Author: Zen and the Art of Computer Programming
1 Introduction
In the field of modern machine learning, algorithm selection is a very important issue. When given a task, how to choose the method that is most suitable for the task and has the best performance from the many available algorithms? How to determine the accuracy, robustness and efficiency of a model? How to rank different algorithms according to specific evaluation criteria? These are key issues in the machine learning algorithm selection process. Most traditional algorithm selection methods focus on aspects such as efficiency or accuracy, while ignoring other aspects such as robustness, interpretability, adaptability, time complexity, memory usage, etc., making it difficult to meet the needs of practical applications. This paper proposes a unified machine learning algorithm selection framework based on the following viewpoints. The framework is based on three basic assumptions:
- Different types of tasks often have different optimization goals. For example, classification tasks may need to maximize accuracy, and regression tasks may need to minimize errors;
- Different data sets will also affect the performance of the algorithm, and the same algorithm may show completely different results on different data sets;
- In the same category of tasks, some algorithms may solve some sub-problems better due to their unique capabilities or characteristics, while other algorithms may be considered more general because of their simplicity and may not necessarily handle all situations well. . Therefore, it is necessary to comprehensively consider various factors, analyze candidate algorithms into categories, and finally decide which algorithm to use. Based on the above assumptions, this article establishes a unified machine learning algorithm selection framework. By using statistical methods, it can accurately evaluate different algorithms for different types of tasks, different data sets, and even different scenarios, thereby providing information for actual algorithm selection. guide. This article systematically discusses the machine learning algorithm selection method based on algorithm evaluation criteria for the first time, and successfully applies this method to Weibo sentiment analysis, news recommendation system, text clustering, image recognition, object detection, recommendation system, sequence prediction, etc. Algorithms in multiple fields are selected and compared. Finally, this paper provides an outlook on future research directions and proposes directions for further improvements.
2. Explanation of basic concepts and terms
2.1 Machine Learning Algorithm
Machine learning is a science about computer programming that aims to automatically learn from data and improve its own programming model, and to discover patterns in never-before-seen data. The main purpose of machine learning is to build an algorithm that can learn from data, extract knowledge, and make predictions. The classification of machine learning algorithms includes five types: supervised learning, unsupervised learning, semi-supervised learning, reinforcement learning and transfer learning. The learning algorithms involved in this article all belong to the category of supervised learning, including supervised learning algorithms, semi-supervised learning algorithms, unsupervised learning algorithms, reinforcement learning algorithms, and transfer learning algorithms.
2.2 Evaluation Criteria
Algorithm evaluation standards are the basis for measuring the quality of an algorithm. The evaluation criteria for machine learning algorithms consist of two parts, namely the objective function and performance indicators. The objective function is the demand and expectation for the learning task and is a measure of the performance of the algorithm on the test data. For example, for classification tasks, it is usually hoped that the algorithm can output a classifier with high accuracy, so the objective function is usually accuracy. Performance indicators refer to parameters such as algorithm running speed, resource usage, robustness, and generalization ability. Typically, the better the objective function, the better the algorithm performance indicators. The performance indicators of an algorithm can be evaluated through performance metrics, such as loss function, precision, recall, F1 value, etc.
2.3 Dataset
Data sets are the basis for algorithm learning and contain input and output data. The input data is used to train the algorithm, and the output data represents the actual prediction value of the algorithm on the input data. The data set is divided into three parts: training set, verification set and test set. The training set is used to train the algorithm, the validation set is used to adjust parameters, and the test set is used to test the effectiveness of the algorithm.
2.4 Model
The model is the result of training based on the data set. Models can be used to make predictions on new data or as input to other models.
2.5 Hyperparameter
Hyperparameters are parameters of machine learning algorithms. They are values set before training and are used to control the internal parameters of the algorithm, such as the number of decision trees, learning rate, regularization coefficient, etc. Hyperparameters should be set before training and then searched to find optimal values.
2.6 Cross-Validation
Cross-validation is a more effective way to evaluate the performance of an algorithm. It divides the data set into two mutually exclusive sets, one as the training set and the other as the test set. The algorithm is trained on the training set and the performance is evaluated on the test set. The number of cross-validation is generally set to 5-10 times.
2.7 Evaluation Metric
The evaluation metric refers to the distance between the algorithm output results and the real results. Commonly used evaluation indicators include accuracy, recall, F1 value, ROC curve, PR curve, etc.
3. Explanation of core algorithm principles, specific operating steps and mathematical formulas
3.1 Principal component analysis (PCA)
Principal Component Analysis is a statistical method used to extract the most characteristic variables from multidimensional data. Principal component analysis is a dimensionality reduction method that maps the original data into a new low-dimensional space so that the data in the low-dimensional space exhibits maximum variation while maintaining as much sample information as possible. The specific steps of principal component analysis are as follows:
Centralize the input data: subtract the average value from each sample feature vector to make the data distribution range between each feature similar to facilitate subsequent calculations.
Find the covariance matrix: Find the covariance matrix of the input data X.
Find the eigenvalues and eigenvectors: Find the eigenvalues and corresponding eigenvectors of the covariance matrix.
Select important features based on the threshold: set a threshold k, retain the eigenvectors corresponding to the first k eigenvalues of the covariance matrix, and form a matrix W by columns to represent the eigenvectors after dimensionality reduction.
Project the original data to a low-dimensional space: Project the input data to the low-dimensional space of the feature vector W to obtain the reduced-dimensional data.
The mathematical formula of PCA is:
Z = X * W (1)
Among them, Z is the dimensionally reduced data, X is the input data, and W is the dimensionally reduced feature vector matrix.
3.2 Logistic Regression
Logistic regression is one of the simplest classification algorithms. Logistic regression is a binary classification model that can be used to determine the probability of an event occurring. It is a linear model that assumes that the outcome of a linear combination of input variables can explain the binary variation of the output variables. Logistic regression converts the output of a linear regression model into predicted probabilities through the sigmoid function. The specific steps are as follows:
Centralize the input data: perform zero-mean processing on the input data X to eliminate the dimensional influence of different features.
Fit the logistic regression model: Fit the logistic regression model to obtain the optimal weight w and bias b.
Use the model to predict: Use the model to predict and get the output probability y.
The mathematical formula for logistic regression is:
y = sigmoid(w * x + b) (2)
Among them, x is the input data and y is the predicted output probability. The sigmoid function is the activation function of the logistic regression model. Its input is the output of the linear model, and the output is a probability value between 0 and 1.
3.3 k nearest neighbor algorithm (KNN)
K Nearest Neighbors (KNN) is an unsupervised learning algorithm for classification and regression. The KNN algorithm determines which category the object should be classified into by comparing the distance between the object to be predicted and each sample. The specific steps are as follows:
Calculate the distance of the object to be predicted: Calculate the distance of the object to be predicted and measure its similarity to the sample.
Find k nearest neighbors: Find the k samples closest to the object to be predicted.
Voting mechanism: Vote on the label labels of the k nearest neighbors to determine the label of the object to be predicted.
The mathematical formula of the KNN algorithm is:
label_pred = mode{labels of K nearest points} (3)
Among them, mode{} represents the mode, and labels of K nearest points represent the label labels of the K nearest neighbor samples.
3.4 SVM algorithm (SVM)
Support Vector Machine (SVM) is a two-class classification method. SVM linearly divides the data by solving the interval maximization or minimization Lagrange multiplier. The goal of SVM is to find an optimal separation hyperplane to divide the input data into positive and negative categories to maximize the class distance. The specific steps are as follows:
Centralize the input data: Zero-mean the input data to eliminate the dimensional impact of different features.
Using the kernel function: The kernel function maps the input data to a high-dimensional space, making the original data linearly inseparable.
Maximize the interval: Solve the optimization problem to find the best separation hyperplane.
Use the kernel technique: map the input data to a high-dimensional space through the kernel function, and transform the linear inseparable problem of the sample into a nuclear norm inseparable problem in the high-dimensional space.
The mathematical formula of SVM is:
f(x) = w^T * x + b
Among them, f(x) is the hyperplane function, w is the normal vector of the separating hyperplane, and b is the intercept of the separating hyperplane.
3.5 Naive Bayes算法（Naive Bayes）
The Bayesian approach is a method based on probability statistics. The Bayesian method considers that the probability of each event depends on all currently known information and tries to find out the influencing factors of the most likely event. In the field of machine learning, Bayesian methods are widely used in classification, clustering, anomaly detection, text classification and other fields. The specific steps are as follows:
Centralize the input data: Zero-mean the input data to eliminate the dimensional impact of different features.
Calculate prior probability: Calculate the prior probability of each category.
Calculate conditional probability: Calculate the conditional probability that the input data appears in each category.
Classification using probability: Classification based on prior probability and conditional probability.
The mathematical formula of Naive Bayes is:
P(C|D) = P(D|C)*P(C)/P(D)
Among them, C represents the target category, D represents the input data, P(C) represents the prior probability, and P(C|D) represents the conditional probability.