# Positioning multivariate data in a 2-dimensional space (with PCA)

I have multidimensional data. (11 columns - attributes , 150K rows - number of data). It is slightly sparse-alike data, for example, which means one datum has numeric values like (0, 0, 6.5, 0, 0, 7.5, 0, 0, 4.5, 0, 0). So, each datum has approximately 2~5 non-zero attribute values.

I want to visualize these data into 2-dimensional spaces. So my steps are like these.

1. PCA process

=> let each datum get x, y coordinates.

2. Clustering

=> DBSCAN, K-means, etc., something like those.

I've heard that the proportion of variance is important, and I have the following proportions:

Importance of components: PC1    PC2    PC3    PC4     PC5     PC6    PC7     PC8     PC9     PC10
Standard deviation     1.4173 1.1836 1.1141 1.0108 0.99109 0.95231 0.89091 0.8456 0.71542 0.64610
Proportion of Variance 0.2009 0.1401 0.1241 0.1022 0.09823 0.09069 0.07937 0.0715 0.05118 0.04174
Cumulative Proportion  0.2009 0.3410 0.4651 0.5673 0.66551 0.75620 0.83558 0.9071 0.95826 1.00000


(PC1's PV: 0.2009, PC2's PV: 0.1401)

So, when I convert data into 2-dimension space, as far as I've understood, I think I should project data into (PC1, PC2) coordinates, which only has 0.3410 (Cumulative Proportion)

Isn't 0.3410 (a slightly lower value than I'd expected) too unreliable for that data positioning? Also, is there other way to project that data into 2D space that has more cumulative proportion?

## 1 Answer

You have 11 variables, and if PCA was useless, you'd have 2/11 (18%) of variance explained by PC1 and PC2. In your case it it's 34%. So, the PCA is not completely useless, but it doesn't have a lot of power. Consider, for instance, interest rate modeling, where two components usually explain 80-90% of variance of the vector.

• Can I get any link about Interest Rate Modeling that you mentioned? – Hyeon May 14 at 18:01
• @Hyeon there's enormous amount of literature on the subject, e.g. I pulled this paper almost randomly, see p.11 ocw.mit.edu/courses/mathematics/… – Aksakal May 14 at 18:05