Ciro Santilli @cirosantilli 35

Given a bunch of points in $n$ dimensions, PCA maps those points to a new $p$ dimensional space with $p\le n$.

$p$ is a hyperparameter, $p=1$ and $p=2$ are common choices when doing dataset exploration, as they can be easily visualized on a planar plot.

The mapping is done by projecting all points to a $p$ dimensional hyperplane. PCA is an algorithm for choosing this hyperplane and the coordinate system within this hyperplane.

The hyperplane choice is done as follows:

www.sartorius.com/en/knowledge/science-snippets/what-is-principal-component-analysis-pca-and-how-it-is-used-507186 provides an OK-ish example with a concrete context. In there, each point is a country, and the input data is the consumption of different kinds of foods per year, e.g.:so in this example, we would have input points in 4D.

The question is then: we want to be able to identify the country by what they eat.

Suppose that every country consumes the same amount of flour every year. Then, that number doesn't tell us much about which country each point represents (has the least variance), and the first PCA axes would basically never point anywhere near that direction.

Another cool thing is that PCA seems to automatically account for linear dependencies in the data, so it skips selecting highly correlated axes multiple times. For example, suppose that dry codfish and olive oil consumption are very high in Portugal and Spain, but very low in Germany and Poland. Therefore, the variation is very high in those two parameters, and contains a lot of information.

However, suppose that dry codfish consumption is also directly proportional to olive oil consumption. Because of this, it would be kind of wasteful if we selected:since the information about codfish already tells us the olive oil. PCA apparently recognizes this, and instead picks the first axis at a 45 degree angle to both dry codfish and olive oil, and then moves on to something else for the second axis.

We can see that much like the rest of machine learning, PCA can be seen as a form of compression.

Forms a normal subgroup of the general linear group.

List databases:

Delete database:or:

View collections within a database:

Show all data from one of the collections: stackoverflow.com/questions/24985684/mongodb-show-all-contents-from-all-collections

Ciro Santilli found out that he likes computer security researchers and vice versa.

It's a bit the same reason why he likes physicists: you can't bullshit with security.

You can't just talk nice and hope for people to belive you.

You can't not try to break things and just keep everyone happy in their false illusion of safety.

You can't do a half job.

If you do any of that, you will get your ass handed to you in a little gift bag.

All of this is closely linked to Ciro Santilli's self perceived creative personality and being naughty and creative are correlated.

Survey by Ciro Santilli: math.stackexchange.com/questions/1985/software-for-drawing-geometry-diagrams/3938216#3938216

Many plotting software can be used to create mathematics illustrations. They just tend to have more data-oriented rather than explanatory-oriented output.

One of the most enduring forms of storage! Started in the 1950s, but still used in the 2020s as the cheapest (and slowest access) archival method. Robot arms are needed to load and read them nowadays.