[machine learning] vectorized computing -- a must on the way of machine learning

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— machine learning —

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— 【 machine learning 】 On the normal equation method & gradient descent —
— 【 machine learning 】 Data standardization of gradient descent —
— 【 machine learning 】logistic Classification regression algorithm —
— The 10th “ Teddy cup “ Thank you for learning summary —

One 、 Solving the matrix

In solving the matrix , There are often many good , Highly optimized linear algebra library , Such as octave,matlib,python numpy, c++,java.
We use these linear algebra libraries , It can be implemented in just a few lines Desired effect .

Read this article （ Need a little knowledge of Linear Algebra ）

Two 、 Patients with a

for example Find the formula ：

$h(x)={\sum }_{i=1}^n{\theta }_i\ast x_i$
We can cycle through each value to find every last $i$ The corresponding result is , But the time complexity of the cycle is $O(n)$ , We can ${\theta }_i(i=1,2,3...n)$ See as $n$ The column vector of dimension ,$x_i$ As $n$ The column vector of dimension , Then the original formula is to find the inner product of two vectors ${\theta }^T\ast x_i$ To find the equation , In this way numpy You only need one line of code in . Here's the picture （ The demo code is octave(matlib Open source Edition ））

c++ Realization

3、 ... and 、 Example 2

• Let's take a more complicated example ：

（ I don't know about gradient descent yet. I suggest you eat the article first ： machine learning 】 On the normal equation method & gradient descent ）
In gradient descent (Gradient descent) Synchronize updates Parameters ${\theta }_i(i=1,2,3...m)in$

We can go through the loop $i$ Get each parameter update , But can we use the method of example 1 Simplification ,

Pictured :

Let's change the equation to The operation between vectors ,
$\theta =\theta -\alpha \ast \delta$
( among ：$\delta$ = ${\sum }_{x=1}^n\frac{（h_{\theta }(x)-y_i{）}^2}{n}\ast x_i$,$h_{\theta }(x)-y_i$ It's a real number ,$x_i$ Is the column vector of the feature dimension )

Now the parameters ${\theta }_i$ It can also be updated synchronously , Meet the requirements

Four 、 At the end

In the face of , The data is at the level of millions , Ten million levels , Or feature millions , Feature level , Vectorization It is very efficient to improve the operation efficiency , Than for Loops are much better to use , This is very common in machine learning , Be sure to master