使用python學線性代數

A neural network is a powerful tool often utilized in Machine Learning because neural networks are fundamentally very mathematical. We will use our basics of Linear Algebra and NumPy to understand the foundation of Machine Learning using Neural Networks. Our article is a showcase of the application of Linear Algebra and, Python provides a wide set of libraries that help to build our motivation of using Python for machine learning.

神經網絡是機器學習中經常使用的強大工具，因為神經網絡從根本上說是非常數學的。 我們將使用線性代數和NumPy的基礎知識來理解使用神經網絡進行機器學習的基礎。 我們的文章展示了線性代數的應用，Python提供了廣泛的庫，有助于建立我們使用Python進行機器學習的動機。

The figure is showing the simplest neural network of two input nodes and one output node.

該圖顯示了具有兩個輸入節點和一個輸出節點的最簡單的神經網絡。

Simplest Neural Network: 2 Input - 1 Output Node

最簡單的神經網絡：2輸入-1輸出節點

Input to the neural network is X₁ and X₂ and their corresponding weights are w₁ and w₂ respectively. The output z is a tangent hyperbolic function for decision making which have input as sum of products of Input and Weight. Mathematically,

輸入到神經網絡的是X ₁和X ₂ ，它們相應的權重分別是w ₁和w ₂ 。 輸出z是用于決策的正切雙曲函數，其輸入為輸入與權重的乘積之和。 數學上

z = tanh(X₁w₁ + X₂w₂)

Where, tanh() is an tangent hyperbolic function because it is one of the most used decision making functions.

其中， tanh()是切線雙曲函數，因為它是最常用的決策函數之一。

So for drawing this mathematical network in a python code by defining a function neural_network( X, W). Note: The tangent hyperbolic function takes input within range of 0 to 1.

因此，通過定義函數Neuro_network(X，W)以python代碼繪制此數學網絡。 注意：正切雙曲函數的輸入范圍為0到1。

Parameter(s):

參數：

Vector X = [[X₁][X₂]] and W = [[w₁][w₂]]

Return value:

返回值：

A value ranging between 0 and 1, as a prediction of the neural network based on the inputs.

一個介于0到1之間的值，作為基于輸入的神經網絡的預測。

Application:

應用：

Machine Learning

機器學習

Computer Vision

計算機視覺

Data Analysis

數據分析

Fintech

金融科技

# Linear Algebra and Neural Network # Linear Algebra Learning Sequence # Simplest Neural Network for 2 input 1 output nodeimport numpy as np# Use of np.array() to define an Input Vector V = np.array([.323,.432]) print("The Vector A : ",V)# defining Weight Vector VV = np.array([.3,.63,]) print("\nThe Vector B : ",VV)# defining a neural network for predicting an # output value def neural_network(inputs, weights):wT = np.transpose(weights)elpro = wT.dot(inputs)# Tangent Hyperbolic Function for Decision Makingout = np.tanh(elpro)return outoutputi = neural_network(V,VV)# printing the expected output print("Expected Output of the given Input data and their respective Weight : ", outputi)

Output:

輸出：

The Vector A : [0.323 0.432]The Vector B : [0.3 0.63] Expected Output of the given Input data and their respective Weight : 0.35316923056117167

翻譯自: https://www.includehelp.com/python/introduction-to-simplest-neural-network.aspx

使用python學線性代數

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