I’ve noticed that there are rapidly growing interests and attentions in data mining and machine learning among astronomers but the level of execution is yet rudimentary or partial because there has been no comprehensive tutorial style literature or book for them. I recently introduced a machine learning book written by an engineer. Although it’s a very good book, it didn’t convey the foundation of machine learning built by statisticians. In the quest of searching another good book so as to satisfy the astronomers’ pursuit of (machine) learning methodology with the proper amount of statistical theories, the first great book came along is The Elements of Statistical Learning. It was chosen for this writing not only because of its fame and its famous authors (Hastie, Tibshirani, and Friedman) but because of my personal story. In addition, the 2nd edition, which contains most up-to-date and state-of-the-art information, was released recently.

First, the book website:

The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman

You’ll find examples, R codes, relevant publications, and plots used in the text books.

Second, I want to tell how I learned about this book before its first edition was published. Everyone has a small moment of meeting very famous people. Mine is shaking hands with President Clinton, in 2000. I still remember the moment vividly because I really wanted to tell him that ice cream was dripping on his nice suit but the top of the line guards blocked my attempt of speaking/pointing icecream dripping with a finger afterward the hand shaking. No matter what context is, shaking hands with one of the greatest presidents is a memorable thing. Yet it was not my cherishing moment because of icecreaming dripping and scary bodyguards. My most cherishing moment of meeting famous people is the half an hour conversation with late Prof. Leo Breinman (click for my two postings about him), author of probability textbook, creator of CART, and the most forefront pioneer in machine learning.

The conclusion of that conversation was a book soon to be published after explaining him my ideas of applying statistics to astronomical data and his advices to each problems. I was not capable to understand every statistics so that his answer about this new coming book at that time was the most relevant and apt one.

This conversation happened during the 3rd Statistical Challenges in Modern Astronomy (SCMA). Not long passed since I began my graduate study in statistics but had an opportunity to assist the conference organizer, my advisor Dr. Babu and to do some chores during the conference. By accident, I read the book by Murtagh about multivariate data analysis, so I wanted to speak to him. Except that, I have no desire to speak renown speakers and attendees. Frankly, I didn’t have any idea who’s who at the conference and a few years later, I realized that the conference dragged many famous people and the density of such people was higher than any conference I attended. Who would have imagine that I could have a personal conversation with Prof. Breiman, at that time. I have seen enough that many famous professors train people during conferences. Getting a chance for chatting some seconds are really hard and tall/strong people push someone small like me away always.

The story goes like this: a sunny perfect early summer afternoon, he was taking a break for a cigar and I finished my errands for the session. Not much to do until the end of session, I decided to take some fresh air and I spotted him enjoying his cigar. Only the worst was that I didn’t know he was the person of CART and the founder of statistical machine learning. Only from his talk from the previous session, I learned he was a statistician, who did data mining on galaxies. So, I asked him if I can join him and ask some questions related to some ideas that I have. One topic I wanted to talk about classification of SN light curves, by that time from astronomical text books, there are Type I & II, and Type I has subcategories, Ia, Ib, and Ic. Later, I heard that there is Type III. But the challenge is observations didn’t happen with equal intervals. There were more data mining topics and the conversation went a while. In the end, he recommended me a book which will be published soon.

Having such a story, a privilege of talking to late Prof. Breiman through an very unique meeting, SCMA, before knowing the fame of the book, this book became one of my favorites. The book, indeed, become popular, around that time, almost only book discussing statistical learning; therefore, it was an excellent textbook for introducing statistics to engineerers and machine learning to statisticians. In the mean time, statistical learning enjoyed popularity in many disciplines that have data sets and urging for learning with the aid of machine. Now books and journals on machine learning, data mining, and knowledge discovery (KDD) became prosperous. I was so delighted to see the 2nd edition in the market to bridge the gap over the years.

I thank him for sharing his cigar time, probably his short free but precious time for contemplation, with me. I thank his patience of spending time with such an ignorant girl with a foreign english accent. And I thank him for introducing a book which will became a bible in the statistical learning community within a couple of years (I felt proud of myself that I access the book before people know about it). Perhaps, astronomers cannot have many joys from this book that I experienced from how I encounter the book, who introduced the book, whether the book was used in a course, how often book is referred, etc. But I assure that it’ll narrow the gap in the notions how astronomers think about data mining (preprocessing, pipelining, and bulding catalogs) and how statisticians treat data mining. The newly released 2nd edition would help narrowing the gap further and assist astronomers to coin brilliant learning algorithms specific for astronomical data. [The END]

—————————– Here, I patch my scribbles about the book.

What distinguish this book from other machine learning books is that not only authors are big figures in statistics but also fundamentals of statistics and probability are discussed in all chapters. Most of machine learning books only introduce elementary statistics and probability in chapter 2, and no basics in statistics is discussed in later chapters. Generally, empirical procedures, computer algorithms, and their results without presenting basic theories in statistics are presented.

You might want to check the book’s website for data sets if you want to try some ideas described there
The Elements of Statistical Learning
In addition to its historical footprint in the field of statistical learning, I’m sure that some astronomers want to check out topics in the book. It’ll help to replace some data analysis methods in astronomy celebrating their centennials sooner or later with state of the art methods to cope with modern data.

This new edition reflects some evolutions in statistical learning whereas the first edition has been an excellent harbinger of the field. Pages quoted from the 2nd edition.

[p.28] Suppose in fact that our data arose from a statistical model $Y=f(X)+e$ where the random error e has E(e)=0 and is independent of X. Note that for this model, f(x)=E(Y|X=x) and in fact the conditional distribution Pr(Y|X) depends on X only through the conditional mean f(x).
The additive error model is a useful approximation to the truth. For most systems the input-output pairs (X,Y) will not have deterministic relationship Y=f(X). Generally there will be other unmeasured variables that also contribute to Y, including measurement error. The additive model assumes that we can capture all these departures from a deterministic relationship via the error e.

How statisticians envision “model” and “measurement errors” quite different from astronomers’ “model” and “measurement errors” although in terms of “additive error model” they are matching due to the properties of Gaussian/normal distribution. Still, the dilemma of hen or eggs exists prior to any statistical analysis.

[p.30] Although somewhat less glamorous than the learning paradigm, treating supervised learning as a problem in function approximation encourages the geometrical concepts of Euclidean spaces and mathematical concepts of probabilistic inference to be applied to the problem. This is the approach taken in this book.

Strongly recommend to read chapter 3, Linear Methods for Regression: In astronomy, there are so many important coefficients from regression models, from Hubble constant to absorption correction (temperature and magnitude conversion is another example. It seems that these relations can be only explained via OLS (ordinary least square) with the homogeneous error assumption. Yet, books on regressions and linear models are not generally thin. As much diversity exists in datasets, more amount of methodology, theory and assumption exists in order to reflect that diversity. One might like to study the statistical properties of these indicators based on mixture and hierarchical modeling. Some inference, say population proportion can be drawn to verify some hypotheses in cosmology in an indirect way. Understanding what regression analysis and assumptions and how statistician efforts made these methods more robust and interpretable, and reflecting reality would change forcing E(Y|X)=aX+b models onto data showing correlations (not causality).

[arXiv:stat.ME:0910.2585]
Variable Selection and Updating In Model-Based Discriminant Analysis for High Dimensional Data with Food Authenticity Applications
by Murphy, Dean, and Raftery

Classifying or clustering (or semi supervised learning) spectra is a very challenging problem from collecting statistical-analysis-ready data to reducing the dimensionality without sacrificing complex information in each spectrum. Not only how to estimate spiky (not differentiable) curves via statistically well defined procedures of estimating equations but also how to transform data that match the regularity conditions in statistics is challenging.

Another reason that astrophysics spectroscopic data classification and clustering is more difficult is that observed lines, and their intensities and FWHMs on top of continuum are related to atomic database and latent variables/hyper parameters (distance, rotation, absorption, column density, temperature, metalicity, types, system properties, etc). Frequently it becomes very challenging mixture problem to separate lines and to separate lines from continuum (boundary and identifiability issues). These complexity only appears in astronomy spectroscopic data because we only get indirect or uncontrolled data ruled by physics, as opposed to the the meat species spectra in the paper. These spectroscopic data outside astronomy are rather smooth, observed in controlled wavelength range, and no worries for correcting recession/radial velocity/red shift/extinction/lensing/etc.

Although the most relevant part to astronomers, i.e. spectroscopic data processing is not discussed in this paper, the most important part, statistical learning application to complex curves, spectral data, is well described. Some astronomers with appropriate data would like to try the variable selection strategy and to check out the classification methods in statistics. If it works out, it might save space for storing spectral data and time to collect high resolution spectra. Please, keep in mind that it is not necessary to use the same variable selection strategy. Astronomers can create better working versions for classification and clustering purpose, like Hardness Ratios, often used to reduce the dimensionality of spectral data since low total count spectra are not informative in the full energy (wavelength) range. Curse of dimensionality!.

• Space Weather Research Lab at NJIT
• SEEDS — Solar Eruptive Event Detection System at George Mason University.
• CACTUS A software package for ‘Computer Aided CME Tracking
• SRON in the Netherlands

These seem quite informative and I believe more statisticians and data scientists (signal and image processing, machine learning, computer vision, and data mining) easily collaborate with solar physicists. All the complexity, as a matter of fact, comes from data processing to be fed in to (machine, statistical) learning algorithms and defining the objectives of learning. Once settled, one can easily apply numerous methods in the field to these time varying solar images.

I’m writing this short posting because I finally found those interesting articles that I collected for my previous post on Space Weather. After finding them and scanning through, I realized that methodology-wise they only made baby steps. You’ll see a limited number key words are repeated although there is a humongous society of scientists and engineers in the knowledge discovery and data mining.

Note that the objectives of these studies are quite similar. They described machine learning for the purpose of automatizing the procedure of detecting features of interest of the Sun and possible forecasting relevant phenomena that affects our own atmosphere due to associated solar activities.

1. Automated Prediction of CMEs Using Machine Learning of CME – Flare Associations by Qahwaji et al. (2008) in Solar Phy. vol 248, pp.471-483.
2. Automatic Short-Term Solar Flare Prediction using Machine Learning and Sunspot Associations by Qahwaji and Colak (2007) in Solar Phy. vol. 241, pp. 195-211
   

   Space weather is defined by the U.S. National Space Weather Probram (NSWP) as “conditions on the Sun and in the solar wind, magnetosphere, ionosphere, and thermosphere that can influence the performance and reliability of space-borne and ground-based technological systems and can endanger human life or health”

   Personally thinking, the section of “jackknife” needs to be replaced with “cross-validation.”

3. Automatic Detection and Classification of Coronal Mass Ejections by Qu et al. (2006) in Solar Phy. vol. 237, pp.419-431.
4. Automatic Solar Filament Detection Using image Processing Techniques by Qu et al. (2005) in Solar Phy., vol. 228, pp. 119-135
5. Automatic Solar Flare Tracking Using Image-Processing Techniques by Qu, et al. (2004) in Solar Phy. vol. 222, pp. 137-149
6. Automatic Solar Flare Detection Using MLP, RBF, and SVM by Qu et al. (2003) in Solar Phy. vol. 217, pp.157-172. pp. 157-172

I’d like add a survey paper on another type of learning methods beyond Support Vector Machine (SVM) used in almost all articles above. Luckily, this survey paper happened to address my concern about the “practices of background subtraction” in high energy astrophysics.

A Survey of Manifold-Based Learning methods by Huo, Ni, Smith
[Excerpt] What is Manifold-Based Learning?
It is an emerging and promising approach in nonparametric dimension reduction. The article reviewed principle component analysis, multidimensional scaling (MDS), generative topological mapping (GTM), locally linear embedding (LLE), ISOMAP, Laplacian eigenmaps, Hessian eigenmaps, and local tangent space alignment (LTSA) Apart from these revisits and comparison, this survey paper is useful to understand the danger of background subtraction. Homogeneity does not mean constant background to be subtracted, often cause negative source observation.

More collaborations among multiple disciplines are desired in this relatively new field. For me, it is one of the best data and information scientific fields of the 21st century and any progress will be beneficial to human kind.

1. I must acknowledge him for his kindness and patience. He was my wikipedia to questions while I was studying the Sun.