{"id":1007,"date":"2018-11-29T02:08:44","date_gmt":"2018-11-28T23:08:44","guid":{"rendered":"http:\/\/kusuaks7\/?p=612"},"modified":"2021-11-25T08:11:01","modified_gmt":"2021-11-25T08:11:01","slug":"learning-ai-if-you-suck-at-math-part4-tensors-illustrated-with-cats","status":"publish","type":"post","link":"https:\/\/www.experfy.com\/blog\/ai-ml\/learning-ai-if-you-suck-at-math-part4-tensors-illustrated-with-cats\/","title":{"rendered":"Learning AI if You Suck at Math\u200a-Part 4-\u200aTensors Illustrated (with Cats!)"},"content":{"rendered":"

Ready to learn Machine Learning? Browse courses<\/a>\u00a0like\u00a0Machine Learning Foundations: Supervised Learning<\/a> developed by industry thought leaders and Experfy in Harvard Innovation Lab.<\/em><\/strong><\/p>\n

Welcome to part four of Learning AI if You Suck at Math. If you missed\u00a0part 1<\/a>,\u00a0part 2<\/a> and part3<\/a>\u00a0be sure to check them out.<\/p>\n

Maybe you\u2019ve downloaded\u00a0TensorFlow\u00a0and you\u2019re ready to get started with some deep learning?<\/p>\n

But then you wonder: What the hell is a tensor?<\/strong><\/p>\n

Perhaps you looked it up on\u00a0Wikipedia<\/a>\u00a0and now you\u2019re more confused than ever. Maybe you found this\u00a0NASA tutorial<\/a>\u00a0and still have no idea what it\u2019s talking about?<\/p>\n

The problem is most guides talk about tensors\u00a0as if you already understand all the terms they\u2019re using<\/em>\u00a0to describe the math.<\/p>\n

Have no fear!<\/p>\n

I hated math as a kid, so if I can figure it out, you can too! We just have to explain everything in simpler terms.<\/p>\n

So what is a tensor and why does it flow?<\/strong><\/p>\n

Tensors = Containers<\/h3>\n

A tensor is the basic building block of modern machine learning.<\/p>\n

At its core it\u2019s a data container. Mostly it contains numbers. Sometimes it even contains strings, but that\u2019s rare.<\/p>\n

So think of it as a bucket of numbers.<\/strong><\/p>\n

There are multiple sizes of tensors. Let\u2019s go through the most basic ones that you\u2019ll run across in deep learning, which will be between 0 and 5 dimensions.<\/p>\n

We can visualize the various types of tensors like this (cats come later!):<\/p>\n

<\/canvas><\/figure>\n

0D Tensors\/Scalars<\/strong><\/h3>\n

Every number that goes into a tensor\/container bucket is called a \u201cscalar.\u201d<\/p>\n

A scalar is a single number.<\/strong><\/p>\n

Why don\u2019t they just call it a number you ask?<\/p>\n

I don\u2019t know. Maybe math peeps just like to sound cool? Scalar does sound cooler than number.<\/p>\n

In fact you can have a single number tensor, which we call a 0D tensor, aka a tensor with 0 dimensions. It\u2019s nothing more than a bucket with a one number in it. Imagine a bucket with a single drop of water and you have a 0D tensor.<\/p>\n

In this tutorial we\u2019ll use Python, Keras and TensorFlow, as well as the Python library NumPy. We set all of that up in\u00a0<\/strong>my last tutorial, Learning AI if You Suck at Math (LAIYSAM) \u2014 Part 3<\/strong><\/a>, so be sure to check that out if you want to get your deep learning workstation running fast.<\/strong><\/p>\n

In Python, these tensors are typically stored in a NumPy arrays.\u00a0NumPy<\/a>\u00a0is a scientific library for manipulating numbers that is used by pretty much every AI framework on the planet.<\/p>\n

import numpy<\/pre>\n
x = np.array(5)<\/pre>\n
print(x)<\/pre>\n
Our output is:<\/p>\n
5<\/pre>\n
On\u00a0Kaggle (the data science competition site)<\/a>\u00a0you will often see Jupyter Notebooks (also installed in LAIYSAM -Part 3) that talk about turning data into a NumPy arrays. Jupyter notebooks are essentially a markup document with working code embedded. Think of it as an explanation and program rolled into one.<\/p>\n
Why the heck would we want to turn data into a NumPy array?<\/strong><\/p>\n
Simple. Because we need to transform any input of data, be that strings of text, images, stock prices, or video into a universal standard that we can work with easily.<\/strong><\/p>\n
In this case we transform that data into buckets of numbers so we can manipulate them with TensorFlow.<\/p>\n
It\u2019s nothing more than organizing data into a usable format. In web programming you might represent via XML, so you can define its features and manipulate it quickly. Same thing. In deep learning we use tensor buckets as our basic Lego block.<\/p>\n
1D Tensors\/Vectors<\/strong><\/h3>\n
If you\u2019re a programmer, you already know about something similar to a 1D tensor:\u00a0an array<\/strong>.<\/p>\n
Every programming language has arrays, which are nothing but a string of data chunks in a single row or column. In deep learning this is called a 1D tensor. Tensors are defined by how many axes they have in total. A 1D tensor has exactly one axis.<\/p>\n
A 1D tensor is called a \u201cvector.\u201d<\/strong><\/p>\n
We can visualize a vector as a single column or row of numbers.<\/p>\n
<\/canvas><\/figure>\n
If we wanted to see this in NumPy we could do the following:<\/p>\n
x = np.array([1,2,3,4])<\/pre>\n
print(x)<\/pre>\n
Our output is:<\/p>\n
array([1,2,3,4])<\/pre>\n
We can also visualize how many axes a tensor has by using NumPy\u2019s ndim function. Let\u2019s try it with a 1D tensor.<\/p>\n
x.ndim<\/pre>\n
Our output is:<\/p>\n
1<\/pre>\n
2D Tensors<\/strong><\/h3>\n
You probably already know about another kind of tensor:\u00a0a matrix.<\/strong><\/p>\n
A 2D tensor is called a matrix.<\/strong><\/p>\n
<\/canvas><\/figure>\n
No, not the movie with Keanu Reeves. Think of an Excel sheet.<\/p>\n
We can visualize this as a grid of numbers with rows and columns.<\/p>\n
Those columns and rows represent two axes. A matrix is a 2D tensor, meaning it is two dimensional, aka a tensor with 2 axes.<\/p>\n
In NumPy we would represent that as:<\/p>\n
x = np.array([[5,10,15,30,25],<\/pre>\n
[20,30,65,70,90],<\/pre>\n
[7,80,95,20,30]])<\/pre>\n
We can store characteristics of people in a 2D tensor. For example, a typical mailing list would fit in here.<\/p>\n
Let\u2019s say we have 10,000 people. We also have the following features or characteristics about each person:<\/p>\n