scholarly journals Principal Component Analysis for Weighted Data in the Procedure of Multidimensional Statistical Forecasting

2021 ◽  
Vol 18 (2) ◽  
pp. 4-11
Author(s):  
V. V. Nikitin ◽  
D. V. Bobin

Purpose of the research. Let’s assume that the dynamics of the state of some object is being investigated. Its state is described by a system of specified indicators. Among them, some may be a linear combination of other indicators. The aim of any forecasting procedure is to solve two problems: first, to estimate the expected forecast value, and second, to estimate the confidence interval for possible other forecast values. The prediction procedure is multidimensional. Since the indicators describe the same object, in addition to explicit dependencies, there may be hidden dependencies among them. The principal component analysis effectively takes into account the variation of data in the system of the studied indicators. Therefore, it is desirable to use this method in the forecasting procedure. The results of forecasting would be more adequate if it were possible to implement different forecasting strategies. But this will require a modification of the traditional principal component analysis. Therefore, this is the main aim of this study. A related aim is to investigate the possibility of solving the second forecasting problem, which is more complex than the first one. Materials and research methods. When estimating the confidence interval, it is necessary to specify the procedure for estimating the expected forecast value. At the same time, it would be useful to use the methods of multidimensional time series. Usually, different time series models use the concept of time lag. Their number and weight significance in the model may be different. In this study, we propose a time series model based on the exponential smoothing method. The prediction procedure is multidimensional. It will rely on the rule of agreed upon data change. Therefore, the algorithm for predictive evaluation of a particular indicator is presented in a form that will be convenient for building and practical use of this rule in the future. The principal component analysis should take into account the weights of the indicator values. This is necessary for the implementation of various strategies for estimating the boundaries of the forecast values interval. The proposed standardization of weighted data promotes to the implementation of the main theorem of factor analysis. This ensures the construction of an orthonormal basis in the factor area. At the same time, it was not necessary to build an iterative algorithm, which is typical for such studies. Results. For the test data set, comparative calculations were performed using the traditional and weighted principal component analysis. It shows that the main characteristics of the component analysis are preserved. One of the indicators under consideration clearly depends on the others. Therefore, both methods show that the number of factors is less than the number of indicators. All indicators have a good relationship with the factors. In the traditional method, the dependent indicator is included in the first main component. In the modified method, this indicator is better related to the second component. Conclusion. It was shown that the elements of the factor matrix corresponding to the forecast time can be expressed as weighted averages of the previous factor values. This will allow us to estimate the limits of the confidence interval for each individual indicator, as well as for the complex indicator of the entire system. This takes into account both the consistency of data changes and the forecasting strategy.

2017 ◽  
Vol 727 ◽  
pp. 447-449 ◽  
Author(s):  
Jun Dai ◽  
Hua Yan ◽  
Jian Jian Yang ◽  
Jun Jun Guo

To evaluate the aging behavior of high density polyethylene (HDPE) under an artificial accelerated environment, principal component analysis (PCA) was used to establish a non-dimensional expression Z from a data set of multiple degradation parameters of HDPE. In this study, HDPE samples were exposed to the accelerated thermal oxidative environment for different time intervals up to 64 days. The results showed that the combined evaluating parameter Z was characterized by three-stage changes. The combined evaluating parameter Z increased quickly in the first 16 days of exposure and then leveled off. After 40 days, it began to increase again. Among the 10 degradation parameters, branching degree, carbonyl index and hydroxyl index are strongly associated. The tensile modulus is highly correlated with the impact strength. The tensile strength, tensile modulus and impact strength are negatively correlated with the crystallinity.


Author(s):  
Ahmad Azhari ◽  
Murein Miksa Mardhia

Human has the ability to think that comes from the brain. Electrical signals generated by brain and represented in wave form.  To record and measure the activity of brainwaves in the form of electrical potential required electroencephalogram (EEG). In this study a cognitive task is applied to trigger a specific human brain response arising from the cognitive aspect.  Stimulation is given by using nine types of cognitive tasks including breath, color, face, finger, math, object, password thinking, singing, and sports. Principal component analysis (PCA) is implemented as a first step to reduce data and to get the main component of feature extraction results obtained from EEG acquisition. The results show that PCA succeeded reducing 108 existing datasets to 2 prominent factors with a cumulative rate of 65.7%. Factor 1 (F1) includes mean, standard deviation, and entropy, while factor 2 (F2) includes skewness and kurtosis.


2021 ◽  
Vol 13 (20) ◽  
pp. 4123
Author(s):  
Hanqi Wang ◽  
Zhiling Wang ◽  
Linglong Lin ◽  
Fengyu Xu ◽  
Jie Yu ◽  
...  

Vehicle pose estimation is essential in autonomous vehicle (AV) perception technology. However, due to the different density distributions of the point cloud, it is challenging to achieve sensitive direction extraction based on 3D LiDAR by using the existing pose estimation methods. In this paper, an optimal vehicle pose estimation network based on time series and spatial tightness (TS-OVPE) is proposed. This network uses five pose estimation algorithms proposed as candidate solutions to select each obstacle vehicle's optimal pose estimation result. Among these pose estimation algorithms, we first propose the Basic Line algorithm, which uses the road direction as the prior knowledge. Secondly, we propose improving principal component analysis based on point cloud distribution to conduct rotating principal component analysis (RPCA) and diagonal principal component analysis (DPCA) algorithms. Finally, we propose two global algorithms independent of the prior direction. We provided four evaluation indexes to transform each algorithm into a unified dimension. These evaluation indexes’ results were input into the ensemble learning network to obtain the optimal pose estimation results from the five proposed algorithms. The spatial dimension evaluation indexes reflected the tightness of the bounding box and the time dimension evaluation index reflected the coherence of the direction estimation. Since the network was indirectly trained through the evaluation index, it could be directly used on untrained LiDAR and showed a good pose estimation performance. Our approach was verified on the SemanticKITTI dataset and our urban environment dataset. Compared with the two mainstream algorithms, the polygon intersection over union (P-IoU) average increased by about 5.25% and 9.67%, the average heading error decreased by about 29.49% and 44.11%, and the average speed direction error decreased by about 3.85% and 46.70%. The experiment results showed that the ensemble learning network could effectively select the optimal pose estimation from the five abovementioned algorithms, making pose estimation more accurate.


2014 ◽  
Vol 578-579 ◽  
pp. 1020-1023
Author(s):  
Jing Zhou Lu ◽  
Jia Chen Wang ◽  
Xu Zhu

In this paper, we introduce a set of techniques for time series analysis based on principal component analysis (PCA). Firstly, the autoregressive (AR) model is established using acceleration response data, and the root mean squared error (RMSE) of AR model is calculated based on PCA. Then a new damage sensitive feature (DSF) based on the AR coefficients is presented. To test the efficacy of the damage detection and localization methodologies, the algorithm has been tested on the analytical and experimental results of a three-story frame structure model of the Los Alamos National Laboratory. The result of the damage detection indicates that the algorithm is able to identify and localize minor to severe damage as defined for the structure. It shows that the suggested method can lead to less amount of computing time, high suitability and identification accuracy.


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