Table of contents

Vector Operations

Vector generation

Vector index

Non-zero member search

Frequency of vector member

Modulus of vector

Vector addition and subtraction, number and dot products, cross products

Vector transpose

Vector normalization

Statistical indicators of vector

Matrix Operations

Basic operations

Matrix generation

Special Matrix

Matrix index

Matrix concatenate

Matrix addition and subtraction

Number and dot products of matrix

Matrix multiplication

Determinant

Inverse of a square matrix

Multidimensional matrix

Matrix dimension

Sum of matrix

Cumulative sum of matrix

Mean of matrix

Standard deviation of matrix

Search for non-zero members

Matrix transformation

Transpose a matrix

Rank of matrix

Matrix normalization

Complex

Complex creation

Real part and imaginary part of complex number

Complex string

Modulus of complex

Phase angle

Complex conjugate

Complex conjugate pairs

Sign function (Signum function)

Shift phase angles

Complex exponentials

Solution of Linear Equations

Matrix inversion

Least square method

Linear Programming

Statistics

Correlations

Covariance

Covariance matrix

Correlation coefficient

Correlation matrix

Parameter estimation and hypothesis testing

Parameter estimation

Hypothesis testing of regression model

p value

Statistical distance between samples

Euclidean distance

Mahalanobis distance

Mathematical modeling

Data exploration

Data size and fields

Categorical data

Numerical data

Correlation between variables

Missing value analysis

Outlier detection: Box plot, Z-score , Median absolute deviation（MAD）

Data pre-processing

Variable preliminary filtering

Missing value handling

Delete missing value

Statistic filling

k-means cluster filling

Linear regression model filling

Flag missing information for individual variable

Flag missing information for multiple variables

Categorical variable handling

Numerical the categorical variables

Smoothing categorical variable

Date time variable processing

Date time feature derive and date time intervals

Date time combination

Data standardization

Min-Max standardization

Z-Score standardization

Automatic normalization

Variable transformation

Logarithmic transformation

Box-Cox transformation

Tangent and arc tangent transformation

Others transformation

Interaction

Ratio

Data discretization

Equi-width binning

Equi-frequency binning

Abnormal distribution processing

Low frequency categorical data processing

High skewness data processing

Outlier processing

Balanced sampling

Under sampling

Oversampling

Dataset split

Random split
Stratified split

Dimension reduction

PCA

Variable selection

Select variables using correlation coefficients
Select variables using p-value
Identification of pseudo-independent variables

Data smoothing

sg data smoothing(polynomial smoothing)

Curve fitting and supervised learning algorithm

Least-squares algorithm linear fitting

Polyfit

Partial least squares fitting

Lasso regression

Ridge regression

Elastic Net regression

SVMs

Unsupervised learning algorithm

kmeans

Model evaluation

Classification model evaluation

Accuracy, Precision, Recall, Specificity, F1

AUC，GINI，KS

ROC curve

Lift curve

Recall curve

Regression model evaluation

MSE, RMSE, MAE, MAPE, R²

Residual plot

Result comparison graph