**4. Conclusion**

In this chapter, we started off by providing a survey on five Robust Principal Component Analysis models recently developed: Robust Subspace Learning, Principal Component Pursuit, Templates for First-Order Conic Solvers, Recursive Projected Compressive Sensing, Bayesian RPCA. We then presented a systematic evalutation and comparative analysis on different datasets used in video-surveillance. PCP demonstrates more robutness on all datasets by providing best global score. The Bayesian RPCA offers also good performance but presents a drawback related to the assumption : the background has necessarily a bigger area than the foreground. For the IALM, its performance is still acceptable.

Futur research directions may concern the evalutation of accelerate hardware implementation of robust PCA (Mu et al. (2011);Anderson et al. (2011)) and robust Independent Components Analysis (Yamazaki et al. (2006)), Incremental Non-negative Matrix Factorization (Bucak et al. (2007)) and Incremental Rank Tensor (Li et al. (2008)).

<sup>7</sup> http://www.salleurl.edu/~ftorre/papers/rpca/rpca.zip

<sup>8</sup> http://home.engineering.iastate.edu/~chenlu/ReProCS/ReProCS\_code.zip

<sup>9</sup> http://perception.csl.uiuc.edu/matrix-rank/Files/inexact\_alm\_rpca.zip

<sup>10</sup> http://tfocs.stanford.edu/code

<sup>11</sup> http://www.ece.duke.edu/~lihan/brpca\_code/BRPCA.zip

## **5. References**

14 Will-be-set-by-IN-TECH


 

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automatically choose for maximize the F-measure.

(2007)) and Incremental Rank Tensor (Li et al. (2008)).

<sup>10</sup> http://tfocs.stanford.edu/code

<sup>7</sup> http://www.salleurl.edu/~ftorre/papers/rpca/rpca.zip

<sup>11</sup> http://www.ece.duke.edu/~lihan/brpca\_code/BRPCA.zip

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Fig. 4. Performance on the Li dataset (Bootstrap issues).


TFOCS provided by S. Becker10 and Bayesian provided by X. Ding11. Additionally, a 5 <sup>×</sup> <sup>5</sup> median filter is postprocessed in order to suppress peak noise. The thresholding value is

For time issues, the current implementations are faraway to achieve real-time. Indeed, the computing of the backgrounds take few hours for a training sequence with 200 frames for each algorithm. This time can be reduced by *C/Cuda* implementation as suggested in (Mu

In this chapter, we started off by providing a survey on five Robust Principal Component Analysis models recently developed: Robust Subspace Learning, Principal Component Pursuit, Templates for First-Order Conic Solvers, Recursive Projected Compressive Sensing, Bayesian RPCA. We then presented a systematic evalutation and comparative analysis on different datasets used in video-surveillance. PCP demonstrates more robutness on all datasets by providing best global score. The Bayesian RPCA offers also good performance but presents a drawback related to the assumption : the background has necessarily a bigger

Futur research directions may concern the evalutation of accelerate hardware implementation of robust PCA (Mu et al. (2011);Anderson et al. (2011)) and robust Independent Components Analysis (Yamazaki et al. (2006)), Incremental Non-negative Matrix Factorization (Bucak et al.

<sup>8</sup> http://home.engineering.iastate.edu/~chenlu/ReProCS/ReProCS\_code.zip <sup>9</sup> http://perception.csl.uiuc.edu/matrix-rank/Files/inexact\_alm\_rpca.zip

4"++!00

area than the foreground. For the IALM, its performance is still acceptable.

.& .

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**4. Conclusion**





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**13** 

Xiang Gao

*P. R. China* 

*Yantai Nanshan University* 

**On-Line Monitoring of Batch** 

**Process with Multiway PCA/ICA** 

Batch processes play an important role in the production and processing of low-volume, high-value products such as specialty polymers, pharmaceuticals and biochemicals. Generally, a batch process is a finite-duration process that involves charging of the batch vessel with specified recipe of materials; processing them under controlled conditions according to specified trajectories of process variables, and discharging the final product

Batch processes generally exhibit variations in the specified trajectories, errors in the charging of the recipe of materials, and disturbances arising from variations in impurities. If the problem not being detected and remedied on time, at least the quality of one batch or subsequent batches productions is poor under abnormal conditions during these batch operations. Prior to completion of the batch or before the production of subsequent batches, batch processes need effective strategy of real-time, on-line monitoring to be detected and diagnosed the faults and hidden troubles earlier and identified the causes of the problems

Based on multivariable statistical analysis, several chemometric techniques have been proposed for online monitoring and fault detection in batch processes. Nomikos and MacGregor (1994, 1995) firstly developed a powerful approach known as multiway principal component analysis (MPCA) by extending the application of principal component analysis (PCA) to three-dimensional batch processes. By again projecting the information contained in the process-variable trajectories onto low-dimensional latent-variable space that summarizes both the variables and their time trajectories, the main idea of their approach is to compress the normal batch data and extract information from massive batch data. A batch process can be monitored by comparing with its time progression of the projections in the reduced space with those of normal batch data after having set up normal batch behaviour. Several studies have investigated the applications of MPCA (Chen & Wang, 2010; Jung-hui & Hsin-hung, Chen, 2006; Kosanovich et al., 1996; Kourti, 2003;

Many of the variables monitored in one process are not independent in some cases, may be combination of independent variables not being measured directly. Independent component analysis (ICA) can extract the underlying factors or components from non-Gaussian

**1. Introduction** 

from the vessel.

for safety and quality.

Westerhuis et al., 1999).

