1. Introduction to SVM
General framework of machine learning: training set => extracting feature vectors => Combining with certain algorithms (classifier: such as decision tree, KNN) => obtaining resultsDefinition of the SVMSupport Vector Machines (SVM) is a dichotomous model that maps the feature vectors of an instance to points in a space. The purpose of THE SVM is to draw a line that “best” distinguishes the two types of points, so that if a new point comes along in the future, the line will also do a good job of classification. SVM is suitable for small and medium-sized data samples, nonlinear, high-dimensional classification problems.
2 Basic concepts of SVM Map the feature vectors of an instance (taking two-dimensional as an example) to some points in the space, such as solid points and hollow points in the figure below, which belong to two different categories. The purpose of SVM is to draw a line that “best” distinguishes the two types of points, so that if a new point comes along in the future, the line will also do a good job of classification.
Q1: How many lines can you draw to distinguish sample points? A: There are an infinite number of lines that can be drawn. The difference is how well they work. Each line can be called a partition hyperplane. For example, the green line above is not good, the blue line is ok, and the red line looks better. The line we hope to find that works best is a partition hyperplane with maximum spacing.
Q2: Why is it called a hyperplane? A: Because the characteristics of the sample are likely to be higher dimensional, the division of the sample space is not a line.
Q3: What are the criteria for drawing lines? / What makes this line work well? / What’s good? A: SVM will look for partition hyperplanes that can distinguish between the two categories and maximize the margin. When the sample is locally disturbed, it has the least influence on the hyperplane, the classification result is the most robust, and the generalization ability is the strongest for the unknown example.
Q4: What is margin? A: For any hyperplane, there is a minimum distance (vertical distance) between the data points on both sides of the hyperplane. The sum of these two minimum distances is the interval. For example, the strip area formed by two dotted lines in the figure below is the margin. The dotted line is determined by the two points closest to the central solid line (that is, determined by the support vector). But now the margin is relatively small. If we draw it in the second way, the margin is obviously larger and closer to our target.
Q6: What are support vectors? A: As can be seen from the figure above, all the points on the dotted line are the same distance from the partition hyperplane. In fact, only these points together determine the position of the hyperplane, so they are called “Support vectors”, hence the “Support vector machine”.
Two, some source code
function varargout = main(varargin)
% MAIN MATLAB code for main.fig
% MAIN, by itself, creates a new MAIN or raises the existing
% singleton*.
%
% H = MAIN returns the handle to a new MAIN or the handle to
% the existing singleton*.
%
% MAIN('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in MAIN.M with the given input arguments.
%
% MAIN('Property'.'Value',...). creates anew MAIN or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before main_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to main_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help main
% Last Modified by GUIDE v2. 5 24-Apr- 2020. 08:53:33
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @main_OpeningFcn, ...
'gui_OutputFcn', @main_OutputFcn, ...
'gui_LayoutFcn', [],...'gui_Callback'[]);if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end
if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
% --- Executes just before main is made visible.
function main_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to main (see VARARGIN)
% Choose default command line output for main
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes main wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = main_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure
varargout{1} = handles.output;
% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
DataGui
% --- Executes on button press in pushbutton2.
function pushbutton2_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
TrainNet
% --- Executes on button press in pushbutton3.
function pushbutton3_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton3 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% --- If Enable = ='on', executes on mouse press in 5 pixel border.
% --- Otherwise, executes on mouse press in 5 pixel border or over pushbutton1.
function pushbutton1_ButtonDownFcn(hObject, eventdata, handles)
% hObject handle to pushbutton1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
Predict
function edit1_Callback(hObject, eventdata, handles)
% hObject handle to edit1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit1 as text
% str2double(get(hObject,'String')) returns contents of edit1 as a double
% --- Executes during object creation, after setting all properties.
function edit1_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0.'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor'.'white');
end
function edit2_Callback(hObject, eventdata, handles)
% hObject handle to edit2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of edit2 as text
% str2double(get(hObject,'String')) returns contents of edit2 as a double
set( handles.edit2,'FontName'.'Symbol');
% --- Executes during object creation, after setting all properties.
function edit2_CreateFcn(hObject, eventdata, handles)
% hObject handle to edit2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0.'defaultUicontrolBackgroundColor'))
set(hObject,'BackgroundColor'.'white');
end
% --- Executes on key press with focus on edit2 and none of its controls.
function edit2_KeyPressFcn(hObject, eventdata, handles)
% hObject handle to edit2 (see GCBO)
% eventdata structure with the following fields (see MATLAB.UI.CONTROL.UICONTROL)
% Key: name of the key that was pressed, in lower case
% Character: character interpretation of the key(s) that was pressed
% Modifier: name(s) of the modifier key(s) (i.e., control, shift) pressed
% handles structure with handles and user data (see GUIDATA)
% --- Executes on button press in pushbutton9.
function pushbutton9_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton9 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% --- Executes on button press in pushbutton8.
function pushbutton8_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton8 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% --- Executes on button press in pushbutton7.
function pushbutton7_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton7 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% --- Executes on button press in pushbutton13.
function pushbutton13_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton13 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
load userData
temp1=get(handles.edit1,'String');
temp2=get(handles.edit2,'String');
biaoji=0;
for i=1:length(userData.username)
if strcmp(userData.username{i},temp1)
if strcmp(userData.password{i},temp2)
biaoji=1;
end
end
end
if biaoji==1
set(handles.text6,'String'.'Successful landing');
set(handles.pushbutton15,'Enable'.'on');
set(handles.pushbutton16,'Enable'.'on');
else
set(handles.text6,'String'.'Login failed');
end
% --- Executes on button press in pushbutton14.
function pushbutton14_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton14 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
set(handles.pushbutton15,'Enable'.'off');
set(handles.pushbutton16,'Enable'.'off');
set(handles.text6,'String'.'Logout successful');
% --- Executes on button press in pushbutton15.
function pushbutton15_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton15 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
main('Visible'.'off');
data_gui1('Visible'.'on');
% --- Executes on button press in pushbutton16.
function pushbutton16_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton16 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
XuiGaiMiMa
% --- Executes on button press in pushbutton17.
function pushbutton17_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton17 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
Zhuce
Copy the code3. Operation results
Matlab version and references
1 Matlab Version 2019
[1] Yang Baoyang, YU Jizhou, Yang Shan. Intelligent Optimization Algorithm and Its MATLAB Example (2nd Edition) [M]. Publishing House of Electronics Industry, 2016. [2] ZHANG Yan, WU Shuigen. MATLAB Optimization Algorithm source code [M]. Tsinghua University Press, 2017. [3] Zhou Pin. Design and Application of MATLAB Neural Network [M]. Tsinghua University Press, 2013. [4] Chen Ming. MATLAB Neural Network Principle and Examples of Fine Solution [M]. Tsinghua University Press, 2013. [5] FANG Qingcheng. MATLAB R2016a Neural Network Design and Application of 28 Cases Analysis [M]. Tsinghua University Press, 2018.