Matrix decomposition is about how to **reduce a matrix into its constituent parts**. It tries to simplify complex matrix operations on the decomposed matrix instead of the original matrix.

There are many ways to decompose a matrix using a range of different techniques.

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Training a machine learning model is about finding a good set of parameters. The best value is the minimum value.

**Global minima**: The point where a function best values takes the minimum value. When the aim is to minimise the function and solve it using optimisation algorithms, the function could have a minimum value at various points. It is called**local minima.****Unconstrained optimisation**is where we see the minimum of a function.**Constrained optimisation**introduces a set of constraints to limit possible value.

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- Math enables you to select the right machine learning algorithm. It gives insight into how the model works, including selecting the
**right model parameter and validation strategies.** - Maths helps with creating the
**right confidence interval and uncertainty measurements**with the model. - Maths is needed to understand aspects such as
**metrics, training time, model complexity, number of parameters, and number of features.** - By knowing the machine learning model's math, you could
**develop a customised model.**

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**Linear Algebra in machine learning is a systematic representation of data that computers can understand**.

- It is the part of mathematics that uses
**vector space**and**matrices**to**represent linear equations**. **Vectors**are special objects that can be added together and multiplied by scalars to produce another object of the same kind.**A matrix**can be thought of as a group of column vectors or row vectors.

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Analytic geometry is concerned with **defining and representing geometrical shapes numerically.** It extracts numerical information from the shapes numerical definitions and representations.

Important terms that will help you start learning this subject:

**Distance Function**: It is a function that gives numerical information for the distance between the elements of a set.**Inner Product**: This term introduces natural geometrical concepts, such as the length of a vector and the angle or distance between two vectors.

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Calculus is concerned with a perpetual change that consists of functions and limits. **Vector calculus involves the differentiation and integration of the vector fields.**

**Useful terms:**

**Derivative**is a function of real numbers that measure the change of the function (output) value concerning a change in its argument (input value)**Differentiation**is the action of calculating a derivative.**Gradient**is another word for derivative and is used for functions with several inputs and one output.

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**Machine Learning is a tool that Data scientists use to obtain valuable patterns. **Learning the math behind machine learning could give you an edge.

These six math subjects are the foundation for machine learning.

- Linear Algebra
- Analytic Geometry
- Matrix Decomposition
- Vector Calculus
- Probability & Distributions
- Optimisation

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**Probability** is the study of randomness. **Probability distribution **is a function that measures the probability of a specific outcome associated with the random variable.

**Probability theory** and **statistics** are about different aspects of uncertainty.

**In statistics**, we use probability to try and find the underlying process of something that has happened and strive to explain the observations.**Machine learning**is similar to statistics. It makes a model that represents the process that generates the data.

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**Statistics is using math to do technical analysis of data**. Instead of guesstimating, data helps us get concrete and factual information.

The most widely used statistical concept in data science is called *Statistical Features.* It includes important measurements like bias, variance, mean, median and percentiles. It’s all code-friendly too.

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Imagine yourself walking into a pizzeria to buy a delicious pizza.

A pizzeria sells *many kinds of pizzas.*

and serves for each kind *three different sizes* (small-medium-large)

To remember all these data , the owner arranged kinds , sizes and prices in a respective way in a table (or The Menu)** **.

In this case, the menu is our *matrix.*

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The biggest problem, thoug h, is that models like this one are performed only on a single task. Future tasks require a new set of data points as well as equal or more amount of resources.

*Transfer learning is an approach in deep learning (and machine learning) where knowledge is transferred from one model to another. *

Deep learning models require a LOT of data for solving a task effectively. However, it is not often the case that so much data is available. For example, a company may wish to build a very specific spam filter to its internal communication system but does not possess lots of labelled data.

What you can do is using a pre-trained image classifier on dog photos to predict cat photos.

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