Science is undergoing a data explosion, and astronomy is leading the way. Modern telescopes produce terabytes of data per observation, and the simulations required to model our observable Universe push supercomputers to their limits. To analyse this data scientists need to be able to think computationally to solve problems. In this course you will investigate the challenges of working with large datasets: how to implement algorithms that work; how to use databases to manage your data; and how to learn from your data with machine learning tools. The focus is on practical skills - all the activities will be done in Python 3, a modern programming language used throughout astronomy. Regardless of whether you’re already a scientist, studying to become one, or just interested in how modern astronomy works ‘under the bonnet’, this course will help you explore astronomy: from planets, to pulsars to black holes. Course outline: Week 1: Thinking about data - Principles of computational thinking - Discovering pulsars in radio images Week 2: Big data makes things slow - How to work out the time complexity of algorithms - Exploring the black holes at the centres of massive galaxies Week 3: Querying data using SQL - How to use databases to analyse your data - Investigating exoplanets in other solar systems Week 4: Managing your data - How to set up databases to manage your data - Exploring the lifecycle of stars in our Galaxy Week 5: Learning from data: regression - Using machine learning tools to investigate your data - Calculating the redshifts of distant galaxies Week 6: Learning from data: classification - Using machine learning tools to classify your data - Investigating different types of galaxies Each week will also have an interview with a data-driven astronomy expert. Note that some knowledge of Python is assumed, including variables, control structures, data structures, functions, and working with files.
Morphological classification of galaxies
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En provenance du cours de The University of Sydney
Data-driven Astronomy
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Learning from data: classification
In this final module we explore the limitations of decision tree classifiers. We then look at ensemble classifiers, using the random forest algorithm to classify images of galaxies into different types.
Rencontrer les enseignants
Tara MurphyAssociate Professor
School of Physics
Simon MurphyPostdoctoral Researcher
School of Physics
[MUSIC].
We already know broadly how decision tree classifiers work, from the last module.
In this lecture, we're going to try them out on a classic problem,
the classification of galaxies.
We're going to use images of galaxies from the Sloan Digital Sky Survey, for
which we have manual classifications.
Each galaxy was classified by volunteers as part of the galaxy zoo project.
And we've selected a subset for which the classifications had a high confidence.
In other words, most volunteers chose the same option.
The galaxies fall into three classes: ellipticals, spirals, and
irregular galaxies that show evidence of a merger.
Each individual galaxy has images taken in the five Sloan filters.
In addition, we have several fitted parameters that are calculated as part of
the Sloan data reduction pipeline.
We'll discuss these more later.
To train a machine-learning classifier,
we need to characterize each galaxy by a set of properties, or features.
When we did decision tree regression in the last module,
we only used the four Sloan colors, this time, we'll use a richer feature set.
The decision tree algorithm uses our training set to build a model to map these
features to the correct classifications.
We'll use ten fold cross validation to evaluate the accuracy of our
classifier before applying it to unknown data.
So the overall methodology is pretty clear and it's basically the process you
should follow whenever you do supervise machine learning.
The place where a lot of the thinking happens from a scientists point of view is
feature selection.
How can we best represent the galaxies in our sample.
One way of thinking about this is to consider the process
you'd go through if you were classifying the galaxies by hand.
Galaxy Zoo has some great visualizations of the decision
trees that the volunteer classifiers were required to follow.
This tree starts with a very high-level decision about whether the object
in the image is round, looks like a disk, or is a star.
Then for each of the two main classes, round or disc like, there is a series
of increasingly specific questions that help provide a final classification.
Having a formal scheme like this is essential when you have thousands
of different volunteers contributing.
But even for an individual expert classifier, it's best practice to try and
formulize your intuition, to increase your classification consistency.
There's also an important difference between decision trees for humans,
versus computers.
A human scheme can have a question such as, is there anything odd,
where the volunteer is expected to use their own judgement.
However, for a machine learning algorithm, the features and
questions need to be quantifiable.
So lets think about the features we might use for automatic classification.
Perhaps the simplest option would just be to use every pixel in the image for
every galaxy.
So if we had 512x512 pixel images for each of the five Sloan filters,
each galaxy would be represented by 1,310,720 features.
This approach of using the raw pixels as features has some advantages.
Firstly, you minimize the possible bias you might introduce through feature
selection.
Secondly it's simpler, you don't have to implement any sophisticated image analysis
features, you can just take the pixels as they are.
However, it also has some disadvantages.
The downside to not introducing bias is that you're not taking advantage of your
expert knowledge.
Using raw pixels doesn't incorporate existing astronomy knowledge about
the problem, like the fact that elliptical galaxies tend to be redder in color
because they're made up of older stars.
The second disadvantage is computational.
Using every pixel in the image means you haven't reduced the dimensionality of
the problem, which makes it computationally expensive.
You're building a model using over one million possible features.
Modern computing power has made this raw data approach feasible again and
highly successful for image classification.
We've provided some resources on deep learning if you're interested in finding
out more.
But for this example,
we're going to concentrate on the feature extraction approach.
Hubble himself said, the degree of classification success largely depends on
the significance of the features selected for classification.
So with that in mind, what features should we use?
A few obvious ones might be the color of the galaxy.
This is a feature Hubble didn't have access to,
since photographic plates only give a single intensity measurement.
But we now know it's a really important indicator of the age of
the stars in each galaxy.
A second one is the ellipticity of the galaxy.
We can get a rough idea of the shape of the galaxy by fitting an ellipse to its
profile and then using the ratio of the semi-major to semi-minor axes
to characterize this shape.
And finally, the luminosity profile of the galaxy.
This is a measure of how the brightness of a galaxy varies as a function of
the radius from its center.
These features attempt to replicate properties that the human eye
identifies when looking at the image of the galaxy.
Now remember, that all features have limitations, just like human observations.
For example, the ellipticity of a galaxy is dependent on the inclination with
respect to our viewing angle.
That's okay because each feature only contributes part of the information
that the classifier and uses to build this model.
So let's say for now, these are the only features we used.
We might represent them in a table like this.
We now train on decision tree classifier on our three classes, elliptical, spirals,
and mergers.
Using ten fold cross validation to evaluate our accuracy.
And finally, here are our results.
Without sophisticated features or optimization of the classified parameters,
we've correctly classified around 4/5ths of the galaxies into
elliptical spiral emerges, a very encouraging initial result.
In the next lecture, we'll dive a little bit deeper into what these results mean.
[MUSIC]
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