An Efficient Factor Model based on Kernel Principal Component Analysis

Author(s):  
Yourong Wang ◽  
Yili Tan ◽  
Yanli Liu ◽  
Zhenyao Fan
2013 ◽  
Vol 16 (04) ◽  
pp. 1350020
Author(s):  
SERGIO M. FOCARDI ◽  
FRANK J. FABOZZI

In this paper, we analyze factor uniqueness in the S&P 500 universe. The current theory of approximate factor models applies to infinite markets. In the limit of infinite markets, factors are unique and can be represented with principal components. If this theory would apply to realistic markets such as the S&P 500 universe, the quest for proprietary factors would be futile. We find that this is not the case: in finite markets of the size of the S&P 500 universe different factor models can indeed coexist. We compare three dynamic factor models: a factor model based on principal component analysis, a classical factor model based on industry, and a factor model based on cluster analysis. Dynamic behavior is represented by fitting vector autoregressive models to factors and using them to make forecasts. We analyze the uniqueness of factors using Procrustes analysis and correlation analysis. Forecasting performance of the factor models is analyzed by forming active portfolio strategies based on the forecasts for each model using sample data from the S&P 500 index in the 21-year period 1989–2010. We find that one or two factors which we can identify with global factors are common to all models, while the other factors for the factor models we analyzed are truly different. Models exhibit significant differences in performance with principal component analysis-based factor models appearing to behave better than the sector-based factor models.


2021 ◽  
Vol 11 (14) ◽  
pp. 6370
Author(s):  
Elena Quatrini ◽  
Francesco Costantino ◽  
David Mba ◽  
Xiaochuan Li ◽  
Tat-Hean Gan

The water purification process is becoming increasingly important to ensure the continuity and quality of subsequent production processes, and it is particularly relevant in pharmaceutical contexts. However, in this context, the difficulties arising during the monitoring process are manifold. On the one hand, the monitoring process reveals various discontinuities due to different characteristics of the input water. On the other hand, the monitoring process is discontinuous and random itself, thus not guaranteeing continuity of the parameters and hindering a straightforward analysis. Consequently, further research on water purification processes is paramount to identify the most suitable techniques able to guarantee good performance. Against this background, this paper proposes an application of kernel principal component analysis for fault detection in a process with the above-mentioned characteristics. Based on the temporal variability of the process, the paper suggests the use of past and future matrices as input for fault detection as an alternative to the original dataset. In this manner, the temporal correlation between process parameters and machine health is accounted for. The proposed approach confirms the possibility of obtaining very good monitoring results in the analyzed context.


2009 ◽  
Vol 147-149 ◽  
pp. 588-593 ◽  
Author(s):  
Marcin Derlatka ◽  
Jolanta Pauk

In the paper the procedure of processing biomechanical data has been proposed. It consists of selecting proper noiseless data, preprocessing data by means of model’s identification and Kernel Principal Component Analysis and next classification using decision tree. The obtained results of classification into groups (normal and two selected pathology of gait: Spina Bifida and Cerebral Palsy) were very good.


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