Unsupervised Machine Learning in Python

Beatriz Manso

Introduction

Machine learning (ML) is a type of artificial intelligence (AI) that allows software applications to become more accurate at predicting outcomes without being explicitly programmed to do so. Machine learning algorithms use historical data as input to predict new output values. ML can be used in many fields including bioinformatics, for genomics, proteomics, microarrays, ...

import os
os.chdir('C:/Users/manso/OneDrive - University of West London/MSc Bioinformatics - UWL/3.DSB - Data Science for Bioinformatics/Practice/DSB W11 - Exploratory Data Analysis with Unsupervised Machine Learning')
os.getcwd()

'C:\\Users\\manso\\OneDrive - University of West London\\MSc Bioinformatics - UWL\\3.DSB - Data Science for Bioinformatics\\Practice\\DSB W11 - Exploratory Data Analysis with Unsupervised Machine Learning'

1. Calculating Distance Matrices

Load Table 1 into Spyder as a data frame using Pandas and view the contents:

import pandas as pd
Table1 = pd.read_excel('Table1.xlsx')
print(Table1) 

  Unnamed: 0  IRX4  OCT4  PAX6
0   patient1    11    10     1
1   patient2    13    13     3
2   patient3     2     4    10
3   patient4     1     3     9

Remove the first column with patient names from the data frame, so that it does not get included in the array:

rmpt = Table1.iloc[0:4,1:4]

Convert Table 1 from a data frame to a numpy array of intergers, this removes the header row too:

import numpy as np
T1data = rmpt.to_numpy()
print(T1data)

[[11 10  1]
 [13 13  3]
 [ 2  4 10]
 [ 1  3  9]]

With the numpy array data, calculate the Euclidean distance metrics:

from Bio.Cluster import distancematrix
distancesE = distancematrix(T1data, dist='e')
print("Euclidean distance \n", distancesE, "\n")

Euclidean distance 
 [array([], dtype=float64), array([5.66666667]), array([66.        , 83.66666667]), array([71.        , 93.33333333,  1.        ])] 

Optionally, convert the array to a data frame for easier reading:

Edf = pd.DataFrame(distancesE)
print("Euclidean distance dataframe \n", Edf, "\n")

Euclidean distance dataframe 
            0          1    2
0        NaN        NaN  NaN
1   5.666667        NaN  NaN
2  66.000000  83.666667  NaN
3  71.000000  93.333333  1.0 

Calculate the Manhattan (city-block) distance metrics:

distancesM = distancematrix(T1data, dist='b')
print("Manhattan \n", distancesM, "\n")
Mdf = pd.DataFrame(distancesM)
print("Manhattan distance dataframe \n", Mdf, "\n")

Manhattan 
 [array([], dtype=float64), array([2.33333333]), array([8., 9.]), array([8.33333333, 9.33333333, 1.        ])] 

Manhattan distance dataframe 
           0         1    2
0       NaN       NaN  NaN
1  2.333333       NaN  NaN
2  8.000000  9.000000  NaN
3  8.333333  9.333333  1.0 

2. Clustering

Load in Table 2 and view it:

T2 = pd.read_csv("Table2.csv", index_col=0)
print(T2)

           t1        t2        t3        t4        t5
g1  -0.129767  0.022354 -0.954649  0.110975  0.388491
g2  -0.337756 -1.188563 -1.449266  0.283642  0.357560
g3   0.196316 -0.582125  0.898658 -0.766928 -1.945763
g4   0.727994  0.134512  0.350455 -0.451750 -0.619588
g5   0.124324  1.729350 -0.062252  0.030506  0.457010
g6  -1.595889  1.141006  1.397045 -0.463734 -1.689223
g7  -0.216876 -0.400143  0.715925 -1.041363  0.971422
g8   0.558435 -1.272570  0.723619 -1.114531 -0.648241
g9  -0.005076  1.475324  0.096234 -0.786503  0.926660
g10 -1.135467  1.630329  0.374782 -1.121340 -0.007128

Scale data (normalisation):

import sklearn
from sklearn import linear_model
from sklearn.preprocessing import StandardScaler
scale = StandardScaler()
T2_scaled = scale.fit_transform(T2)
print(T2_scaled)

[[ 0.076251   -0.22554605 -1.42739099  1.29334503  0.5870607 ]
 [-0.23104779 -1.33310594 -2.03408429  1.64061069  0.55516874]
 [ 0.55803174 -0.77842989  0.84586172 -0.47227618 -1.81971411]
 [ 1.34357502 -0.12296089  0.17344077  0.16160417 -0.45233774]
 [ 0.45166593  1.33575151 -0.33278304  1.13150784  0.65770773]
 [-2.08991155  0.79762475  1.45717952  0.13750113 -1.55520469]
 [-0.05244971 -0.61198092  0.62172256 -1.02421519  1.18810151]
 [ 1.0930545  -1.40994286  0.63116058 -1.17136901 -0.48188123]
 [ 0.26047923  1.1034079  -0.13838587 -0.51164515  1.14194924]
 [-1.40964837  1.2451824   0.20327903 -1.18506333  0.17914984]]

Calculate Euclidean distance:

from Bio.Cluster import distancematrix
dist_ET2 = distancematrix(T2_scaled, dist='e')
print("Table 2 Euclidean distance: \n", dist_ET2, "\n")

Table 2 Euclidean distance: 
 [array([], dtype=float64), array([0.36216175]), array([2.92309087, 3.8657521 ]), array([1.30809654, 2.4039169 , 0.75407804]), array([0.76158706, 2.1506048 , 2.91600446, 1.07050406]), array([3.99703235, 5.37946501, 2.06221099, 3.10023792, 3.16763863]), array([2.01941951, 3.02142589, 1.96044454, 1.29723814, 1.97746689,
       3.14230818]), array([2.77835436, 3.56907668, 0.60193643, 0.74125617, 3.09626178,
       3.71041983, 0.95190177]), array([1.40549674, 2.9496775 , 2.67431881, 1.15386568, 0.61255355,
       3.17193985, 0.77662124, 2.13487526]), array([2.66778462, 4.23365772, 2.57664138, 2.33304707, 1.87111517,
       1.39849893, 1.30199887, 2.78668881, 0.86132717])] 

(Optionally) Convert distance matrix to data frame for easier reading:

DT2 = pd.DataFrame(dist_ET2)
print("Table 2 Euclidean distance dataframe: \n", DT2, "\n")

Table 2 Euclidean distance dataframe: 
           0         1         2         3         4         5         6  \
0       NaN       NaN       NaN       NaN       NaN       NaN       NaN   
1  0.362162       NaN       NaN       NaN       NaN       NaN       NaN   
2  2.923091  3.865752       NaN       NaN       NaN       NaN       NaN   
3  1.308097  2.403917  0.754078       NaN       NaN       NaN       NaN   
4  0.761587  2.150605  2.916004  1.070504       NaN       NaN       NaN   
5  3.997032  5.379465  2.062211  3.100238  3.167639       NaN       NaN   
6  2.019420  3.021426  1.960445  1.297238  1.977467  3.142308       NaN   
7  2.778354  3.569077  0.601936  0.741256  3.096262  3.710420  0.951902   
8  1.405497  2.949678  2.674319  1.153866  0.612554  3.171940  0.776621   
9  2.667785  4.233658  2.576641  2.333047  1.871115  1.398499  1.301999   

          7         8  
0       NaN       NaN  
1       NaN       NaN  
2       NaN       NaN  
3       NaN       NaN  
4       NaN       NaN  
5       NaN       NaN  
6       NaN       NaN  
7       NaN       NaN  
8  2.134875       NaN  
9  2.786689  0.861327   

Calculate Spearman's rank correlation:

dist_ST2 = distancematrix(T2_scaled, dist='s')
print("Table 2 Spearman's rank correlation': \n", dist_ST2, "\n")

Table 2 Spearman's rank correlation': 
 [array([], dtype=float64), array([0.]), array([1.5, 1.5]), array([1.3, 1.3, 0.1]), array([0.6, 0.6, 1.7, 1.6]), array([1.6, 1.6, 0.7, 1.1, 1. ]), array([1.3, 1.3, 1.1, 1.2, 1.6, 1.1]), array([1.2, 1.2, 0.4, 0.3, 1.9, 1.4, 0.5]), array([1.1, 1.1, 1.7, 1.6, 0.8, 1.3, 0.4, 1.1]), array([1.6, 1.6, 1.2, 1.5, 0.7, 0.2, 0.9, 1.6, 0.7])] 

(Optionally) Convert to Spearman’s rank correlation matrix to data frame for easier reading:

ST2 = pd.DataFrame(dist_ET2)
print("Table 2 Spearman’s rank correlation dataframe: \n", ST2, "\n")

Table 2 Spearman’s rank correlation dataframe: 
           0         1         2         3         4         5         6  \
0       NaN       NaN       NaN       NaN       NaN       NaN       NaN   
1  0.362162       NaN       NaN       NaN       NaN       NaN       NaN   
2  2.923091  3.865752       NaN       NaN       NaN       NaN       NaN   
3  1.308097  2.403917  0.754078       NaN       NaN       NaN       NaN   
4  0.761587  2.150605  2.916004  1.070504       NaN       NaN       NaN   
5  3.997032  5.379465  2.062211  3.100238  3.167639       NaN       NaN   
6  2.019420  3.021426  1.960445  1.297238  1.977467  3.142308       NaN   
7  2.778354  3.569077  0.601936  0.741256  3.096262  3.710420  0.951902   
8  1.405497  2.949678  2.674319  1.153866  0.612554  3.171940  0.776621   
9  2.667785  4.233658  2.576641  2.333047  1.871115  1.398499  1.301999   

          7         8  
0       NaN       NaN  
1       NaN       NaN  
2       NaN       NaN  
3       NaN       NaN  
4       NaN       NaN  
5       NaN       NaN  
6       NaN       NaN  
7       NaN       NaN  
8  2.134875       NaN  
9  2.786689  0.861327   

Perform hierarchical clustering of scaled data using Euclidean distance:

from Bio.Cluster import treecluster
T2tree = treecluster(data=T2_scaled)

Hierarchical clustering of scaled data using Spearman’s rank correlation:

T2tree2 = treecluster(data=T2_scaled, dist='s')
T2tree3 = treecluster(data=None, distancematrix=dist_ST2)

T2tree

<Bio.Cluster.Tree at 0x2a8f7af9600>