Figure 1.
The hemagglutination inhibition (HI) data in temporal order.
High reactor are in the diagonal zone, and the low reactors and the missing values will appear more when the approaching the challenge zone.
Figure 2.
Data distribution in the H3N2 HI dataset.
Three types of data are present in HI data: type I, a regular HI titre marked in red cross; Type II, the value is defined as ‘less than a threshold’, e.g. , where
, and these values indicate the testing antigen and antiserum have a weak (or low) immunological reaction. Type II values are marked in green diagonal cross; Type III, missing values, which are blank. This HI dataset includes
entries, which represent
data presence. Among these entries,
(
) are Type II values.
Table 1.
The local RMSE values from -fold cross validations using H3N2 HI dataset (1968–2003) with different window sizes (W) in sliding window based Alternating Gradient Descent.
Table 2.
Comparison between MC-MDS and metric MDS.
Figure 3.
Computational simulation demonstrates that temporal model can reduce the biases generated by the Type II data (low reactors) in hemagglutination inhibition (HI) dataset.
(a) HI matrix ( data absense) with neither Type II nor Type III data, using multidimensional scaling (MDS); (b) HI matrix (
data absense, data structure: randomly distributed) with Type III data but without Type II data, using Alternating Gradient Descent (AGD) and MDS; (c) HI matrix (
data absense, data structure: similar to H3N2 data as shown in Figure 1) with both Type II data and Type III data, using AGD and MDS; (d)HI matrix (
data absense, data structure: similar to H3N2 data as shown in Figure 1) with both Type II and Type III data, using MC-MDS. (e)HI matrix (
data absense, data structure: similar to H3N2 data as shown in Figure 1) with both Type II and Type III data, using Metric MDS. (f) Another independent run by the same setting and method as (e).
Figure 4.
The influenza antigenic cartography constructed by MC-MDS for H3N2 viruses from 1968 to 2003.
The viruses labeled with the cluster names HK68, EN72, VI75, TX77, BK79, SI87, BE89, BE92, WU95, SY97 and FU02 are defined by [8]. One unit (grid) corresponds to a two-fold change in HI assay.
Figure 5.
The antigenic cartography by MC-MDS for H3N2 HI data from 1987 to 1995.
The influenza viruses labeled with the cluster names SI87, BE89, BE92, WU95 are defined by [8]. One unit (grid) corresponds to a two-fold change in HI assay. This data is a subset of the HI data shown in Figure 2.