 6 42
## 2014 22 22 100
## 2015 14 16 100
## 2016 21 28 107
## 2017 29 19 116
## 2018 25 12 132
## 2019 27 7 259