Decomposing the press in 1930s China: A Principal Component Analysis

This is the continuation of the multiple correspondence analysis conducted in the previous essay. In this new instalment, we concentrate on the four main continuous variables in our dataset of periodicals (number of pages, page size, number of columns, circulation). We rely on Principal Component Analysis (PCA) to examine more systematically how these variables relate to other and what clusters they form, or more accurately, how periodicals cluster together based on similar patterns of size, layout and circulation.

PCA is an exploratory data analysis method that aims to summarize and visualize the information in a data set containing individuals (observations) described by multiple inter-correlated quantitative variables. Each variable could be considered as a different dimension. PCA reduces the dimensionality of a multivariate data to two or three principal components which can be visualized graphically, with minimal loss of information.

In this experiment, we perform the PCA on the 1931 dataset because it presents a high level of data consistency. We treat “periodicity” and “language” as supplementary variables. The dataset and the code used for this experiment can be found here.

Statistics

The PCA captured 66% of information, 42% on the first dimension and 25% on the second. This was expected given the relatively small number of variables (4).

It is important beforehand to explore the distribution and quality of information before delving into further analysis. This will prevent us to overstate the importance of poorly projected variables or pay too much attention to weakly contributing observations, which may seriously distort our final interpretation. The following series of plots offers three alternative ways of visualizing the quality of projection and the contribution of each variable:

• Barplots show the variables relative contribution and quality of projection on the two axes.
• Correlation plots show pairwise relations between variables.
• PCA graphs, including clustered variables based on k-means. On the clustered graphs, we grouped the two variables related to the format and layout (size of page and number of columns)

Barplots

Variables Contribution

As shown on the barplots above, the size of pages and the number of columns are the two variables that most contribute to the first dimension, whereas circulation is the most contributing variable on the second dimension.

Individuals: Contribution and Quality of projection (Cos2)

The barplot on the left shows that the Directory and Chronicle, the Shenbao and the Xinwenbao are the most contributing periodicals on two first dimensions. The quality of projection is quite evenly distributed among the 30 best projected periodicals.

Correlation plots

Overall, the correlation plots support our previous observations:

The first plot (cos2) confirms that the circulation variable is strongly (and positively) associated with the second dimension. The size of points represents the strength of the association (quality of projection) while the color gradient shows its nature (positive/negative). Empty cells visualize the absence of relation.

The second plot further reveals that circulation is the most contributing variable (on the second dimension only). “Page size” contributes strongly to the first and even more to the fourth dimension. The number of pages contributes mostly to the third dimension. The variable “number of columns” contributes less strongly to the third and first dimensions. It may be worth exploring additional dimensions (3 and 4).

 

Graphs

All four variables are relatively well-projected on the two first dimensions. The size of pages and the number of columns are strongly related, which was expected. Both are strongly and positively associated with the first dimension, which means that periodicals on the right will have larger pages and more columns than those on the left.

The number of page is negatively projected on the first dimension, which means that the periodicals on the left are more substantial than those on the right, which include fewer pages.
These two groups of variables are symmetrically opposed. As we have shown in previous essays, the most substantial periodicals have smaller pages with few columns, whereas periodicals with few pages have larger pages and many columns. We expect the former group to include less frequent publications (annuals, quarterlies, monthlies), whereas the latter should consist mostly of daily newspapers (broadsheets).

The last variable (circulation) is exclusively and positively associated with the second dimension. This means that the periodicals at the top of the graph enjoy larger circulation than those below. It is remotely related to other variables. Its closest neighbor is the number of pages, which is partially, positively projected on the second dimension. This group certainly points to reference directories with relatively large circulation due to their low frequency of publication (annual).

Biplots

Biplots represent individuals and variables simultaneously on the same graph. The biplot showing individuals grouped by periodicity is particularly interesting. It highlights a clear grouping of periodicals based on their periodicity. Dailies are clustered on the right and they are associated with large pages and many columns (green dots). On the opposite, lengthy publications with small pages and few columns on the left refer to annuals and a few monthlies (red group). Weeklies (pink), monthlies (green) and quarterlies (blue) tend to include more but smaller pages with fewer columns (left). Weeklies show smaller circulation (bottom left corner).

The biplot showing language groups is also insightful. It confirms our previous observations that Japanese dailies tended to include more columns than other periodicals (purple dots on the right). English publications (essentially weeklies and monthlies) were generally more substantial but included smaller pages with fewer columns (green dots). French and Russian newspapers contained larger pages with more columns than their German counterparts. Chinese periodicals are scattered all over the plot.

Hierarchical Clustering

Based on this PCA, we performed a hierarchical clustering (HCPC) on all four dimensions. Periodicity is the strongest determinant in the partition (p-value 1.285764e-55). The algorithm detected 4 clusters:

1. Cluster 1 (red) on the left includes less frequent periodicals with many but smaller pages and fewer columns. Among the parangons (representative periodicals) of this group, we find the Commercial Directory of Shanghai, and the Directory and Chronicle which confirms our previous hypothesis. The group also includes reference monthlies such as Public Education Monthly and Current Events (Shishi yuebao).
2. Cluster 2 (middle, green) groups average publications, with no strong determinant.
3. Cluster 3 (right, turquoise) consists of daily broadsheets with large pages and multiple columns.
4. Cluster 4 (top, purple) refers to widely circulated newspapers (Shenbao, Xinwenbao). This specific  group is determined mostly by circulation, though it also shares with broadsheets large pages and multiple columns.

In the next essay, we move to another topic. We will rely on text analysis to explore the titles of periodicals using word frequency, collocations and more sophisticated techniques of topic modeling to detect underlying patterns in naming periodicals.

References

Kassambara, Alboukadel. “Principal Component Methods in R: Practical Guide”. 2017. http://www.sthda.com/english/articles/31-principal-component-methods-in-r-practical-guide/117-hcpc-hierarchical-clustering-on-principal-components-essentials/

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