catalogs
1 Introduction to pattern recognition
2.3.1 Introduction to Algorithm Principles
1 Introduction to pattern recognition
pattern recognitionIt is a technique for analyzing and learning from data to extract patterns from it and make decisions. This field covers a wide range of techniques and methods that can be used to process various types of data, including images, speech, text, and more. Here are some common pattern recognition techniques:Resource access: Follow the public number at the end of the article and reply Pattern Recognition ExperimentsThese techniques usually do not exist in isolation, but intersect and integrate with each other to solve more complex problems. In practical applications, it is crucial to select the appropriate pattern recognition technique based on the specific problem and data characteristics.
- image recognition：
- computer vision: The use of computers and algorithms to simulate human vision so that machines can understand and interpret image content. Common applications include face recognition, object detection, and image classification.
- Convolutional Neural Network (CNN): A deep learning model specialized in image recognition that extracts features from images through structures such as convolutional layers and pooling layers.
- speech recognition：
- Natural Language Processing (NLP): Techniques involved in the processing and understanding of human language. Includes text analysis, sentiment analysis, named entity recognition, etc.
- speech recognition: Converts speech signals into text so that machines can understand and process voice commands. Common applications include voice assistants and voice search.
- Pattern Recognition in Biomedicine：
- biometric identification: Includes fingerprint recognition, iris recognition, and genetic sequence analysis for biomedical research and secure identity verification.
- Medical Image Analysis: Analyzing medical images, such as MRIs and CT scans, using pattern recognition technology to assist doctors in making diagnoses.
- time series analysis：
- time series pattern recognition: Modeling and analysis of time series data for forecasting trends, detecting anomalies, etc. It has a wide range of applications in finance, meteorology, stock market, etc.
- Data mining and machine learning：
- clustering algorithm: Grouping similar objects in a dataset, often used in unsupervised learning, e.g. K-mean clustering.
- classification algorithm: Build models to categorize data, such as decision trees, support vector machines, etc.
- regression analysis: Used to establish relationships between inputs and outputs for predicting numerical type results.
- deep learning: Learning a representation of data through a multi-layer neural network is suitable for handling large-scale and complex data.
- Pattern Recognition in Security：
- behavioral analysis: Monitoring and identifying anomalous behavior, such as intrusion detection systems.
- biometric identification: For authentication and access control, e.g. fingerprint, facial recognition.
2 K-means clustering
2.1 Purpose of the study
- Understand the core principles of the K-mean clustering algorithm, including initialization, data point assignment, and cluster center updating.
- Acquire basic skills in implementing K-mean clustering algorithms using C++ in Visual Studio Code, including project construction, data processing, and algorithm implementation.
- By selecting challenging datasets, the K-mean clustering algorithm is practically applied and analyzed for the effect of different K-values on the clustering effect, as well as the visual presentation of the clustering results.
2.2 Research environment
- The C++ programming language and its associated libraries：
- Language support: VSCode has strong C++ language support, providing code highlighting, auto-completion and other features that make coding more efficient.
- Eigen library: As an important tool for linear algebra, the Eigen library is integrated to perform efficient linear algebra operations, providing powerful support for mathematical computation.
- OpenCV library：
- Image Processing: The OpenCV library, as an important tool in the field of computer vision, provides a wide range of functions for image processing and visualization. It includes a series of operations such as image reading, processing, feature extraction, etc., which provides basic support for image-related applications.
- Visualization: OpenCV also supports intuitive image visualization, allowing developers to visualize the effects of image processing, which helps with debugging and optimization.
- C++ Compiler Configuration：
- GCC Configuration: When using VSCode for C++ development, make sure that you have configured the C++ compiler, which is commonly known as the GNU Compiler Collection (GCC). Proper configuration ensures that the code compiles and executes correctly.
- hardware environment：
- Computing resources: In order to process image data, sufficient computational resources are required, including enough memory and powerful CPU/GPU. this guarantees efficient processing and computation of large-scale image data.
- Memory Management: When dealing with large-scale image data, proper memory management becomes crucial to prevent memory overflow and improve the efficiency of program operation.
2.3 Content of the study
2.3.1 Introduction to Algorithm Principles
K-means clustering (K-means) is a commonly used unsupervised learning algorithm for grouping samples in a dataset into K different classes or clusters. Its main goal is to group the data by minimizing the variance of the samples within the clusters. The following is the algorithmic principle of K-mean clustering:The whole process can be summarized in the following steps:
- Initialization: First, K initial cluster centers are selected, which can be randomly selected data points or obtained by other methods. These centers will be used as representatives of the clusters.
- Assign data points: For each data point, it is assigned to the cluster to which the closest clustering center belongs. Here the Euclidean distance is usually used to measure the distance between the data point and the clustering center.
- Update the clustering center: For each cluster, the average of all the data points in it is calculated and that average is used as the new cluster center. This step is equivalent to realigning the clusters so that the variance of the samples within the cluster is minimized.
- Repeat iterations: Steps 2 and 3 are repeated until a stopping condition is met. The stopping condition may be that a predetermined number of iterations is reached, or when the change in the clustering centers is small, i.e., convergence to a stable cluster assignment.
The advantages of K-mean clustering include simplicity and ease of implementation and computational efficiency, but it also has some disadvantages, such as sensitivity to the selection of initial clustering centers and sensitivity to outliers. When applying K-mean clustering, it is usually necessary to standardize the data to ensure that the scales of different features do not affect the clustering results.
- Initialization: Select K initial clustering centers.
- Distribution: Assign each data point to the cluster to which the nearest clustering center belongs.
- Updated: Calculate the new center of each cluster, expressed as the average of the samples within the cluster.
- Iteration: Repeat the allocation and update steps until the stop condition is met.
🌕2.3.2 Data set preparation
A dataset containing 20 samples was chosen so that the effect of K-means clustering could be clearly demonstrated.
🌕2.3.3 experimental step
a. Project build: Create a C++ project in VSCODE, configure the compilation environment, and build the project file structure.
b. Data loading and pre-processing:Read the dataset and perform the necessary data preprocessing to ensure that the data format meets the requirements of K-means clustering.
c. Algorithm implementation: Implement the K-mean clustering algorithm using C++, including key steps such as cluster center initialization, data point assignment, and cluster center update.
d. Parameter tuning: Different values of K are tried and the optimal one is selected by evaluating the metrics (e.g., intra-cluster sum of squares).
C program:
// c_means.cpp : Defines the entry point for the console application.
//
#include "stdafx.h"
#include "math.h"
#define NUM 2
#define NN 20
#define cnum 2
typedef struct {
double x[NUM];
} PATTERN;
PATTERN p[NN]={
//First question
// {0,0},{1,0},{0,1},{1,1},{2,1},{1,2},{2,2},{3,2},{6,6},{7,6},
// {8,6},{6,7},{7,7},{8,7},{9,7},{7,8},{8,8},{9,8},{8,9},{9,9}
//Second question
// {8,9},{9,9},{0,1},{1,1},{2,1},{1,2},{2,2},{3,2},{6,6},{7,6},
// {8,6},{6,7},{7,7},{8,7},{9,7},{7,8},{8,8},{9,8},{0,0},{1,0}
//Third question
{1,1},{9,9},{1,0},{0,1},{2,1},{1,2},{2,2},{3,2},{6,6},{7,6},
{8,6},{6,7},{7,7},{8,7},{9,7},{7,8},{8,8},{9,8},{8,9},{0,0}
};
PATTERN z[cnum],oldz[cnum];
int nj[cnum];
int cindex[cnum][NN];
double Eucliden(PATTERN x,PATTERN y)
{
int i;
double d;
d=0.0;
for (i=0;i<NUM;i++) {
d+=(x.x[i]-y.x[i])*(x.x[i]-y.x[i]);
}
d=sqrt(d);
return d;
}
bool zequal(PATTERN z1[],PATTERN z2[])
{
int j;
double d;
d=0.0;
for (j=0;j<cnum;j++) {
d+=Eucliden(z1[j],z2[j]);
}
if (d<0.00001) return true;
else return false;
}
void C_mean()
{
int i,j,l;
double d,dmin;
for (j=0;j<cnum;j++) {
z[j]=p[j];
}
do {
for (j=0;j<cnum;j++) {
nj[j]=0;
oldz[j]=z[j];
}
for (i=0;i<NN;i++) {
for (j=0;j<cnum;j++) {
d=Eucliden(z[j],p[i]);
if (j==0) {dmin=d;l=0;}
else {
if (d<dmin) {
dmin=d;
l=j;
}
}
}
cindex[l][nj[l]]=i;
nj[l]++;
}
for (j=0;j<cnum;j++) {
if (nj[j]==0) continue;
for (i=0;i<NUM;i++) {
d=0.0;
for (l=0;l<nj[j];l++) {
d+=p[cindex[j][l]].x[i];
}
d/=nj[j];
z[j].x[i]=d;
}
}
} while (!zequal(z,oldz));
}
void Out_Result()
{
int i,j;
printf("Result: \n");
for (j=0;j<cnum;j++) {
printf("nj[%d]=%d\n",j,nj[j]);
for (i=0;i<nj[j];i++) {
printf("%d,",cindex[j][i]);
}
printf("\n");
}
}
int main(int argc, char* argv[])
{
C_mean();
Out_Result();
return 0;
}Program Analysis:
This code implements the K-mean clustering algorithm for dividing a set of data points into two clusters. The following is a detailed analysis of the code:Overall, this is a simple implementation of K-mean clustering for 2D data points that can be implemented by modifying the
- Data Structure Definition:
typedef struct { double x[NUM]; } PATTERN;: defines a structurePATTERNEach structure contains a single structure with a length ofNUMarray of data points to store the coordinates of the data points.PATTERN p[NN] = {...};: defines a file that contains theNNArray of data pointsp, where the coordinates of each data point are stored in thex[NUM]in the array. The number and coordinates of data points are specified by modifying the structure and the array.PATTERN z[cnum], oldz[cnum];: defines two arrayszrespond in singingoldz, which are used to store the current clustering center and the clustering center of the previous iteration, respectively.int nj[cnum];: defines an array of integersnj, which is used to store the number of data points for each cluster.int cindex[cnum][NN];: defines a two-dimensional array of integerscindexthat is used to store the index of each cluster’s data points in the original data set.- Distance calculation function:
double Euclidean(PATTERN x, PATTERN y): Calculates the Euclidean distance between two data points. This function calculates the sum of the squares of the differences in each dimension by traversing the array of coordinates and then takes the square root to get the Euclidean distance.- A function that determines whether two cluster centers are equal:
bool zequal(PATTERN z1[], PATTERN z2[]): Determine whether two sets of clustering centers are equal by calculating the sum of the Euclidean distances between the two sets of centers if less than a small threshold (0.00001), are considered equal.- K-means clustering algorithm body functions:
void C_mean(): This function implements the main logic of K-mean clustering. Initialize the cluster centers and then keep updating the cluster centers through an iterative process until the cluster centers no longer change (converge).- Result output function:
void Out_Result(): Outputs the final clustering results, including the number of data points in each cluster and the index of the data points in the original dataset.- Main function:
int main(int argc, char* argv[]): Main function callsC_mean()Perform the clustering and then callOut_Result()Output results.- Annotation:
- There are three sets of data point annotations in the code, representing three different data sets. Depending on the requirements, you can choose one of the sets of data point collections for clustering test.
NUM、NNrespond in singingcnumand coordinates of data points to adapt to different problems. In practice, the algorithm parameters may need to be adjusted or more complex extensions may be required depending on the situation.
2.3.4 Analysis of results
Output the clustering results and show the clustering effect through graphs.
![[Pattern Recognition] K-mean Clustering Algorithm Decryption and Practice](https://imgs.developpile.com/imgs/8ab3d913a34248729535da55264d734c.png "[Pattern Recognition] K-mean Clustering Algorithm Decryption and Practice")
2.4 Research experience
- Project construction and data processing：
- Hands-on practice with C++ language, in-depth study of basic structures and syntax, and mastery of the steps to create C++ projects in the Visual Studio Code environment.
- A clearer understanding of the code organization structure and modular design provides fundamental support for subsequent algorithm implementation.
- Learn to load and preprocess data using the C++ standard library to ensure that the data will be processed correctly in the K-means clustering algorithm.
- algorithmic implementation：
- The core steps of K-mean clustering are studied in depth, including initialization of cluster centers, assignment of data points, and updating of cluster centers.
- The strongly typed nature of C++ is utilized to better understand the data structures and operations involved in algorithms.
- The practice improved programming skills while deepening the understanding of mathematical principles in clustering algorithms.
- Analysis of the tuning process and results：
- Realizing the sensitivity of K-mean clustering to the value of K, the effect of the number of clusters on the effectiveness of the algorithm was better understood by trying different values of K during the tuning process.
- Visualization tools were used to intuitively understand the clustering effect and to gain a deeper understanding of the distribution of data points and the relationship between different clusters.
- Such in-depth analysis helps to better understand the structure and characteristics of the dataset, providing rich information for subsequent data mining and analysis.