Non-negative Matrix Factorization

Energy Control Problem Code in MATLAB: Non-Intrusive Load Monitoring (NILM) for HVAC Systems This repository contains the dataset we collected for HVAC energy disaggregation, as well as the source code and demonstrations from our paper in IEEE Transactions on Power Systems. To the best of our knowledge, this is the first dataset collected for studying Non-Intrusive Load Monitoring (NILM) applied to Heating, Ventilation, and Air Conditioning (HVAC) systems. Energy disaggregation or Non-Intrusive Load Monitoring (NILM) addresses the problem of extracting device-level energy consumption information by monitoring the aggregated signal at a single measurement point, without the need to install meters on each individual device. This can be framed as a source separation problem where the aggregated signal is represented as a linear combination of the basic vectors in a matrix factorization framework. In this work, we utilize machine learning to predict the energy consumption pattern of each device over the course of a day. The project is part of our collaboration with [institution name]. Prerequisites: MATLAB R2015a Datasets (Temporarily unavailable. Will be available once the required permissions are granted. Apologies for the inconvenience!) Experiments We designed two different experiments to evaluate our proposed algorithm. The first experiment disaggregates the energy of the entire household into the energy consumption of all devices within the home.

Matlab基础向量与矩阵运算 在Matlab中，矩阵运算是核心功能之一，主要包括以下几种操作： 矩阵加法：对于两个矩阵A和B，它们的维度必须相同才能进行加法运算。运算符是+，例如：C = A + B; 矩阵乘法：矩阵的乘法规则是：A的列数必须等于B的行数，运算符是*，例如：C = A * B; 矩阵转置：使用单引号(')来转置矩阵，例如：C = A'; 矩阵求逆：对于方阵A，可以使用inv函数来求逆，例如：B = inv(A); 点积与叉积：Matlab支持向量的点积和叉积，例如：dot_product = dot(A, B);cross_product = cross(A, B); 通过这些基本的矩阵操作，可以完成大量的数学计算，广泛应用于数据分析、工程计算等领域。

非等值连接 SQL SELECT e.ename, e.job, e.sal, s.gradeFROM emp e, salgrade sWHERE e.sal BETWEEN s.losal AND s.hisal;

赫斯特分解算法（Hurst Factorization）是一种用于时间序列分析的重要工具。该算法利用数学方法分解时间序列数据，揭示其中的长期记忆性质。MATLAB开发环境为其提供了强大的实现平台，使其在金融和工程领域得到广泛应用。

矩阵运算和数组运算的对照表： | 矩阵算法 | 数组算法 | 命令形式 | 功能含义 ||------------------|--------------------|--------------------|---------------------------------------|| A’ | A.’ | 求矩阵A的共轭转置 | 求数组A的非共轭转置 || x±A | x±A | 标量x与矩阵A元素和或差 | 标量x与数组A元素和或差 || x×A | x.*A | 标量x与方阵A各元素积 | 标量x与数组A各元素积 || x×inv(A) | - | 标量x与方阵A的逆矩阵积 | - || x./A, A.\x | - | 标量x分别除以矩阵A元素 | 标量x分别除以数组A元素 |

在本例中，矩阵相乘的变换意义通过将M和P相乘，得到的矩阵设为Q。Q的第一行第一列元素为Q(1,1) = 0.1×4000 + 0.3×2000 + 0.15×5800 = 1870。由此可以看出，Q表示了夏季消耗的原材料总成本。从线性变换的角度来看，Q矩阵把以件数为单位的产品空间映射到了以元为单位的成本空间。

This code is an exercise that adds the diagonal elements of any matrix. The sum of the diagonal elements can be easily calculated using MATLAB functions. To achieve this, use the built-in function to access and sum up the elements along the diagonal of the matrix.

矩阵运算 A = [1 2 3 ; 4 5 6 ; 7 8 9]; B = [1 2 3 ; 4 5 6]; C = [1 0 1 ; 0 2 3 ; 4 5 0];A + C = A + CBA = B * AdetA = det(A)traceA = trace(A)BT = B'invA = inv(A)rankA = rank(A)[EigenVectors, EigenValues] = eig(A)

矩阵分解的推荐算法MATLAB实现，直接运行main.m

在数值线性代数中，雅可比方法是一种迭代算法，用于确定严格对角占优线性方程组的解。该方法通过求解每个对角线元素并插入一个近似值，随后迭代该过程直到收敛。此算法是矩阵对角化雅可比变换方法的精简版。该方法以卡尔·古斯塔夫·雅各比（Carl Gustav Jacobi）的名字命名。