Eigenanalysis for Lossy Compression

Eigenanalysis is a method for reducing a set of data to the principle dimensions along which that data varies. In the context of imaging data, it has been applied very successfully to Eigenfaces:

Where a set of faces is broken down into a smaller set of face "prototypes" that can recombined in varying portions to recreate the original data set with a limited accuracy.

In the context of music, I can imagine that the spectral characteristics of songs have some self-similarity: portions repeat, chords are repeated in different voices and different octaves, rhythms repeat, etc. I can imagine a lossy compression algorithm that takes the frequency domain representation of a song, does Eigenanalysis on these vectors, and stores the song simply as the collection of N eigenvectors and the reduced representation of each frequency-domain chunk.

Quantization methods may be employed for further reducing bit usage due to similarity between adjacent chunks. Or different portions of the spectrum can be analyzed separately, which allows for better representation of lower frequencies and less information dedicated to higher frequencies. This unfortunately does not account for the obvious relationship between the lower and higher frequencies.

A more advanced implementation may involve doing eigenanalysis on mutiple chunks simultaneously in a moving window, or at different scales, which will help with rhythmic repetition.

The octave or overtone relationship is a little more complicated, and would require something like a constant-Q transforms to get a logarithmic frequency domain.

Google Earth Live

"Google Earth Live" is a hypothetical service offered by Google in the not-to-distant future. It is predicated upon Google releasing a matrix of satellites into orbit that regularly poll large sections of the Earth at high resolution, and offering this data for free via the Google Earth interface.

When this is available, how would you use it (practically)? And what sort of art would you make with it?

The obvious: make timelapse videos of yourself as you go throughout your day, from the perspective of the satellite.

Non-Metamer Monochromes

Monochromatic paintings have a tradition going back to the early 1900s, exemplified by Malevich and Rodchenko, and later by Rauschenberg.

I'd like to produce a series of monochromes that uses a single non-metamer. By non-metamer, I mean a color that has the same frequency spectrum as the color being replicated. For example, the green of a leaf, the blue of the sky, or the red of a sunset. Instead of just resembling these colors, various paints would be analyzed for their spectral response and mixed in the correct proportions so they precisely recreated these colors.

Alternative Prime Spirals

The Ulam spiral is based on the idea of arranging integers in a rectilinear 2D spiral.

And noticing that certain diagonal patterns fall out that aren't explainable by simple equations that describe some of the "holes".

What other orderings might reveal interesting patterns? How about a 2D Hilbert curve?

Or maybe a 3D one? How might you continue a spiral in a cubic 3D space? Would you get diagonal planes describing the primes? How about a higher dimensional space — maybe higher dimensional planes?

Jesus Glitch

The holy is often found in unexpected places. Jesus in naan, Mary in a Chicago underpass. Dan Paluska has immortalized this concept with his Holy Toaster.

Why don't we ever see Jesus in corrupted image files?

Image compression algorithms are generally rated on their ability to convincingly ignore non-perceptually-relevant features. I propose a new metric for these algorithms: how likely they are, when corrupted, to produce an image of a holy figure.

Six Pieces for Life

Live like you only have until the next:

1. day
2. week
3. month
4. year
5. decade
6. century