---
title: \vspace{1in}Detecting Ransomware Addresses on the Bitcoin Blockchain using Random Forest and Self Organizing Maps
subtitle: \vspace{.5in}HarvardX PH125.9x Final Capstone CYO Project
          \vspace{.5in}
author: "Kaylee Robert Tejeda"
date: "11/11/2021"
abstract: "Ransomware is a persisent and growing threat in the world of cybersecurity. A specific area of focus involves detecting and tracking payments made to ransomware operators. While many attempts towards this goal have not made use of sophisticated machine learning methods, even those that have often result in models with poor precision or other performance issues. A two-step method is developed to address the issue of false positives and improve on previous results." 
keywords: 
- Bitcoin
- blockchain
- ransomware
- machine learning
- Random Forest
- Self Organizing Maps
- SOMs
- cryptocurrency
output: pdf_document
geometry: margin=2cm
---
```{r tic, echo=FALSE, include=FALSE}
##############################################################################
## Uncomment these commands to time the compilation of the script.
## the tictoc library needs to be installed for this to work.
##############################################################################

library(tictoc)
tic(quiet = FALSE)

```  

\def\bitcoinA{%
  \leavevmode
  \vtop{\offinterlineskip %\bfseries
    \setbox0=\hbox{B}%
    \setbox2=\hbox to\wd0{\hfil\hskip-.03em
    \vrule height .3ex width .15ex\hskip .08em
    \vrule height .3ex width .15ex\hfil}
    \vbox{\copy2\box0}\box2}}
    
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, out.width="400px", dpi=120)
def.chunk.hook  <- knitr::knit_hooks$get("chunk")
knitr::knit_hooks$set(chunk = function(x, options) {
  x <- def.chunk.hook(x, options)
  ifelse(options$size != "normalsize", paste0("\n \\", options$size,"\n\n", x,
                                              "\n\n \\normalsize"), x)
})

```

\newpage
&nbsp;
\vspace{25pt}
\tableofcontents

\newpage

## Introduction

  Ransomware attacks have gained the attention of security professionals, law enforcement, and financial regulatory officials.$^{[1]}$  The pseudo-anonymous Bitcoin network provides a convenient method for ransomware attackers to accept payments without revealing their identity or location.  The victims (usually hospitals or other large organizations) come to find that much if not all of their important organizational data have been encrypted with a secret key by an unknown attacker. They are instructed to make a payment to a specific Bitcoin address before a certain deadline to have their data decrypted before being deleted permanently.  
  
  The legal and financial implications of ransomware attacks are not of concern for the purpose of this analysis.  Many parties are interested in tracking illicit activity (such as ransomware payments) around the Bitcoin blockchain as soon as possible to minimize financial losses.  Daniel Goldsmith explains some of the reasons and methods of blockchain analysis at [Chainalysis.com](https://www.chainalysis.com/).$^{[2]}$  A ransomware attack could be perpetrated on an illegal darknet market site, for example. The news of such an attack might not be published at all, let alone in popular media. By analyzing the transaction record with a blockchain explorer such as [BTC.com](https://btc.com/), suspicious activity could be flagged in real time given a sufficiently robust model. It may, in fact, be the first public notice of such an event. Any suspicious addresses could then be blacklisted or banned from using other services. 
  
  Lists of known ransomware payment addresses have been compiled and analyzed using various methods.  One well known paper entitled "BitcoinHeist: Topological Data Analysis for Ransomware Detection on the Bitcoin Blockchain"$^{[3]}$ will be the source of our data set and the baseline to which we will compare our results.  In that paper, Akcora, et al. use Topological Data Analysis (TDA) to classify addresses on the Bitcoin blockchain into one of 28 known ransomware address groups. Addresses with no known ransomware associations are classified as "white".  The blockchain is then considered as a heterogeneous Directed Acyclic Graph (DAG) with two types of nodes describing *addresses* and *transactions*.  Edges are formed between the nodes when a transaction can be associated with a particular address.  
  
  Addresses on the Bitcoin network may appear many times, with different inputs and outputs each time.  The Bitcoin network data has been divided into 24-hour time intervals with the UTC-6 timezone as a reference.  Speed is defined as the number of blocks the coin appears in during a 24-hour period and provides information on how quickly a coin moves through the network.  Speed can be an indicator of money laundering or coin mixing, as normal payments only involve a limited number of addresses in a 24 hour period, and thus have lower speeds when compared to "mixed" coins.  The temporal data can also help distinguish transactions by geolocation, as criminal transactions tend to cluster in time.

 With the graph defined as such, the following six numerical features$^{[2]}$ are associated with a given address:
   
   1)  *Income* - the total amount of coins sent to an address
   
   2)  *Neighbors* - the number of transactions that have this address as one of its output addresses
   
   3)  *Weight* - the sum of fraction of coins that reach this address from address that do not have any other inputs within the 24-hour window, which are referred to as "starter transactions"
   
   4)  *Length* - the number of non-starter transactions on its longest chain, where a chain is defined as an
acyclic directed path originating from any starter transaction and ending at the address in question
   
   5)  *Count* - The number of starter addresses connected to this address through a chain
   
   6)  *Looped* - The number of starter addresses connected to this address by more than one path
   
These variables are defined rather abstractly, viewing the blockchain as a topological graph with nodes and edges.  The rationale behind this approach is to quantify specific transaction patterns. Akcora$^{[3]}$ gives a thorough explanation in the original paper of how and why these features were chosen.  We shall treat the features as general numerical variables and will not seek to justify their definitions.  Several machine learning methods will be applied to the original data set from the paper by Akcora$^{[3]}$, and the results will be compared.

### Data

   This data set was discovered while exploring the [UCI Machine Learning Repository](https://archive.ics.uci.edu/ml/index.php)$^{[4]}$  as suggested in the project instructions.  The author of this report, interested in Bitcoin and other cryptocurrencies since (unsuccessfully) mining them on an ASUS netbook in rural Peru in late 2010, used *cryptocurrency* as a preliminary search term.  This brought up a single data set entitled ["BitcoinHeist: Ransomware Address Data Set"](https://archive.ics.uci.edu/ml/datasets/BitcoinHeistRansomwareAddressDataset#).  The data set was downloaded and the exploration began.

  
```{r install-load-libraries download-data, echo=FALSE, include=FALSE}

# Set the repository mirror to “0-Cloud” for maximum availability
r = getOption("repos") 
r["CRAN"] = "http://cran.rstudio.com"
options(repos = r)
rm(r)

# Install necessary packages if not already present
if(!require(tidyverse)) install.packages("tidyverse")
if(!require(caret)) install.packages("caret")
if(!require(randomForest)) install.packages("randomForest")
if(!require(kohonen)) install.packages("kohonen")
if(!require(parallel)) install.packages("parallel")
if(!require(matrixStats)) install.packages("matrixStats")

# Load Libraries
library(tidyverse)
library(caret)
library(randomForest)
library(kohonen)
library(parallel)
library(matrixStats)

# Download data
url <- 
  "https://archive.ics.uci.edu/ml/machine-learning-databases/00526/data.zip"
dest_file <- "data/data.zip"
if(!dir.exists("data"))dir.create("data")
if(!file.exists(dest_file))download.file(url, destfile = dest_file)

# Unzip as CSV
if(!file.exists("data/BitcoinHeistData.csv"))unzip(dest_file, 
                                                   "BitcoinHeistData.csv", 
                                                   exdir="data")

# Import data from CSV
ransomware <- read_csv("data/BitcoinHeistData.csv")

```

A summary of the data set tells the range of values and size of the sample.

```{r data-summary, echo=FALSE, size="tiny"}

# Summary
ransomware %>% summary() %>% knitr::kable()

```

A listing of the first ten rows provides a sample of the features associated with each observation.

```{r data-head, echo=FALSE, size="tiny"}

# Inspect data
ransomware %>% head() %>% knitr::kable()

```

This data set has 2,916,697 observations of ten features associated with a sample of transactions from the Bitcoin blockchain.  The ten features include *address* as a unique identifier, the six features defined previously (*income, neighbors, weight, length, count, loop*), two temporal features in the form of *year* and *day* (of the year as 1 to 365), and a categorical feature called *label* that categorizes each address as either "white" (meaning not connected to any ransomware activity), or one of 28 known ransomware groups as identified by three independent ransomware analysis teams (Montreal, Princeton, and Padua)$^{[3]}$ . 

The original research team downloaded and parsed the entire Bitcoin transaction graph from January 2009 to December 2018. Based on a 24 hour time interval, daily transactions on the network were extracted and the Bitcoin graph was formed. Network edges that transferred less than \bitcoinA 0.3 were filtered out since ransom amounts are rarely below this threshold. Ransomware addresses are taken from three widely adopted studies: Montreal, Princeton and Padua. "White" Bitcoin addresses were capped at one thousand per day while the entire network has up to 800,000 addresses daily.$^{[5]}$

### Goal

  The goal of this project is to apply different machine learning algorithms to the same data set used in the original paper to produce an acceptable predictive model for categorizing ransomware addresses correctly.  Improving on the results of the original paper in some way, while not strictly necessary for the purposes of the project, would be a notable sign of success.  
  
###  Outline of Steps Taken 

1. Analyze data set numerically and visually.  Notice any pattern, look for insights.
2. Binary separation using Self Organizing Maps.
3. Improved Binary separation using Random Forest.
4. Categorical classification using Self Organizing Maps.
5. Visualize clustering to analyze results further.
6. Generate Confusion Matrix to quantify results.

---

## Data Analysis

### Hardware Specification

   All of the analysis in this report was conducted on a single laptop computer, a Lenovo Yoga S1 from late 2013 with the following specs:
   
   - CPU:  Intel i7-4600U @ 3.300GHz (4th Gen quad-core i7 x86_64)
   - RAM:  8217MB DDR3L @ 1600 MHz  (8 GB)
   - OS:   Slackware64-current (15.0 RC1) `x86_64-slackware-linux-gnu` (64-bit GNU/Linux)
   - R version 4.0.0 (2020-04-24) -- "Arbor Day" (built from source using scripts from [slackbuilds.org](https://slackbuilds.org/))
   - RStudio Version 1.4.1106 "Tiger Daylily" (2389bc24, 2021-02-11) for CentOS 8 (converted using `rpm2tgz`)

###  Data Preparation

  It is immediately apparent that this is a rather large data set.  The usual practice of partitioning out eighty to ninety percent of the data for a training set results in a data set that is too large to process given the hardware available.  For reasons that no longer apply, the original data set was first split in half with 50% reserved as "validation set" and the other 50% used as the "working set".  This working set was again split in half, to give a "training set" that was of a reasonable size to deal with.  At this point the partitions were small enough to work with, so the sample partitions were not further refined.  This is a potential area for later optimization. Careful sampling was carried out to ensure that the ransomware groups were represented in each sample.
  
```{r data-prep, echo=FALSE, include=FALSE}

# Turn labels into factors, "bw" is binary factor for ransomware/non-ransomware
ransomware <- ransomware %>%
  mutate(label=as.factor(label), 
         bw=as.factor(ifelse(label=="white", "white", "black")))

# Validation set made from 50% of BitcoinHeist data, for RAM considerations
test_index <- createDataPartition(y = ransomware$bw, 
                                  times = 1, p = .5, list = FALSE)

workset <- ransomware[-test_index,]
validation <- ransomware[test_index,]

# Split the working set into a training set and a test set @ 50%, RAM dictated
test_index <- createDataPartition(y = workset$bw,
                                  times = 1, p = .5, list = FALSE)

train_set <- workset[-test_index,]
test_set <- workset[test_index,]

# Find proportion of full data set that is ransomware
ransomprop <- mean(ransomware$bw=="black")

# Check for NAs
no_nas <- sum(is.na(ransomware))

```

#########################################################################

### Exploration and Visualization 

  The ransomware addresses make up less than 2% of the overall data set.  This presents a challenge as the target observations are sparse within the data set, especially when we consider that this is then divided into 28 subsets.  In fact, some of the ransomware groups have only a single member, making categorization a dubious task.  At least there are no missing values to worry about.
  
```{r cv-calcs, echo=FALSE}

# Keep only numeric columns, ignoring temporal features
ransomware_num <- ransomware %>% 
  select(income, neighbors, weight, length, count, looped)

# Check for variation across numerical columns using coefficients of variation
#
# Calculate standard deviations for each column
sds <- ransomware_num %>% as.matrix() %>% colSds()

# Calculate means for each column
means <- ransomware_num %>% as.matrix() %>% colMeans()

# Calculate CVs for each column
coeff_vars <- sds %/% means

#  Select the two features with the highest coefficients of variation
selected_features <- names(sort(coeff_vars, decreasing=TRUE))[1:2]

#Sample every 100th row due to memory constraints
train_samp <- train_set[seq(1, nrow(train_set), 100), ]

# Keep only numeric columns with highest coefficients of variation
train_num <- train_samp %>% select(selected_features[1], selected_features[2])

# Binary labels, black = ransomware, white = non-ransomware, train set
train_bw <- train_samp$bw 

#Sample every 100th row due to memory constraints to make test sample same size.
test_samp <- test_set[seq(1, nrow(train_set), 100), ]

# Dimension reduction again, selecting features with highest CVs
test_num <- test_samp %>% select(selected_features[1], selected_features[2])

# Binary labels for test set 
test_bw <- test_samp$bw 

```  

The proportion of ransomware addresses in the original data set is `r ransomprop`.  The total number of NA or missing values in the original data set is `r no_nas`.

```{r data-sparsness, echo=FALSE}

labels <- ransomware$label  %>% summary() 

knitr::kable(
    list(labels[1:15], labels[16:29]),
  caption = 'Ransomware group labels and frequency counts for full data set',
  booktabs = TRUE)

```

Let's take a look at the distribution of the different features.  Note how skewed the non-temporal features are, some of them being bimodal.  Looks better on a log scale x-axis.

```{r histograms, echo=FALSE, warning=FALSE, fig.align="center"}
########################################################
## Histograms of each of the columns to show skewness
## Plot histograms for each column using facet wrap
########################################################

# Remove non-numerical and temporal columns to look for patterns in 
# topologically defined features
train_hist <- train_samp %>% select(-address, -label, -bw, -day, -year)

# Apply pivot_longer function to facilitate facet wrapping
train_long <- train_hist %>%         
  pivot_longer(colnames(train_hist)) %>% 
  as.data.frame()

# Log scale on value axis, 
histograms <- ggplot(train_long, aes(x = value)) +  
  geom_histogram(aes(y = ..density..), bins=20) + 
  geom_density(col = "green", size = .5) +
  scale_x_continuous(trans='log2') +
  facet_wrap(~ name, scales = "free")

histograms + theme(axis.text.x = element_text(size = 8, angle=30, hjust=1))


```


Now we can compare the relative spread of each feature by calculating the coefficient of variation for each column.  Larger coefficients of variation indicate larger relative spread compared to other columns.

```{r cv-results, echo=FALSE, fig.align="center"}

# Summarize results in a table and a plot 
knitr::kable(coeff_vars)

plot(coeff_vars)

```

From this, it appears that `r selected_features[1]` has the widest range of variability, followed by `r selected_features[2]`.  These are also the features that are most strongly skewed to the right, meaning that a few addresses have really high values for each of these features while the bulk of the data set has very low values for these numbers.

Now do the following (after filling in methods, results, and conclusions, since those are done already):
  
  !) Break into groups somehow.  Graph variables per group?  Show how the variables are distributed for each ransomware group?  Percent ransomware per each day of the week, for example.  Is ransomware more prevalent on a particular day of the week?  Break other numerical values into bins, and graph percentage per bin.  Look for trends and correlations between groups/variables, and display them here.  MORE OF THIS....

```{r shrimp-percentage, echo=FALSE, include=FALSE}

# Count how many wallets have less than one full bitcoin
shrimp <- ransomware %>% filter(income < 10^8 )

```  
  
The percentage of wallets with less than one full bitcoin as their balance is `r mean(shrimp$bw == "black")` .

###############################################################################

### Insights Gained from Exploration

  From the previous visual and statistical exploration of the data, it becomes clear what the challenge is.  Ransomware related addresses are very sparse in the data set, making up less than 2% of all addresses.  That small percentage is also further classified into 28 groups.  Perhaps the original paper was a bit too ambitious in trying to categorize all the addresses into 29 categories, including the "white" addresses.  To simplify our approach, we will categorize the addresses in a binary way, either "white" or "black", where "black" signifies an association with ransomware transactions.  Asking this as a "ransomware or not-ransomware" question allows for application of methods that are known to be impractical otherwise.

---

## Modeling approach

  Akcora et al. applied a Random Forest approach to the data, however "Despite improving data scarcity, [...] tree based methods (i.e., Random Forest and XGBoost) fail to predict any ransomware family".[3, 11]  Considering all ransomware addresses as belonging to a single group might improve the predictive power of such methods, making Random Forest worth another try.  
  
  The topological description of the data set inspired a search for topological machine learning methods, although one does not necessitate the other.  Searching for *topo* in the documentation for the `caret` package [6] resulted in the entry for Self Organizing Maps, supplied by the `kohonen` package.  The description at CRAN [7] was intriguing enough to merit further investigation. 
  
  Initially, the categorization of ransomware into the 28 different families was attempted using SOMs.  This proved to be very resource intensive, requiring more time and RAM than was available at the time.  Although it did help to illuminate how SOMs are configured, the resource requirements of the script became a deterrent.  It was at this point that the SOMS were applied in a binary way, classifying all ransomware addresses as merely "black".  This seemed to reduce RAM usage to the point of being feasible on the available hardware.  
  
   Being unsure of the SOM method, since it was not covered in the coursework at any point, a familiar method was sought out to compare the results to.  This is when Random Forest was applied to the data set in a binary way.  Much to the surprise of the author, not only did the Random Forest approach result in an acceptable model, it surpassed the model produced by the SOM approach.
   
   The author was tempted to leave it there and write up a comparison of the two approaches to the binary problem.  However, a nagging feeling that more could be done eventually inspired a second look at the categorical problem of categorizing the ransomware addresses into the 28 families.  Given the high accuracy and precision of the Random Forest approach to the binary problem, it became apparent that the sparseness of the ransomware in the larger set had been eliminated completely, as had any chances of false positives.  There are a few cases of false negatives, depending on how the randomization is done during the sampling process.  However, the Random Forest method has never produced a false positive yet, meaning it never seems to predict a truly white address as being black.  Hence, by applying the Random Forest method first, we have essentially filtered out any possibility of false positives, which is exactly what plagued the original paper by Akcora et al.[3] 
   
   Finally, a two-part method was devised to first separate the addresses into black and white groups, and then further classify the black addresses into ransomware families.  Let's explore each of these separately.
  
### Method Part 0:  Binary SOMS as a first attempt to isolate ransomware addresses.

Lets see how well the SOM approach can model the data in a black/white fashion.

```{r binary SOMs, echo=FALSE, include=FALSE}
##############################################################################
## This is a first attempt using SOMs to model the data set as "black" and
## "white" addresses only.
##
## NOTE:  This is the most computationally heavy part of the paper and takes
## several hours to run to completion.  It is also completely optional, only
## used to compare with the better method. If, for some reason, you want to 
## compile the report without this section, you can just comment it all out
## or remove it because nothing is needed from Method Part 0 for any of the
## other methods.  In other words, it can be safely skipped if you are short on 
## tine or RAM.
##############################################################################

# Keep only numeric columns, ignoring dates and looped.
som1_train_num <- train_set %>% select(length, weight, count, neighbors, income)

# SOM function can only work on matrices
som1_train_mat <- as.matrix(scale(som1_train_num))

# Switching to supervised SOMs
som1_test_num <- test_set %>% select(length, weight, count, neighbors, income)

# Note that when we rescale our testing data we need to scale it
# according to how we scaled our training data.
som1_test_mat <- 
  as.matrix(scale(som1_test_num, center = attr(som1_train_mat, "scaled:center"),
                  scale = attr(som1_train_mat, "scaled:scale")))

# Binary outputs, black=ransomware, white=non-ransomware, train set
som1_train_bw <- train_set$bw %>% classvec2classmat()

# Same for test set
som1_test_bw <- test_set$bw %>% classvec2classmat()

# Create Data list for supervised SOM
som1_train_list <-
  list(independent = som1_train_mat, dependent = som1_train_bw)

############################################################################
## Calculate idea grid size according to:
## https://www.researchgate.net/post/How-many-nodes-for-self-organizing-maps
############################################################################

# Formulaic method 1
grid_size <- round(sqrt(5*sqrt(nrow(train_set))))
# Based on categorical number, method 2
#grid_size = ceiling(sqrt(length(unique(ransomware$bw))))
grid_size

# Create SOM grid
som1_train_grid <- 
  somgrid(xdim=grid_size, ydim=grid_size, topo="hexagonal", toroidal = TRUE)

## Now build the model.
som_model1 <- xyf(som1_train_mat, som1_train_bw,
                 grid = som1_train_grid, 
                 rlen = 100,
                 mode="pbatch", 
                 cores = detectCores(), # detectCores() - 1 
                 keep.data = TRUE
)


# Now test predictions

som1_test_list <- list(independent = som1_test_mat, dependent = som1_test_bw)

ransomware.prediction1 <- predict(som_model1, newdata = som1_test_list)


# Confusion Matrix
som1_cm_bw <- 
  confusionMatrix(ransomware.prediction1$prediction[[2]], test_set$bw)

# Now test predictions of validation set

# Switching to supervised SOMs
valid_num <- validation %>% select(length, weight, count, neighbors, income)

# Note that when we rescale our testing data we need to scale it 
# according to how we scaled our training data.
valid_mat <- 
  as.matrix(scale(valid_num, center = attr(som1_train_mat,  "scaled:center"),
                  scale = attr(som1_train_mat, "scaled:scale")))

valid_bw <- validation$bw

valid_list <- list(independent = valid_mat, dependent = valid_bw)

# Requires up to 16GB of RAM, skip if resources are limited
ransomware.prediction1.validation <- predict(som_model1, newdata = valid_list)

# Confusion Matrix
cm_bw.validation <- 
  confusionMatrix(ransomware.prediction1.validation$prediction[[2]],
                  validation$bw)

```  

Here are the results of the binary SOM model.

Test set:

```{r binary som results1, echo=FALSE}

som1_cm_bw %>% as.matrix() %>% knitr::kable()

```  

Validation set:

```{r binary som results2, echo=FALSE}

cm_bw.validation %>% as.matrix() %>% knitr::kable()

```  

This winds up being the most resource intensive and least accurate method out of those tried.  It was left out of the final version of the script and is not really worth running except to compare to the next method.


### Method Part 1:  Binary Random Forest to isolate ransomware addresses before categorization.

A Random Forest model is trained using ten-fold cross validation and a tuning grid with the number of variables randomly sampled as candidates at each split `mtry` set to the values $={2, 4, 6, 8, 10, 12}$, each one being checked for optimization.


```{r random-forest-prep, echo=FALSE, inculde=FALSE, warning=FALSE}
##############################################################################
## This is a better attempt using Random Forest to model the data set as
## "black" and "white" addresses only.
##############################################################################

# Cross Validation, ten fold
control <- trainControl(method="cv", number = 10)

# Control grid with variation on mtry
grid <- data.frame(mtry = c(2, 4, 6, 8, 10, 12))

# Run Cross Validation using control and grid set above
rf_model <- train(train_num, train_bw, method="rf", 
                  trControl = control, tuneGrid=grid)

# Supervised fit of model using cross validated optimization
fit_rf <- randomForest(train_samp, train_bw,
                       minNode = rf_model$bestTune$mtry)

# Measure accuracy of model against test sample
y_hat_rf <- predict(fit_rf, test_samp)
cm_test <- confusionMatrix(y_hat_rf, test_bw)


# Measure accuracy of model against full ransomware set
ransomware_y_hat_rf <- predict(fit_rf, ransomware)
cm_ransomware <- confusionMatrix(ransomware_y_hat_rf, ransomware$bw)


```  

The confusion matrix for the test set shows excellent results, specifically in the areas of accuracy and precision.

```{r random-forest-output_test1, echo=FALSE}

# Confusion matrix for test set
cm_test %>% as.matrix() %>% knitr::kable()

```  

Here are the overall results...

```{r random-forest-output_test2, echo=FALSE}

# overall results
cm_test$overall %>% knitr::kable()

```  

Here are the results by class...

```{r random-forest-output_test3, echo=FALSE}

# by class.
cm_test$byClass %>% knitr::kable()

```  

The confusion matrix for the full ransomware set is very similar to that of the test set.

Here is the confusion matrix for the full ransomware data set.

```{r random-forest-output_big1, echo=FALSE}

# Confusion matrix for full ransomware set,
cm_ransomware %>% as.matrix() %>% knitr::kable()

```  

Here are the big overall results....

```{r random-forest-output_big2, echo=FALSE}

# overall results 
cm_ransomware$overall %>% knitr::kable()

```  

Here are the big set results by class....

```{r random-forest-output_big3, echo=FALSE}

#  by class.
cm_ransomware$byClass %>% knitr::kable()

```  


### Method Part 2:  Categorical SOMs to categorize predicted ransomware addresses.

Now we train a new model after throwing away all "white" addresses.  The predictions from the Random Forest model are used to isolate all "black" addresses for further classification into ransomware addresses using SOMs.

```{r soms-prep, echo=FALSE, include=FALSE}

##############################################################################
## Now we use the Random Forest model to classify the data set into "black" 
## and "white" categories with better precision.
##############################################################################

# Now use this prediction to reduce the original set to only "black" addresses
# First append the full set of predictions to the original set.
ransomware$prediction <- ransomware_y_hat_rf

# Filter out all the predicted "white" addresses, 
# leaving only predicted "black" addresses
black_addresses <- ransomware %>% filter(prediction=="black")

# Split the reduced black-predictions into a training set and a test set @ 50%
test_index <- createDataPartition(y = black_addresses$prediction,
                                  times = 1, p = .5, list = FALSE)

train_set <- black_addresses[-test_index,]
test_set <- black_addresses[test_index,]

# Keep only numeric columns, ignoring temporal variables.
train_num <- train_set %>% 
  select(income, neighbors, weight, length, count, looped)

# SOM function can only work on matrices. 
train_mat <- as.matrix(scale(train_num))

# Select non-temporal numerical features only
test_num <- test_set %>% 
  select(income, neighbors, weight, length, count, looped)

# Testing data is scaled according to how we scaled our training data.
test_mat <- as.matrix(scale(test_num, 
                            center = attr(train_mat, "scaled:center"),
                            scale = attr(train_mat, "scaled:scale")))

# Categorical labels for training set
train_label <- train_set$label %>% classvec2classmat()

# Same for test set
test_label <- test_set$label %>% classvec2classmat()

# Create data list for supervised SOM
train_list <- list(independent = train_mat, dependent = train_label)

############################################################################
## Calculate idea grid size according to:
## https://www.researchgate.net/post/How-many-nodes-for-self-organizing-maps
############################################################################

# Formulaic method 1, makes a larger graph in this case
grid_size <- round(sqrt(5*sqrt(nrow(train_set))))

# Based on categorical number, method 2, smaller graph with less cells
#grid_size = ceiling(sqrt(length(unique(ransomware$label))))

# Create SOM grid
train_grid <- somgrid(xdim=grid_size, ydim=grid_size, 
                      topo="hexagonal", toroidal = TRUE)

## Now build the SOM model using the supervised method xyf()
som_model2 <- xyf(train_mat, train_label,
                  grid = train_grid, 
                  rlen = 100,
                  mode="pbatch", 
                  cores = detectCores(), # Use all cores
                  # cores = detectCores() - 1,  # Leave one core for system
                  keep.data = TRUE
)

# Now test predictions of test set, create data list for test set
test_list <- list(independent = test_mat, dependent = test_label)

# Generate predictions
ransomware_group.prediction <- predict(som_model2, newdata = test_list)

# Confusion Matrix
cm_labels <- confusionMatrix(ransomware_group.prediction$prediction[[2]],
                             test_set$label)


```  

When selecting the grid size for a Self Organizing Map, there are at least two different schools of thought. The two that were tried here are explained (with supporting documentation) on a Researchgate forum.[8]  The first method is based on the size of the training set, and in this case results in a larger, more accurate map.  The second method is based on the number of known categories to classify the data into, and in this case results in a smaller, less accurate map.  For this script, a grid size of `r grid_size` has been selected.  

A summary of the results for the categorization of black addresses into ransomware families follows.  For the full table of predictions and statistics, see the Appendix.

Here are the overall results.

```{r cm_overall, echo=FALSE}

# Overall section of the confusion matrix formatted through kable()
cm_labels$overall %>% knitr::kable()

```  

Here are the results by class.

```{r soms-output-by-class, echo=FALSE, size="tiny"}

# By Class section of the confusion matrix formatted through kable()
cm_labels$byClass %>% knitr::kable()

```  

### Clustering Visualizations:  Heatmaps and K-means clustering 

Here are some graphs, tell a bit more about them.

```{r binary som graphs, echo=FALSE, fig.align="center"}

# Be careful with these, some are really large and take a long time to produce.

# Visualize neural network mapping
plot(som_model2, type = 'mapping', pch = 19, palette.name = topo.colors)
cat(" \n")

# Distance map
plot(som_model2, type = 'quality', pch = 19, palette.name = topo.colors)
cat(" \n")

# Visualize counts
plot(som_model2, type = 'counts', pch = 19, palette.name = topo.colors)
cat(" \n")

# Visualize fan diagram
plot(som_model2, type = 'codes', pch = 19, palette.name = topo.colors)
cat(" \n")

# Visualize heatmap for variable 1
plot(som_model2, type = 'property', property = som_model2$codes[[1]][,1],
     main=colnames(train_num)[1], pch = 19, palette.name = topo.colors)
cat(" \n")

# Visualize heatmap for variable 2
plot(som_model2, type = 'property', property = som_model2$codes[[1]][,2],
     main=colnames(train_num)[2], pch = 19, palette.name = topo.colors)
cat(" \n")

# Visualize heatmap for variable 3
plot(som_model2, type = 'property', property = som_model2$codes[[1]][,3],
     main=colnames(train_num)[3], pch = 19, palette.name = topo.colors)
cat(" \n")

# Visualize heatmap for variable 4
plot(som_model2, type = 'property', property = som_model2$codes[[1]][,4],
     main=colnames(train_num)[4], pch = 19, palette.name = topo.colors)
cat(" \n")

# Visualize heatmap for variable 5
plot(som_model2, type = 'property', property = som_model2$codes[[1]][,5],
     main=colnames(train_num)[5], pch = 19, palette.name = topo.colors)
cat(" \n")

# Visualize heatmap for variable 6
plot(som_model2, type = 'property', property = som_model2$codes[[1]][,6],
     main=colnames(train_num)[6], pch = 19, palette.name = topo.colors)
cat(" \n")

```  

K-means clustering offers a nice way of visualizing the final SOM grid and the categorical boundaries that were formed by the model.

```{r clustering-setup, echo=FALSE, include=FALSE}
#############################################################################
## K-Means Clustering to visualize the categorization of the SOM
## For a good tutorial, see:
## https://www.polarmicrobes.org/microbial-community-segmentation-with-r/
#############################################################################

# Set number of clusters to be equal to number of known ransomware groups
n_groups <- length(unique(ransomware$label)) - 1

# Generate k-means clustering
som.cluster <- kmeans(data.frame(som_model2$codes[[1]]), centers=n_groups)

```  

K-means clustering categorizes the SOM grid by adding boundaries to the classification groups.  This is the author's favorite graph in the entire report.

```{r clustering-plot, echo=FALSE, fig.align="center"}

# Plot K-means clustering results
plot(som_model2,
     main = 'K-Means Clustering',
     type = "property",
     property = som.cluster$cluster,
     palette.name = topo.colors)
add.cluster.boundaries(som_model2, som.cluster$cluster)

```  

---

##  Results & Performance

### Results

   The first attempt to isolate ransomware using SOMs resulted in a model with an accuracy of `r toString(cm_bw.validation$overall["Accuracy"])` and precision `r toString(cm_bw.validation$byClass[3])`.
   
   The the second attempt to isolate ransomware using Random forest resulted in a model with an accuracy of `r toString(cm_ransomware$overall["Accuracy"])` and precision `r toString(cm_ransomware$byClass[3])`.
   
   Classifying the ransomware predicted by the second attempt into 28 ransomware families resulted in a model with an overall accuracy of `r toString(cm_labels$overall["Accuracy"])` and minimum nonzero precision of `r toString(min(cm_labels$byClass[,5][which(cm_labels$byClass[,5] > 0)]))`.


### Performance

  The script runs on the aforementioned hardware in less than five minutes and uses less than 4GB of RAM.  Given that the Bitcoin network produces one new block every ten minutes on average, then real-time analysis could theoretically be conducted on each block as it is announced using even moderate computing resources.  Just for kicks, the final script was also run on a more humble computer with the following specifications:

#### ASUS Eee PC 1025C  
     
   - CPU:  Intel Atom N2600 @ 1.600GHz (64-bit Intel Atom quad-core x86)
   - RAM:  3911MB DDR3 @ 800 MT/s  (4 GB)
   
   This is a computer known for being slow and clunky.  Even on this device, which runs the same operating system and software as the hardware listed previously, the total run time for the script is around 1665 seconds.  At nearly 28 minutes, this is not fast enough to analyze the Bitcoin blockchain in real time, but it does show that the script can be run on very modest hardware to completion.
   
#### Pine64 Quartz64

  - CPU:  Rockchip RK3566 SoC aarch64 (64-bit quad-core ARM)
  - RAM:  DDR4 xxxxMB (8 GB)
  
  Single board computer / Development board.  This was run to benchmark a modern 64-bit ARM processor.  The script runs in about xxxx minutes on this platform, just for reference.

---

## Summary

### Comparison to results from original paper

   In the original paper by Akcora et al., they tested several different sets of parameters on their TDA model.  According to them, "In the best TDA models for each ransomware family, we predict **16.59 false positives for each
true positive**. In turn, this number is 27.44 for the best non-TDA models."[3]  In fact, the highest Precision (a.k.a. Positive Predictive Value, defined as TP/(TP+FP)) they achieved was only 0.1610.  By comparison, although several of our predicted classes had zero or NA precision values, the lowest non-zero precision value is `r toString(min(cm_labels$byClass[,5][which(cm_labels$byClass[,5] > 0)]))`, with many well above that, approaching one in a few cases.

  One might say that we are comparing apples to oranges in a sense, because their method was one single model, while these results are from a two-method stack.  Still, given the run time of the final script, I think the two-model approach is superior in this case, especially when measured in terms of precision and avoiding false positives.


### Limitations

  SOMs seem like they are easy to misconfigure.  Perhaps a dual Random Forest approach would be better.  this has not been attempted yet, as the two method approach presented here was satisfactory enough to present in a report.

### Future Work

  I only scratched he surface of the SOM algorithm which seems to have many implementations and parameters that could be investigated further and possibly optimized via cross-validation.  Also, a dual Random Forest approach to first isolate the ransomware addresses and also 
  
  The script itself has a few areas that could be further optimization.  The sampling method does what it needs to do, but the ratios taken for each set could possibly be optimized. 

### Conclusion

   This paper/report presents a reliable method for classifying Bitcoin addresses into known ransomware families, while at the same time avoiding false positives by filtering them out using a binary method before classifying them further.  It leaves the author of the paper wondering how much harder it would be to perform the same task for ransomware that uses privacy coins.  Certain cryptocurrency networks utilize privacy coins, such as Monero, that obfuscate transactions from being analyzed in the same way that the Bitcoin network has been analyzed here.  Some progress has been made towards analyzing such networks[9], but the developers of such networks continually evolve the code to complicate transaction tracking.  This could be another good area for future research.

## References  

[1] Adam Brian Turner, Stephen McCombie and Allon J. Uhlmann (November 30, 2020) [Analysis Techniques for Illicit Bitcoin Transactions](https://doi.org/10.3389/fcomp.2020.600596)

[2] Daniel Goldsmith, Kim Grauer and Yonah Shmalo (April 16, 2020) [Analyzing hack subnetworks in the
bitcoin transaction graph](https://doi.org/10.1007/s41109-020-00261-7) 

[3] Cuneyt Gurcan Akcora, Yitao Li, Yulia R. Gel, Murat Kantarcioglu (June 19, 2019) [BitcoinHeist: Topological Data Analysis for Ransomware Detection on the Bitcoin Blockchain](https://arxiv.org/abs/1906.07852)

[4] UCI Machine Learning Repository https://archive.ics.uci.edu/ml/index.php

[5]  BitcoinHeist Ransomware Address Dataset  
https://archive.ics.uci.edu/ml/datasets/BitcoinHeistRansomwareAddressDataset

[6]  Available Models - The `caret` package http://topepo.github.io/caret/available-models.html

[7] Ron Wehrens and Johannes Kruisselbrink, Package ‘`kohonen`’ @ CRAN (2019) https://cran.r-project.org/web/packages/kohonen/kohonen.pdf

[8] How many nodes for self-organizing maps? (Oct 22, 2021) https://www.researchgate.net/post/How-many-nodes-for-self-organizing-maps

[9] Malte Möser, Kyle Soska, Ethan Heilman, Kevin Lee, Henry Heffan, Shashvat Srivastava,
Kyle Hogan, Jason Hennessey, Andrew Miller, Arvind Narayanan, and Nicolas Christin (April 23, 2018) [An Empirical Analysis of Traceability in the Monero Blockchain](https://arxiv.org/pdf/1704.04299/)

\newpage

## Appendix:  

### Categorical SOM ransowmare family prediction table and confusion matrix

Here are the full prediction results for the categorization of black addresses into ransomware families.  It is assumed that all white address have already been removed.

```{r soms-output-table, echo=FALSE}

# Final results of categorization of "black" addresses
# into ransomware families.
cm_labels

``` 

```{r toc, echo=FALSE}

#End timer
toc()

```  


```{r empty block, echo=FALSE, include=FALSE}

##############################################################################
## Description of block goes here.
## Include notes and resources as necessary.
##############################################################################

# First comment goes here.

```  