Sunday, August 5, 2012

Visualize a random forest that classifies digits

My last post uses random forest proximity to visualize a set of diamond shapes (the random forest is trained to distinguish diamonds from non-diamonds).

This time I looked at the digits data set that Kaggle is using as the basis of a competition for "getting started". The random forest is trained to classify the digits, and this is an embedding of 1000 digits into 2 dimensions preserving proximities from the random forest as closely as possible:

The colors of the points show the correct label. The larger points are digits classified incorrectly, and you can see that in general those are ones that the random forest has put in the wrong "region". I've shown some of the digits themselves (instead of colored points) -- the red ones are incorrectly classified.

Here's the same but just for the 7's:

The random forest has done a reasonable job putting different types of 7's in different areas, with the most "canonical" 7's toward the middle.

You can see all of the other digits

Note that this random forest is different from the one in my last post -- here it's built to classify the digits, not separate digits from non-digits. I wonder what kind of results a random forest to distinguish 7's from non-7's would look like?

Code is on Github.

Random forests for visualizing data

Recently I read about using random forests as a way to visualize data. Here's how it works:
  1. Have a data set
  2. Create a set of fake data by permuting the columns randomly -- each column will still have the same distribution, but the relationships are destroyed.
  3. Train a random forest to distinguish the fake data from the original data.
  4. Get a "proximity" measure between points, based on how often the points are in the same leaf node.
  5. Embed the points in 2D in such a way as to distort these proximities as little as possible.
I decided to try this in a case where I would know what the outcome should be, as a way of thinking about how it works. So I generated 931 images of diamonds varying in two dimensions:
  1. Size
  2. Position (only how far left/right)

Then I followed the above procedure, getting this:

Neat! The random forest even picked up on a feature of this space that I wasn't expecting it to: for the same difference in position, small diamonds need to be closer to each other than large diamonds. None of my diamonds have a diameter smaller than 4 pixels, but imagine of the sizes got so small the diamond wasn't even there -- then position wouldn't matter at all of those diamonds.

I set one column of pixels to random values, and the method still worked just as well. (Which makes sense, as the random forest only cares about pixels that help it distinguish between diamonds and non-diamonds.)

A cool technique that I'd love to try some more! For one, I'd like to understand better how it differs from various manifold learning methods. One nice feature is that you could easily use this with a mix of continuous and categorical variables.

Note that starting with Euclidean distance between images (as vectors in R^2500) and mapping points to 2D doesn't seem to produce anything useful:

Code available on github.

Tuesday, July 10, 2012

Tweaks to Instapaper "Read Later" Button

I love Instapaper (please support it by becoming a premium member!). Being able to easily save articles for reading later lets me move the article-reading time from when I shouldn't be getting distracted to when I'm happy to relax on the couch (or train, or airplane, or line at the coffee shop, ...) with an interesting article.

Tonight I worked on fixing two small things that were bugging me:

  1. When I'm reading an article, I'd like to know where I came across it. The code below uses the javasript "document.referrer" property and adds a link back to the referrer, before saving to Instapaper.
  2. I don't like when I hit "Read Later" before the page has finished loading and get a complaint that I should wait for the page to load. This lets me hit "Read Later" while it's loading and get back to ordering my coffee.
You can use the code below just like the original "Read Later" link, but I'll warn you it's had about 5 minutes of testing. Please give me any feedback you have! 

I'd like to have much more extensive history/referral tracking, and even what it's supposed to do now doesn't always work. Let me know if you can help!

Saturday, April 21, 2012

Chrome is smart about "back" and redirects?

This website I made creates an image based on the parameters in a URL. For example, this url: 

...creates this image:

If you go to "" (with no parameters), I'll make up some  parameters and redirect you a URL like the one below. Unfortunately, this creates a frustrating e xperience with the "back" button (that I'm sure you've experienced elsewhere).

I feel bad about it, but I'vese never fixed that. Probably the best thing would be to make up parameters and show the corresponding image at the root url, without redirecting. Still, I haven't changed that. Sorry world!

But I wondered: Why can't browsers be smart enough to know that when you press the "back" button, you don't want to go back to somewhere that's going to redirect you again.

Then I noticed that Chrome is that smart! Try it:

IE 9 and Safari on my iPad are not that smart, but Safari on my iPhone goes "back" to where I was previously, just like Chrome.

Does anyone know how this is actually working? Does Chrome know that that page redirected me and then not even think about going back to it? Or does it check what's there, and when it sees the redirect decides instead to go back even further? Or something else?