ML | T-distributed stochastic neighbor embedding (t-SNE) algorithm

Michael Zippo 18.07.2021

What is dimension reduction?
Dimension reduction — it is a method of representing n-dimensional data (multidimensional data with many elements) in 2 or 3 dimensions.

An example of dimensionality reduction can be discussed as a classification problem, i.e. the student will play football or not, which depends on both temperature and humidity, and can be summarized in a single basic characteristic, since both functions are highly correlated. Therefore, we can reduce the number of functions in such tasks. The problem of three-dimensional classification is difficult to imagine, and two-dimensional can be compared with a simple two-dimensional space, and the problem of one-dimensional — with a simple line.

How does t-SNE work?
The t-SNE nonlinear dimensionality reduction algorithm finds patterns in the data based on the similarity of data points to features, point similarity is calculated as the conditional probability that point A will choose point B as its neighbor.
It then tries to minimize the difference between these conditional probabilities (or similarities) in high-dimensional and low-dimensional space to perfectly represent data points in low-dimensional space.

Space and time complexity

Applying t-SNE to the MNIST dataset

# Import required modules.

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

from sklearn.manifold import TSNE

from sklearn.preprocessing import StandardScaler

Code # 1: Reading data

< code>

# Reading data using pandas

df = pd.read_csv ( ’mnist_train.csv’ )

# print the first five lines df

print (df.head ( 4 ))

# save tags to l variable.

l = df [ ’ label’ ]

# Remove the tag and save the data pixels per d.

d = df.drop ( "label" , axis = 1 )

Output:

Code # 2: data preprocessing

# Data preprocessing: data standardization

from sklearn.preprocessing import StandardScaler

standardized_data = StandardScale r (). fit_transform (data)

print (standardized_data.shape)

Output:

Code # 3 :

# TSNE
# Choose the best 1000 points as TSNE
# takes a long time for 15K points

data_1000 = standardized_data [ 0 : 1000 ,:]

labels_1000 = labels [ 0 : 1000 ]

   
   model   =   TSNE (n_components   =   2  , random_state   =   0  )  
   # setting parameters  
  # number of components = 2  
  # default bewilderment = 30  
  # default learning rate = 200  
  # default Maximum number of iterations  
  # for optimization = 1000