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第十一届“认证杯”数学中国
数学建模国际赛
承 诺 书
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我们的参赛队号为：1440
我们选择的题目是：C
参赛队员 (签名) ：
队员 1：唐邵沅
队员 2：王雨轩
队员 3：潘偌羽
参赛队教练员 (签名)： 赵剑
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第十一届“认证杯”数学中国
数学建模国际赛
编 号 专 用 页
参赛队伍的参赛队号：（请各个参赛队提前填写好）：
1440
竞赛统一编号（由竞赛组委会送至评委团前编号）：
竞赛评阅编号（由竞赛评委团评阅前进行编号）：
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Human activities classification algorithm—Based on PCA
method and MLP model
Human behavior-action recognition is a very broad field, and wearable activity
recognition systems make it easier to recognize human behavior-action and improve
the quality of life in many critical areas.
In the first step, a multilayer perceptron classification model is developed, which
is divided into the following five steps: in the first step, the data are pre-processed by
missing value checking, abnormal data removal and data integration, and testers'
attributes and behavioral attributes are added. In the second step, exploratory data
analysis is performed to find that different units and sensors obtain different data
patterns. In the third step, principal component analysis was used to reduce the
dimensionality of the data, and the principal components with a cumulative
contribution of more than 95% were selected as representative features. In the fourth
step, the Z-score model was used to standardize the data. In the fifth step, a multilayer
perceptron classification model is used to classify the sensor data using behavioral
actions as labels.
For problem 2, a grid search model is introduced based on the model of problem
1 to select the parameters with the best classification performance so as to improve
the generalization of the model; confusion matrix, accuracy, recall, and F-score
indicators are introduced to evaluate the generalization of the model, and the
evaluation results are obtained: accuracy -99.4947%, recall -99.4947%, and F-score
-99.4956%, indicating that the optimized classification The model has a high
generalizability.
For problem 3, the overfitting of the model was investigated and it was found
that both the sample side and the model side could lead to the overfitting of the model.
For the sample side, the model of problem 2 is studied and it is found that: data
standardization, reasonable division of training set and principal component analysis
can effectively prevent model overfitting; for the model side, appropriate batch_size is
selected and training is ended early. The K-fold cross-validation method was
introduced to observe the accuracy of the test set and the accuracy of the training set
with different sample data, and the results were obtained: the human behavior
classification model was not overfitted.
Finally, the sensitivity analysis of the model was carried out in terms of
parameter sensitivity and data sensitivity, respectively. For the data sensitivity of the
model, the sensitivity of the model to different data samples was observed by adding
perturbations to the data samples; for the parameter sensitivity of the model, the other
parameters were kept constant and the batch_size was changed. it can be concluded
that the MLP neural network classification model has good sensitivity resistance.
Key words: MLP、PCA、Z-score、k-fold cross validation、EDA、GridSearchCV
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Content
1 Introduction .................................................................................................................5
1.1 Problem Background ........................................................................................ 5
1.2 Restatement of the Problem ..............................................................................5
1.3 Our Work ...........................................................................................................6
1.3.1. The Analysis to Problem 1 ............................................................................6
1.3.2. The Analysis to Problem 2 ............................................................................6
1.3.3. The Analysis to Problem 3 ............................................................................7
2 Assumptions and Justifications ...................................................................................8
3 Notations ..................................................................................................................... 8
4 Model construction of problem 1 ..............................................................................10
4.1 Inertial Sensor Data Dimensionality Reduction model .................................. 10
4.2 MLP model ..................................................................................................... 11
4.3 Results of problem 1 ....................................................................................... 12
5 Model construction of problem 2 ..............................................................................13
5.1 Evaluation to generalization ability ................................................................ 13
5.1.1. Confusion matrix ........................................................................................ 13
5.1.2. Secondary indicators ...................................................................................14
5.1.3. F1 score .......................................................................................................14
5.1.4. Grid Search model ...................................................................................... 14
5.2 Results of problem 2 ....................................................................................... 14
5.2.1. Conclusion in confusion matrix ..................................................................14
5.2.2. Accuracy, Recall and F-score ......................................................................15
6 Model construction of problem 3 ..............................................................................16
6.1 Theory of cross-validation method ................................................................. 16
6.2 Results of problem 3 ....................................................................................... 17
7 Sensitivity analysis ................................................................................................... 19
7.1 Parameter sensitivity .......................................................................................19
7.2 Data sensitivity ............................................................................................... 20
8 Evaluation of models ................................................................................................ 21
9 Future Work .............................................................................................................. 21
10 Reference ................................................................................................................ 22
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1 Introduction
1.1 Problem Background
In recent years, the integration of inertial sensors has been improving, and the
price is getting lower. At the same time, the development of deep neural network has
improved the accuracy and scope of human activity recognition. Therefore, the
activity recognition system based on inertial sensors has received more and more
attention. This activity recognition system combined with personal alarm system has a
wide range of applications in life, such as worker assistance, video surveillance,
health detection, medical research and so on.
As figure 1 shows, the whole process of human activities recognition can be
divided into four stages. Firstly, the body-worn sensors can capture the activity signal
when people have wearable equipment with them. After that, the sensors will translate
the signals into classifiers, which can extract features and use algorithm to build
models. Taking advantages of some mathematics tools, we can eventually make
activity inference to detect different human activities.
Figure1: An illustration of sensor-based activity recognition using ordinary
pattern recognition approach
1.2 Restatement of the Problem
According to the conditions given in the question, we have obtained 19 activities
(sitting, standing, lying on the back, lying on the right side, going up the stairs, going
down the stairs, standing still in the elevator, using the micro inertial sensors and
magnetometers placed in different parts of the subject's body. Move around in an
elevator, walk in a parking lot, walk on a treadmill at 4 km/h in a flat position and 15
degree incline position, walk on a treadmill at 4 km/h in a 15 degree incline position,
run on a treadmill at 8km/h, Sensor data for exercise on the treadmill, exercise on the
cross trainer, horizontal cycling on the exercise bike, vertical cycling on the exercise
