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+{
+ "cells": [
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Intro to Genomic Data Science\n",
+ "---"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\dna0.png\" width=\"700\">\n",
+ "\n",
+ "Source: <a href=\"https://wallpapercave.com/dna-background\">DNA Wallpaper Cave</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This introductory tutorial on applying machine learning to bioinformatics data will be broken up into two parts:\n",
+ "\n",
+ "1) [Data Acquisition & Preprocessing](https://towardsdatascience.com/analyzing-microbiome-data-320728b56b8e)\n",
+ " - Where do we find public genomic data sets?\n",
+ " - How do we download them?\n",
+ " - How do we interpret this data biophysically?\n",
+ " - How do we clean and preprocess this data?\n",
+ "\n",
+ "\n",
+ "\n",
+ "2) [Visualizing High-Dimensional Data](https://towardsdatascience.com/visualizing-high-dimensional-microbiome-data-eacf02526c3a)\n",
+ " - How do we visualize high-dimensional data?\n",
+ " - What kinds of dimensionality reduction techniques are appropriate?\n",
+ " - Why do we want to use unsupervised methods before other ML techniques?\n",
+ "\n",
+ "(see corresponding links for expanded Medium articles written by my colleague and I)\n",
+ "\n",
+ "---"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Background"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "Macroscopic Ecological Biomes\n",
+ "\n",
+ "<img src=\"images\\macroscopic_biomes.jpg\" width=\"600\">\n",
+ "\n",
+ "Source: <a href=\"https://www.impactlab.com/2011/08/25/90-of-plant-and-animal-species-on-earth-not-yet-discovered/\">Impact Lab</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When we think of different ecosystems such as deserts, rainforests, grasslands, or coral reefs, we know that different communities of organisms are specialized to live in those areas of the world. \n",
+ "\n",
+ "But while many of us spend the majority of our time indoors, few of us realize the extent to which every surface we touch is home to specialized organisms that colonize those spaces — doorknobs, kitchen counters, tables, chairs, bathrooms, refrigerators, etc. "
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "Microscopic Biomes ~ Microbiomes\n",
+ "\n",
+ "<img src=\"images\\petridish0.jpg\" width=\"600\">\n",
+ "\n",
+ "Source: <a href=\"https://news.syr.edu/blog/2018/01/22/suart-galleries-presents-hidden-beauty-exploring-the-aesthetics-of-medical-science/\">Syracuse University</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Similar to our macroscopic world of deserts, rainforests, and grasslands, at the microscopic level we can infer that different compositions or groups of microorganisms and fungi may be specialized to live in different locations or surfaces around us. \n",
+ "\n",
+ "We call these special communities of microorganisms a [Microbiome](https://en.wikipedia.org/wiki/Microbiota)."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\swab0.jpg\" width=\"500\">\n",
+ "\n",
+ "Source: <a href=\"https://complianceplusservices.com/covid-19\">Compliance Services</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Our Task\n",
+ "\n",
+ "What if we solely knew the genetic differences between these communities of organisms? \n",
+ "\n",
+ "Could we perhaps reverse engineer the location of where these organisms came from using genetic sequence data and some simple data science detective work?\n",
+ "\n",
+ "---"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Where to find genomic data?"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To investigate the genetic differences between microbiomes we were able to find a data set using [Qiita](https://qiita.ucsd.edu/static/doc/html/index.html)."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\qiita0.png\" width=\"800\">\n",
+ "\n",
+ "Source: <a href=\"https://qiita.ucsd.edu/\">Qiita</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Qiita (pronounced ‘cheetah’) is a multi-omics software package and database that holds microbial ecology datasets and offers:\n",
+ "- A nice interface to search for different types of -omics data\n",
+ "- Ability to find reference data from papers\n",
+ "- Info regarding file types and associated metadata\n",
+ "\n",
+ "It is based on the [QIIME](https://en.wikipedia.org/wiki/QIIME) bioinformatics pipeline that transforms and processes raw sequencing data to common formats that are friendly to data analysis. \n",
+ "\n",
+ "Other common bioinformatics pipelines are MOTHUR, DADA2, and USEARCH, etc. For a comparison of the different pipelines, [see here](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0227434)."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "### Acquiring the Data"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To access the data* you’ll need to create an account and then [download the data](https://qiita.ucsd.edu/study/description/10423) (~6.4 GB) collected by the [Caporaso Lab](https://caporasolab.us/) at the Pathogen & Microbiome Institute from Northern Arizona University, by clicking on the *All QIIME maps and BIOMs* on the left-hand side."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\qiita1.png\" width=\"800\">\n",
+ "\n",
+ "Source: <a href=\"https://qiita.ucsd.edu/study/description/10423\">Caporaso Lab, Northern Arizona University</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Once done*, you’ll need to:\n",
+ "1) Unzip the file\n",
+ "2) Place it in a folder called *data*\n",
+ "3) Transform the data into a format we can work with using a package called [biom-format](https://biom-format.org/).\n",
+ "\n",
+ "In step 3, we can convert .BIOM files to .tsv by running the following two commands inside this notebook, or alternatively on your terminal without the \"%\". \n",
+ "\n",
+ "*For the sake of ease & brevity, I have uploaded a preprocessed version of the data set used in the first part of this tutorial. The .tsv file can be [obtained here](https://drive.google.com/file/d/19GYJK87j3SS9AWUnQoqxkcDjyH7LOtvd/view?usp=sharing). (~94 KB)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "%pip install biom-format\n",
+ "\n",
+ "%biom convert -i data/BIOM/60899/all.biom -o data/BIOM/60899/feature_table.tsv — to-tsv"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "### Reading in our data"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "This command will convert our .biom files to a more familiar .tsv format, from which we can then go into our Jupyter notebook and read into a Pandas dataframe by:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
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+ " <th></th>\n",
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+ " <th></th>\n",
+ " <th></th>\n",
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+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th></th>\n",
+ " <th># Constructed from biom file</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>#OTU ID</th>\n",
+ " <th>10423.4T6YHGRF7KF2C</th>\n",
+ " <th>10423.19X1DXDQX9QY9</th>\n",
+ " <th>10423.5EJZONDFDCFIN</th>\n",
+ " <th>10423.15PCQYUJZDX1S</th>\n",
+ " <th>10423.749Z5IK1KL20W</th>\n",
+ " <th>10423.11WHV0MTK27VM</th>\n",
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+ " </tr>\n",
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+ " </tr>\n",
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+ "</div>"
+ ],
+ "text/plain": [
+ " # Constructed from biom file\n",
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+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "import pandas as pd\n",
+ "\n",
+ "feature_table_raw = pd.read_csv('data/feature_table.tsv', sep = '\\t', )\n",
+ "feature_table_raw.head()"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "### How do we interpret this data?\n",
+ "\n",
+ "\n",
+ "[See this link](https://blogs.iu.edu/ncgas/2021/09/17/introduction-to-illumina-sequencing/) for some nice graphics giving a basic overview of how a genetic sequencing machine works:\n",
+ "\n",
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "Illumina Sequencing\n",
+ "\n",
+ "<img src=\"images\\illumina_explained.png\" width=\"600\">\n",
+ "\n",
+ "Source: <a href=\"https://blogs.iu.edu/ncgas/2021/09/17/introduction-to-illumina-sequencing/\">Indiana University</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>\n"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The [BIOM file format](http://biom-format.org/) is commonly found in -omics datasets where it is used to represent OTU tables. \n",
+ "\n",
+ "OTUs stand for [Operational Taxonomic Units](https://en.wikipedia.org/wiki/Operational_taxonomic_unit) which can be thought of as clusters of organisms grouped by genetic sequence similarity of a particular region of the genome. \n",
+ "\n",
+ "In essence, they act as a proxy for “species” at different taxonomic levels when the clusters of organisms are unknown. \n",
+ "\n",
+ "The observations or rows in this table are OTUs and the corresponding matrix records the number of times each OTU is observed in each sample."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "### Converting these sequences to corresponding organisms using BLAST\n",
+ "\n",
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\blast_equation.jpg\" width=\"500\">\n",
+ "\n",
+ "Source: <a href=\"https://www.ncbi.nlm.nih.gov/books/NBK62051/\">BLAST Glossary</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Since the scientists who originally collected this data most likely took swabs of various surfaces and locations and then sequenced the DNA of the microorganisms and fungi that were picked up by this swab, we don’t necessarily know the composition of the actual species beforehand. \n",
+ "\n",
+ "All we have are different groups of strings of DNA (composed of A, T, C, Gs) from which we can then compare to a reference database by running the BLAST local alignment search algorithm on it.\n",
+ "\n",
+ "Such a tool can be [found here](https://blast.ncbi.nlm.nih.gov/Blast.cgi) offered by the NIH. In our case, this step was already done for us."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\blast_alignment_species.png\" width=\"700\">\n",
+ "\n",
+ "Source: <a href=\"https://en.wikipedia.org/wiki/Sequence_alignment\">Wikipedia - Sequence Alignment</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "### Data Preprocessing"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Fortunately, our dataset already came with a corresponding metadata file with information regarding sample ids, location where the sequencing was performed, the type of experiment the data came from, the sequencing machine used, the timestamps of the swab collection, the geolocation, and much more. \n",
+ "\n",
+ "#### Finding corresponding ground truth of geolocation\n",
+ "\n",
+ "We can open our metadata file in pandas by doing the following:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sample_table = pd.read_csv('data/mapping_files/60899_mapping_file.txt', sep = '\\t')"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\first_row_raw_data.png\" width=\"1000\">\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Converting .BIOM file to Feature Table\n",
+ "\n",
+ "We can then create a helper function that takes the output from our .biom file and converts it to something that is easier to work with, which we’ll call a feature table:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def convert_tsv(df):\n",
+ " \"\"\"\n",
+ " Helper function to take the output of the biom-format package from a .biom file\n",
+ " Converts it to a feature table\n",
+ " \"\"\"\n",
+ " length = df.shape[0]\n",
+ " df = df.reset_index().T\n",
+ " df.set_index(0)\n",
+ " \n",
+ " # We remove the DNA sequence for an encoding, taking less space\n",
+ " new_header = ['Sample_id'] + list(range(length-1))\n",
+ " df = df[1:]\n",
+ " df.columns = new_header\n",
+ " df = df.reset_index().drop('index', axis=1)\n",
+ " \n",
+ " return df"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Then we can run our above helper function on our previous raw table and rename our index:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "feature_table = convert_tsv(feature_table_raw)\n",
+ "feature_table = feature_table.set_index('Sample_id').astype(float).astype(int)\n",
+ "\n",
+ "print(feature_table.shape)"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can see that we start with a table that has 1,497 rows and 25,756 columns. \n",
+ "\n",
+ "Because each column represents a particular genetic sequence or OTU (which corresponds to our features or dimensions), we can see that we are dealing with incredibly high-dimensional data. This is quite common when dealing with metagenomic data sets and presents new challenges that traditional data science techniques may not be able to handle."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Dealing with High-Dimensional Data \n",
+ "\n",
+ "Problem: Overabundance of Columns or Features\n",
+ "\n",
+ "Solution*:\n",
+ "1) Make column names shorter\n",
+ "2) Thresholding to get a subset of the data"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Solution Part 1 - To help us deal with this high dimensionality, we used our helper function to rename every column that was originally labeled with a genetic sequence to a corresponding integer, so that we don’t have really long strings of genetic sequences as column names. Each of these columns contains either frequencies or counts of that particular OTU for each row. Each row represents a sample id that might identify for example a particular swab."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Solution Part 2 - From here we can undergo a few common practices used to clean bioinformatics data. By making sure each sequence has more than 20,000 reads associated with it and has been seen in at least 3 different samples (in essence, applying a series of thresholds), we can subset our data such that we now have 301 rows and 1,894 columns."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "*Note that there is much that can be improved upon at this step, and many scientific papers have been written about this. We are approaching this from a quick-and-dirty perspective."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Make sure the sequence has more than 20,000 reads total\n",
+ "feature_table = feature_table.loc[(feature_table.sum(axis='columns') > 20000)]\n",
+ "\n",
+ "# Make sure the sequence has been seen in at least 3 different samples\n",
+ "feature_table = feature_table[feature_table.columns[((feature_table > 0).sum() > 3)]]\n",
+ "\n",
+ "# Check dimensions of our data\n",
+ "print(feature_table.shape)"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\feature_table0.png\" width=\"800\">\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Since we applied thresholds to reduce our feature table, we will also remove those corresponding entries from our metadata table:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# Subset sample table\n",
+ "sample_table = sample_table.set_index('#SampleID')\n",
+ "sample_table = sample_table.loc[feature_table.index]"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "From here we can now use our metadata to double-check and see that we have samples that come from 3 different cities:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sample_table['city'].drop_duplicates()"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\sample_id_cities.png\" width=\"500\">\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Next Steps...\n",
+ "\n",
+ "We have walked through the steps explaining the nature of microbiome metagenomic data, how to obtain it, how to load it, and how to preprocess it and get it into a format from which we can now do analysis on.\n",
+ "\n",
+ "In the next half of this tutorial, we’ll show you how to apply various machine learning algorithms and dimensionality reducing techniques to help visualize and interpret high dimensional data so that we can infer an underlying geographic structure from our data without having to resort to labels provided via our metadata."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "### Dimensionality Reduction & Visualization\n"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Purpose:\n",
+ "\n",
+ "Unsupervised machine learning methods can allow us to understand and explore data in situations where we are not given explicit labels. One type of unsupervised machine learning methods falls under the family of clustering. Getting a general idea of groups or clusters of similar data points can inform us of any underlying structural patterns in our data, such as geography, functional similarities, or communities when we otherwise would not know this information beforehand.\n",
+ "\n",
+ "We will be applying our dimensional reduction techniques to Microbiome data acquired from UCSD’s Qiita platform. This will then allow us to apply clustering and other machine learning techniques."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "*Brief Reminder: Our microbiome dataset has columns that represent counts of bacterial DNA sequences present, and our rows represent samples of individual communities of bacteria.* "
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\three_cities.png\" width=\"700\">\n",
+ "\n",
+ "Source: <a href=\"https://towardsdatascience.com/visualizing-high-dimensional-microbiome-data-eacf02526c3a\">Pexels - modified by user</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Bacterial communities are expected to be unique across the three different locations, and we hope to visualize that through the high-dimensional microbiome data. "
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Representing high-dimensional data in two dimensions\n",
+ "\n",
+ "To visualize this complex, sparse, and high dimensional metagenomic data as something our eyes can interpret on a two-dimensional computer screen, we will be needing to drastically reduce our dimension size, or in other words, the number of features in our data. \n",
+ "\n",
+ "Rather than the 25,000 columns of our dataset which currently represent a portion of the genetic sequence of each organism and their counts in our microbiome, we instead would like a notion of “the most important features” to plot. \n",
+ "\n",
+ "We will explores 3 different dimensionality reduction and visualization techniques applied to microbiome data and explains what these visualizations can tell us about the structure inherent in our data."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import pandas as pd\n",
+ "import matplotlib.pyplot as plt\n",
+ "import seaborn as sns"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Assigning color as ground truth labels\n",
+ "\n",
+ "For demonstration purposes, since we actually do have labels for this data set, we can confirm whether or not our data set produces nice visualizations by assigning a different color to each point corresponding to a different geographic location. In reality, you will often not have this if you are already taking the unsupervised machine learning approach."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "### 1 - Principal Component Analysis (PCA)"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Our first dimensionality reduction technique and one of the most commonly used ones is called [Principal Component Analysis (PCA)](https://en.wikipedia.org/wiki/Principal_component_analysis). \n",
+ "\n",
+ "PCA attempts to reduce the feature space down to representations of the variation found within the data. It does this by taking all of your data points and rotating to an axis that clearly shows the maximum amount of variability. That axis is known as your ‘first principal component’. Mathematically speaking, the placement of this line goes through the centroid of your data, while also minimizing the squared distance of each point to that line. It is also the axis with the most variation in the data. "
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "PCA Explained\n",
+ "\n",
+ "<img src=\"images\\PCA_explained.png\" width=\"600\">\n",
+ "\n",
+ "Source: <a href=\"https://prwatech.in/blog/machine-learning/principal-component-analysis-tutorial/\">prwatech</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "After re-aligning our data, we will then collapse all data points onto that dimension. Once this step is done, we rinse and repeat, keeping in mind that every time we find a new principal component, that new line will always be perpendicular to the previous principal component. \n",
+ "\n",
+ "[See here](https://setosa.io/ev/principal-component-analysis/) for a nice visual explanation of PCA.\n",
+ "\n",
+ "To do PCA we can run the following code on our previously built feature table from Part 1 of our series."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from sklearn.decomposition import PCA\n",
+ "\n",
+ "pca = PCA(n_components=2)\n",
+ "principalComponents = pca.fit_transform(np.array(feature_table))\n",
+ "plot_df = pd.DataFrame(data = principalComponents, columns = ['dim1', 'dim2'], index = feature_table.index)\n",
+ "\n",
+ "# We can then plot this like so:\n",
+ "sns.scatterplot(x = 'dim1', y = 'dim2', data = plot_df)"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\PCA_unlabeled.png\" width=\"500\">\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "And if we are given labels to check how our dimensionality reduction went (reminder that in reality this is not guaranteed), we can replot our PCA with colors:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "plot_df = pd.concat([plot_df, sample_table['city']], axis = 1)\n",
+ "\n",
+ "sns.scatterplot(x = 'dim1', y = 'dim2', hue = 'city', data = plot_df)"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\PCA_labeled.png\" width=\"500\">\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Problems with PCA\n",
+ "\n",
+ "When we transform our data from 1,894 features down to 2, we can see two discernable dimensions the data is being placed into. \n",
+ "\n",
+ "However, once we look at the true meaning of the data after the geographic origin of the data has been revealed, we see that this visualization technique doesn’t give us a good representation of the geographic data. \n",
+ "\n",
+ "Unfortunately, this common technique falls apart when applied to the level of sparsity that microbiome data produces.\n",
+ "\n",
+ "**It is important to note that after applying PCA we could get a variety of shapes for our plots. To interpret the different shapes you can get, we recommend you check out this post [here](https://www.nxn.se/valent/2017/6/12/how-to-read-pca-plots).*"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "### 2 - t-Distributed Stochastic Neighborhood Embedding (t-SNE)\n",
+ "\n",
+ "Another technique used to explore high-dimensional data like our microbiome data is to use something known as [t-distributed stochastic neighbor embedding t-SNE](https://jmlr.org/papers/volume9/vandermaaten08a/vandermaaten08a.pdf). \n",
+ "\n",
+ "Unlike PCA which works by trying to keep dissimilar data points far apart in our lower-dimensional representations using linear methods, t-SNE attempts to handle data that lie on non-linear lower-dimensional manifolds by trying to keep similar data points close together."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "t-SNE Explained\n",
+ "\n",
+ "<img src=\"images\\t-SNE_explained.png\" width=\"600\">\n",
+ "\n",
+ "Source: <a href=\"https://nuancesprog.ru/p/14951/ \">Nuancesprog</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "t-SNE works by minimizing the divergence between 2 distributions:\n",
+ "1) The first distribution comes from our pairwise similarities of objects in our original high-dimensional input space. \n",
+ "2) The second distribution is that of our pairwise similarities of objects in our corresponding lower-dimensional embedding. \n",
+ "\n",
+ "In essence, we are trying to minimize the divergence between these two distributions of our original high dimensional space and the corresponding lower-dimensional one."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "To run t-SNE let’s use the implementation by scikit-learn and run that on our feature table from before:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from sklearn.manifold import TSNE\n",
+ "\n",
+ "tsne = TSNE(metric = 'jaccard', perplexity=30.0)\n",
+ "embeddings = tsne.fit_transform(feature_table)\n",
+ "\n",
+ "plot_df = pd.DataFrame(data = embeddings, columns = ['dim1', 'dim2'], index = feature_table.index)"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Important Assumptions of t-SNE\n",
+ "\n",
+ "**1) Distance Metric**: One of our parameters for t-SNE is the metric we used to calculate the distances between our instances of our features. \n",
+ "\n",
+ "The default is Euclidean distance, but since we are using counts as our entries for each row, we will instead use a metric called the Jaccard distance. \n",
+ "\n",
+ "In essence, the Jaccard distance metric is the number of counts in two sets divided by the number in either set, multiplied by 100, and then subtracting this all from 1. It technically measures the *dissimilarity* between sample sets.\n",
+ "\n",
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "Comparison of Different Distance Metrics\n",
+ "\n",
+ "<img src=\"images\\distance_metrics.png\" width=\"500\">\n",
+ "\n",
+ "Source: <a href=\"https://towardsdatascience.com/9-distance-measures-in-data-science-918109d069fa \">Towards Data Science</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**2) Perplexity**: This allows us to balance how much we would like to emphasize our local vs. global relationships in our data. \n",
+ "\n",
+ "We chose to stick with the default setting of perplexity=30, however we highly recommend this exploration of t-SNE and perplexity [here](https://distill.pub/2016/misread-tsne/).\n",
+ "\n",
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "t-SNE vs. PCA\n",
+ "\n",
+ "<img src=\"images\\t-SNE_vs_PCA.png\" width=\"600\">\n",
+ "\n",
+ "Source: <a href=\"https://towardsdatascience.com/tsne-degrades-to-pca-d4abf9ef51d3\">Towards Data Science</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Our t-SNE plots\n",
+ "\n",
+ "Let us plot the results from our t-SNE embedding, showing both a plot without labels (again, like how you would expect in real unsupervised scenarios) and a plot with our known labels:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "sns.scatterplot(x = 'dim1', y = 'dim2', data = plot_df)"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\t-SNE_unlabeled.png\" width=\"600\">\n",
+ "\n",
+ "</center>\n",
+ "<div>\n",
+ "\n",
+ "\n",
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\t-SNE_labeled.png\" width=\"600\">\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "When the labels are revealed, we can see that this embedding is a decent representation of the underlying geographic structure present in our microbiome genetic data as evidenced by the data points taken from the same geographic region being separated in their own (tri?)quadrants."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "### Uniform Approximation and Projection (UMAP)"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The last dimensionality reduction technique we will use to represent our high dimensional microbiome metagenomic data is called Uniform Approximation and Projection (UMAP). \n",
+ "\n",
+ "UMAP improves upon t-SNE’s performance by not only working better with larger datasets in a markedly shorter time but also by preserving much more of the original global structure of our data. \n",
+ "\n",
+ "For a nice in-depth comparison of t-SNE vs. UMAP, we recommend [this tutorial here](https://towardsdatascience.com/how-exactly-umap-works-13e3040e1668)."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\t-SNE_vs_UMAP.png\" width=\"600\">\n",
+ "\n",
+ "Source: <a href=\"https://towardsdatascience.com/how-exactly-umap-works-13e3040e1668\">Towards Data Science</a>\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The mathematical underpinnings of UMAP center around first building a weighted graph, where edge weights represent the likelihood of a connection between points. This is determined by a radius that expands out from each point and connecting points with overlapping radii. As each point’s radius grows, its likelihood of connection decreases."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Assumptions of UMAP\n",
+ "\n",
+ "**1) Local vs. Global Structure**: Our *n_neighbors* parameter corresponds to the number of nearest neighboring points used to construct our original graph, with low values emphasizing local structure, and high values emphasizing global structure.\n",
+ "\n",
+ "**2) Minimum Distance**: The *min_dist* parameter represents the minimum distance we would like between points in our lower-dimensional embedding, with low values giving us more closely packed groups of points, and larger values giving more loosely packed groups of points.\n",
+ "\n",
+ "I recommend playing around with the [interactive visualizations here](https://pair-code.github.io/understanding-umap/) to get an intuitive feel for UMAP’s hyperparameters."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let’s now create our new lower-dimensional embedding with UMAP:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import umap\n",
+ "\n",
+ "reducer = umap.UMAP(n_components = 2, n_neighbors = 15, metric = 'jaccard', random_state = 0)\n",
+ "embeddings = reducer.fit_transform(feature_table)\n",
+ "plot_df = pd.DataFrame(data = embeddings, columns = ['dim1', 'dim2'], index = feature_table.index)\n",
+ "\n",
+ "# Like before, we can plot our lower dimensional embedding without labels:\n",
+ "sns.scatterplot(x = 'dim1', y = 'dim2', data = plot_df)"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\UMAP_unlabeled.png\" width=\"600\">\n",
+ "\n",
+ "</center>\n",
+ "<div>\n",
+ "\n",
+ "<div>\n",
+ "<center>\n",
+ "\n",
+ "<img src=\"images\\UMAP_labeled.png\" width=\"600\">\n",
+ "\n",
+ "</center>\n",
+ "<div>"
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As we can see once we apply colors to reveal our labels, it seems that UMAP does a much better job at conveying the underlying geographic structure from our original high-dimensional metagenomic data set to the above lower-dimensional visualization, with each “spoke” or “petal” of the plot representing that area’s local community of microorganisms, also known as those microbiomes."
+ ]
+ },
+ {
+ "attachments": {},
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "\n",
+ "## Conclusion\n",
+ "\n",
+ "Microbiome data present a unique challenge due to its inherently high-dimensional and sparse nature. To reduce dimensionality we applied three techniques: PCA, t-SNE, and UMAP. In terms of grouping similar data such as microbial samples with a similar geographic origin, UMAP performed the best.\n",
+ "\n",
+ "#### Where to go from here?\n",
+ "\n",
+ "Following up on the above, we can use these 2D embeddings combined with our favorite clustering algorithms to infer classes from the data. Instead of specifying dimensionality reduction down to two dimensions, we can try to reduce it down to any number of dimensions and then apply clustering on top of that. \n",
+ "\n",
+ "This clustering can then allow us to create \"labels\" from which we can then feed into a supervised learning framework like a neural network. "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "venv",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
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