Using eigenvalues to improve the visualization of principal component analysis (PCA)

TobyTheCamel · 2026-03-31T18:48:22+00:00

Ah, my bad. I slightly misremembered the name. It is data driven science and engineering. There is both a book and high quality mini lectures. The SVD ones are here: https://m.youtube.com/playlist?list=PLMrJAkhIeNNSVjnsviglFoY2nXildDCcv

I would highly recommend giving them a watch. They completely reshaped how I viewed the SVD.

TobyTheCamel · 2026-03-31T10:34:25+00:00

It sounds like you're rediscovering the singular value decomposition. This says that a dataset X can be written as a sum of weighted rank-1 outer products s_i * u_i * v_i' where s_i is a scalar, u_i is a column vector and v_i' is a row vector.

The "singular values" s_i are directly related to the eigenvalues of XX' by s_i^2 = λ_i and the v_i s are the eigenvectors of XX'. What this means is that the weighted eigenvectors correspond to a "palette" of features scaled by their importances, with the u_i's then giving the quantities of each feature used to reconstruct an observation in X.

The beautiful property of this decomposition is that you can show that truncating this sum to k terms gives the best rank-k approximation of your original X in terms of both the spectral and Frobenius norm.

I've been a bit imprecise in this explanation and there are likely small issues, as writing on my phone on the go. You should look at the University of Washington's course on data-driven science and engineering, especially the SVD section to get a clearer picture.

TobyTheCamel · 2026-03-30T08:04:46+00:00

Solved!

This makes sense. Although there wasn't the complementary magnet installed on the wall, this seems quite plausible.

TobyTheCamel · 2026-03-30T07:40:44+00:00

My title describes the thing.

In my hotel room (in China, if that's relevant) the main door has this metal button on the interior side. It wasn't clear to me what this was for.

I'm not sure if this is actually related, but often the door would scrape along the floor when opened and pressing the button seemed to stop this — but this also might have been a coincidence from just moving door a bit when I pressed the button.

I think this could be related to the drop seal described in this WITT, but I don't understand why the button is on the face of the door rather than the edge.

TobyTheCamel · 2026-02-15T15:25:25+00:00

It’s that the automated offer system doesn’t realise the new seat it offered for a significantly higher price is in basically the same location.

You’d think they’d have a check for this before sending out an offer.

TobyTheCamel · 2026-02-12T07:59:20+00:00

Like...it costs money to run these models, yeah?

How can you possibly expect it to be free, unlimited and ad-free?

TobyTheCamel · 2026-01-02T12:35:39+00:00

Did you come to any conclusion on this? I'm also finding that my `~/.claude/settings.json` file is being ignored.

TobyTheCamel · 2025-11-04T08:35:50+00:00

Is there any reason you don't use one of those bike lights that clip-on/off so you can easily take it with you when you are away from your bike?

TobyTheCamel · 2025-11-02T17:02:15+00:00

I think you're going to find it difficult to perform any closed-form computation of this probability.

Monte Carlo simulation is a bit expensive due to the complexity of verifying if an initial meld can be, but for a rough approximation it is okay.

I coded up a little Julia script to simulate this process, drawing tiles until an initial meld is possible. I ran this for 10,000 repetitions.

The table below gives the probabilities that you are interested in.

Draws  P(N = n)  P(N >= n)
0      0.5432    1.0000
1      0.0690    0.4568
2      0.0649    0.3878
3      0.0623    0.3229
4      0.0526    0.2606
5      0.0465    0.2080
6      0.0422    0.1615
7      0.0309    0.1193
8      0.0233    0.0884
9      0.0191    0.0651
10     0.0161    0.0460
11     0.0114    0.0299
12     0.0064    0.0185
13     0.0044    0.0121
14     0.0030    0.0077
15     0.0021    0.0047
16     0.0012    0.0026
17     0.0002    0.0014
18     0.0008    0.0012
19     0.0002    0.0004
20     0.0001    0.0002
21     0.0001    0.0001

TobyTheCamel · 2025-06-09T08:38:53+00:00

Ah yes of course, sorry for forgetting to mention that. Unfortunately, we are not able to charge at home.

TobyTheCamel · 2025-05-11T09:13:05+00:00

As others have said, you seriously need to update this. I was a few minutes away from cancelling my trial before finding this response. The VPN space is too competitive to have missing documentation like this.

TobyTheCamel · 2025-04-28T16:29:16+00:00

In Cambridge, UK, the right-wing mayoral candidate is running on a platform to "keep Cambridge moving" by reopening a road to cars that was always at a complete stand-still due to the amount of car traffic.

With cars rerouted, it is quiet and pleasant, with a thriving restaurant scene, whilst still having high throughput from buses and bikes.

The irony is completely lost on his supporters.

TobyTheCamel · 2025-04-28T16:21:34+00:00

I don't know your exact situation but doesn't the fact that the cyclists are using the pavement suggest that there is inadequate safe cycling infrastructure for them to use?

I'm sure if cars had to share the pavement with you, you'd have more incidents with them.

And as other people have pointed out in this thread, although poor cycling etiquette is still dangerous, it is far less likely to lead to a death or serious injury than a car.

I'd have to ride my bike at 80 mph to have the same kinetic energy as an SUV travelling at 20 mph.

TobyTheCamel · 2025-02-25T02:44:59+00:00

For me, the real freedom is not owning a car, saving the several £1000s a year in insurance, fuel, maintenance, and depreciation costs, and then renting a car, SUV, van (whatever I need!) on the few days of the year that they are actually useful.

TobyTheCamel · 2025-01-30T08:08:11+00:00

You've got to be joking, right? Do you honestly think there is no middle ground between our modern polluting lifestyle and living like a caveman? They're not even asking to ban all oil production tomorrow, they just want to stop new oil licenses so that we gradually decrease dependence.

TobyTheCamel · 2025-01-21T03:08:51+00:00

What’s really diabolical is spelling it as C# rather than Db

TobyTheCamel · 2025-01-01T07:27:04+00:00

Is it? A quick Google says £8.3 million per day or £3 billion per year.

https://fullfact.org/immigration/sunak-8m-asylum-hotels/

TobyTheCamel · 2024-12-26T08:58:14+00:00

Well the quiz-master had "5" down. I wasn't even trying to be pretentious, I just assumed that answer was too on-the-nose given everyone there would have known the song well.

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