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Analysis of call centre arrival data using singular value decomposition. (English) Zbl 1089.62155
Data of the number of calls arriving to a call centre during a year (in 2002) are considered. A 17-h operating period is divided into 408 150-s intervals and the data is the matrix $$X=(x_{ij})$$, where $$x_{ij}$$ is the number of calls during the $$j$$-th time period of the $$i$$-th day. A singular value decomposition of $$X$$ is used for the dimension reduction, i.e., $$X=\sum_{k=1}^r s_k u_k v_k^T$$, where $$r$$ is the rank of $$X$$, $$s_k$$ are the singular numbers, $$u_k$$ are the left singular vectors (inter-day feature vectors), and $$v_k$$ are the right singular vectors (intra-day feature vectors). The use of $$s_k$$, $$u_k$$ and $$v_k$$ is analogous to the use of eigenvalues and eigenvectors in principal component analysis. The authors use them for cluster analysis of the days and description of the patterns of call number changes during a day. A forecast for the number of calls is proposed based on the first singular vector decomposition: $$x_{ij}=s_1 u_{1,i}v_{1,j}+\varepsilon_{ij}$$, where $$\varepsilon_{ij}$$ are approximation errors, and $$u_{1,i}$$ follow an AR(1) model with varying coefficients: $$u_{1,i}=a(d_{i-1})+b(d_{i-1})u_{1,(i-1)}+\varepsilon_i$$, $$d_i$$ being the factor denoting the day-of-week for the $$i$$-th day.

##### MSC:
 62P99 Applications of statistics 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62H25 Factor analysis and principal components; correspondence analysis 62P30 Applications of statistics in engineering and industry; control charts 90B99 Operations research and management science
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##### References:
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