[译]How to implementing an algorithm from a scientific paper

Emmanuel Goossaert on 2018-10-18


作者:Emmanuel Goossaert

原文地址: http://codecapsule.com/2012/01/18/how-to-implement-a-paper/


I have implemented many complex algorithms from books and scientific publications, and this article sums up what I have learned while searching, reading, coding and debugging. This is obviously limited to publications in domains related to the field of Computer Science. Nevertheless, you should be able to apply the guidelines and good practices presented below to any kind of paper or implementation.


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As usual, comments are open at the bottom of this post, and I am always happy to welcome questions, corrections and contributions!


1 – Before you jump in

1 - 入坑之前

There are a few points you should review before you jump into reading a technical paper and implementing it. Make sure you cover them carefully each time you are about to start working on such a project.


1.1 – Find an open source implementation to avoid coding it

1.1 - 避免重复造轮子

Unless you want to implement the paper for the purpose of learning more about the field, you have no need to implement it. Indeed, what you want is not coding the paper, but just the code that implements the paper. So before you start anything, you should spend a couple of days trying to find an open source implementation on the internet. Just think about it: would you rather lose two days looking for the code, or waste two months implementing an algorithm that was already available?


1.2 – Find simpler ways to achieve your goal

1.2 - 少走弯路

Ask yourself what you are trying to do, and if simpler solutions would work for what you need. Could you use another technique – even if the result is only 80% of what you want – that does not require to implement the paper, and that you could get running within the next two days or so with available open source libraries? For more regarding this, see my article The 20 / 80 Productivity Rule.

问一下自己你想要做什么,是不是有更简单的方法来解决你的需求。你是否愿意使用其他只能达到80%的效果的技术?这样的话你在接下来的几天就可以直接使用开源库在实现自己的问题。有关这方面的更多信息,请参阅我的文章 The 20 / 80 Productivity Rule

1.3 – Beware of software patents

1.3 - 小心软件专利

If you are in the U.S., beware of software patents. Some papers are patented and you could get into trouble for using them in commercial applications.


1.4 – Learn more about the field of the paper

1.4 - 工欲善其事必先利其器

If you are reading a paper about the use of Support Vector Machines (SVM) in the context of Computational Neuroscience, then you should read a short introduction to Machine Learning and the different types of classifiers that could be alternatives to SVM, and you should as well read general articles about Computational Neuroscience to know what is being done in research right now.


1.5 – Stay motivated

1.5 - 世上无难事,只要肯攀登

If you have never implemented a paper and/or if you are new to the domain of the paper, then the reading can be very difficult. Whatever happens, do not let the amount and the complexity of the mathematical equations discourage you. Moreover, speed is not an issue: even if you feel that you understand the paper slower than you wish you would, just keep on working, and you will see that you will slowly and steadily understand the concepts presented in the paper, and pass all difficulties one after the other.


2 – Three kinds of papers

2 - 三种论文

It is never a good idea to pick a random paper and start implementing in right away. There are a lot of papers out there, which means there is a lot of garbage. All publications can fit into three categories:


2.1 – The groundbreaking paper

2.1 - 开创性论文

Some really interesting, well-written, and original research. Most of these papers are coming out of top-tier universities, or out of research teams in smaller universities that have been tackling the problem for about six to ten years. The later is easy to spot: they reference their own publications in the papers, showing that they have been on the problem for some time now, and that they base their new work on a proven record of publications. Also, the groundbreaking papers are generally published in the best journals in the field.


2.2 – The copycat paper

2.2 模仿性论文

Some research group that is just following the work of the groundbreaking teams, proposing improvements to it, and publishing their results of the improvements. Many of these papers lack proper statistical analysis and wrongly conclude that the improvements are really beating the original algorithm. Most of the time, they really are not bringing anything except for unnecessary additional complexity. But not all copycats are bad. Some are good, but it’s rare.


2.3 – The garbage paper

2.3 - 垃圾论文

Some researchers really don’t know what they are doing and/or are evil. They just try to maintain their status and privileges in the academic institution at which they teach. So they need funding, and for that they need to publish, something, anything. The honest ones will tell you in the conclusion that they failed and that the results are accurate only N% of the time (with N being a bad value). But some evil ones will lie, and say that their research was a great success. After some time reading publications, it becomes easy to spot the garbage paper and ditch them.

一些研究人员真的不知道他们在做什么或者说是坏透了。 他们只是试图在他们教授的学术机构中保持自己的地位和特权。 所以他们需要资金,为此他们需要发布,不管有没有。 诚实的人会在结论中告诉你他们失败了,结果只有N%的时间是准确的(N是一个坏的值)。 但是一些坏透了的人会说谎,并说他们的研究取得了巨大的成功。 经过一段时间阅读出版物后,你会很容易发现这些辣鸡并丢弃它们。

3 – How to read a scientific paper

3 - 如何阅读一篇论文

A lot has already been written on the topic, so I am not going to write much about it. A good starting point is: How to Read a Paper by Srinivasan Keshav. Below are a few points that I found useful while I was reading scientific publications.

关于这个主题已经写了很多,所以我不打算写太多。 一个很好的开始是:Srinivasan Keshav撰写的论文How to Read a Paper。以下是我在阅读出版物时发现的一些有用的观点。

3.1 – Find the right paper

3.1 - 找正确的论文

What you want to implement is an original paper, one that started a whole domain. It is sometimes okay to pick a copycat paper, if you feel that it brings real improvements and consistency to a good but immature groundbreaking paper.


So let’s say you have a paper as your starting point. You need to do some research in its surroundings. For that, the strategy is to look for related publications, and for the publications being listed in the “References” section at the end of the paper. Go on Google Scholar and search for the titles and the authors. Does any of the papers you found do a better job than the paper you had originally? If yes, then just ditch the paper you were looking at in the first place, and keep the new one you found. Another cool feature of Google Scholar is that you can find papers that cite a given paper. This is really great, because all you have to do is to follow the chain of citations from one paper to the next, and you will find the most recent papers in the field. Finding the good paper from a starting point is all about looking for papers being cited by the current paper, and for papers citing the current paper. By moving back and forth in time you should find the paper that is both of high quality and fits your needs.

所以,假设你有一篇论文作为起点。你需要在周围做一些研究。为此,策略是寻找相关出版物,以及本文末尾“参考文献”部分列出的出版物。继续使用Google学术搜索并搜索标题和作者。看一看你找到的任何一篇论文都比你最初的论文做得好吗?如果是的话,那么首先就放弃你正在看的Paper,并保留你找到的新Paper。 Google学术搜索的另一个很酷的功能是,您可以找到引用特定论文的论文。这真的很棒,因为您所要做的就是遵循从一篇论文到下一篇论文的引文链,您将找到该领域的最新论文。从一个起点寻找好的论文就是要寻找当前论文引用的论文,以及引用当前论文的论文。通过及时来回移动,你会找到既高质量又符合您需求的Paper。

Important: note that at this stage of simple exploration and reckoning, you should not be reading and fully understand the papers. This search for the right paper should be done just by skimming over the papers and using your instinct to detect the garbage (this comes with experience).

重要提示:注意在简单探索和推算的这个阶段,你不用阅读并完全理解论文。 这种搜索正确的论文应该只是通过浏览论文并用你的直觉来判断论文是否对你有用(经验总结)。

3.2 – Do not read on the screen

3.2 - 不要阅读电子版

Print the publication on hard paper and read the paper version. Also, do not reduce the size in order to print more on each page. Yes, you will save three sheets of paper, but you will lose time as you will get tired faster reading these tiny characters. Good font size for reading is between 11 and 13 points.


3.3 – Good timing and location

3.3 - 时间地点很重要

Do not read a paper in the middle of the night, do it at a moment of the day when your brain is still fresh. Also, find a quiet area, and use good lighting. When I read, I have a desk lamp pointing directly at the document.


3.4 – Marker and notes

3.4 - 好记性不如烂笔头

Highlight the important information with a marker, and take notes in the margin of whatever idea that pops in your head as you read.


3.5 – Know the definitions of all the terms

3.5 - 了解术语的意义

When you are used to read mostly news articles and fiction, your brain is trained to fill-in meaning for words that you do not know, by using context as a deduction device. Reading scientific publications is a different exercise, and one of the biggest mistake is to assume false meaning for a word. For instance in this sentence “The results of this segmentation approach still suffer from blurring artifacts”. Here two words, “segmentation”, and “artifacts”, have a general meaning in English, but also have a particular meaning in the domain of Computer Vision. If you do not know that these words have a particular meaning in this paper, then while reading without paying attention, your brain will fill-in the general meaning, and you might be missing some very important information. Therefore you must (i) avoid assumptions about words, and whenever in doubt look up the word in the context of the domain the publication was written, and (ii) write a glossary on a piece of paper of all the concepts and vocabulary specific to the publication that you did not know before. If you encounter for the first time concepts such as “faducial points” and “piece-wise affine transform”, then you should look-up their precise definitions and write them down in your glossary. Concepts are language-enabled brain shortcuts, and allow you to understand the intent of the authors faster.

当你习惯了阅读新闻和小说后,你的大脑像一个扣除装置一样根据上下文自动补充了那些你不知道的单词。阅读论文是一个不同的练习,其中一个最大的问题就是会错意。例如在这个句子中,“The results of this segmentation approach still suffer from blurring artifacts”。这里有两个单词,“segmentation”, and “artifacts”,这在日常英语中很简单,但是在计算机领域中它却有着特殊的含义。如果你不知道这些单词在这篇文章中的特殊含义,再加上阅读时没有很好的集中注意力,那么你的大脑就会自动脑补了这些单词的意思,你可能会因此错过一些重要的信息。所以你必须:(1)避免猜测单词的意思,每当出现疑问时,在出版物的上下文查找单词。(2)将此前你不知道的词汇和概念做一个词汇表写在一张纸上。如果你第一次遇到诸如“faducial points”和“piece-wise affine transform”这样的概念,那么你应该查询它们的精确定义并将它们写在你的词汇表中。概念是支持语言的大脑的捷径,会帮助你快速理解作者所要表达的意图。

3.6 – Look for statistical analysis in the conclusion

3.6 - 在结论中寻找统计分析

If the authors present only one curve from their algorithm and one curve from another algorithm, and say “look, it’s 20% more accurate”, then you know you’re reading garbage. What you want to read is: “Over a testing set of N instances, our algorithm shows significant improvement with a p-value of 5% using a two-sample t-test.” The use of statistical analysis shows a minimum of driving from the author, and is a good proof that the results can be trusted for generalization (unless the authors lied to make their results look more sexy, which can always happen).


3.7 – Make sure the conclusions are demonstrating that the paper is doing what you need

3.7 - 确定结论证明了论文做的是你需要的

Let’s say you want an algorithm that can find any face in a picture. The authors of the paper say in the conclusion that their model was trained using 10 poses from 80 different people (10 x 80 = 800 pictures), and that the accuracy of face detection with the training set was 98%, but was only 70% with the testing set (picture not used during training). What does this mean? This means that apparently, the algorithm has issues to generalize properly. It performs well when used on the training set (which is useless), and perform worse when used in real-world cases. What you should conclude at this point is that maybe, this paper is not good enough for what you need.


3.8 – Pay attention to the input data used by the authors

3.8 - 留意作者使用的输入数据

If you want to perform face detection with a webcam, and the authors have used pictures taken with a high-definition camera, then there are chances that the algorithm will not perform as well in your case as it did for the authors. Make sure that the algorithm was tested on data similar to yours or you will end up with a great implementation that is completely unusable in your real-world setup.


3.9 – Authors are humans

3.9 - 人无完人

The authors are humans, and therefore they make mistakes. Do not assume that the authors are absolutely right, and in case an equation is really hard to understand or follow, you should ask yourself whether or not the authors made a mistake there. This could just be a typo in the paper, or an error in the maths. Either case, the best way to find out is to roll out the equations yourself, and try to verify their results.


3.10 – Understand the variables and operators

3.10 - 搞懂变量和函数

The main task during the implementation of a publication is the translation of math equations in the paper into code and data. This means that before jumping into the code, you must understand 100% of the equations and processes on these equations. For instance, “C = A . B” could have different meaning. A and B could be simple numbers, and the “.” operator could simply be a product. In that case, C would be the product of two numbers A and B. But maybe that A and B are matrices, and that “.” represents the matrix product operator. In that case, C would be the product matrix of the matrices A and B. Yet another possibility is that A and B are matrices and that “.” is the term-by-term product operator. In that case, each element C(i,j) is the product of A(i,j) and B(i,j). Notations for variables and operators can change from one mathematical convention to another, and from one research group to another. Make sure you know what each variable is (scalar, vector, matrix or something else), and what every operator is doing on these variables.

一篇论文的实现主要是将论文中的数学方程式转换成代码和数据。这意味着在上手编码之前,你必须完全了解这些方程和过程。例如,“C = A . B”可能有不同含义。A和B可以是简单的数字,“.”可能表示乘积。在这种情况下,C可以是数字AB的乘积,但是AB可能是矩阵,而“.”代表矩阵乘积。在这种情况下,每个元素C(i,j)是A(i,j)和B(i,j)的乘积。变量和运算符的符号也可以从一个数学约定变成另一个,也可以从一个研究组变成另一个。要确保明白每个变量是什么(标量、向量、矩阵或其他),以及每个运算符对这些变量的作用。

3.11 – Understand the data flow

3.11 - 搞懂数据流

A paper is a succession of equations. Before you start coding, you must know how you will plug the output of equation N into the input of equation N+1.


4 – Prototyping

4 - 模型

Once you have read and understood the paper, it’s time to create a prototype. This is a very important step and avoiding it can result in wasted time and resources. Implementing a complex algorithm in languages such as C, C++ or Java can be very time consuming. And even if you have some confidence in the paper and think the algorithm will work, there is still a chance that it won’t work at all. So you want to be able to code it as quickly as possible in the dirtiest way, just to check that it’s actually working.

如果你阅读并理解了论文,就可以创建模型了。 这是非常重要的一步,没有这步可能导致浪费时间和资源。 在诸如C,C ++或Java之类的语言中实现复杂算法可能非常耗时。 即使你对论文有信心并认为算法可行,但它仍然有可能根本不起作用。 所以你应该以最快的方式尽快编码去检查它是否真的有效。

4.1 – Prototyping solutions

The best solution for that is to use a higher level versatile language or environment such as Matlab, R, Octave or SciPy/NumPy. It is not that easy to represent a mathematical equation in C++ and then print the results to manually check them. On the contrary, it is extremely straightforward to write equations in Matlab, and then print them. What would take you two to three weeks in C++ will take take you two days in Matlab.

4.2 – Prototyping helps the debugging process

An advantage of having a prototype is that when you will have your C++ version, you will be able to debug by comparing the results between the Matlab prototype and the C++ implementation. This will be developed further in the “Debugging” section below.

4.3 – Wash-off implementation issues beforehand

You will certainly make software design mistakes in your prototype, and this is a good thing as you will be able to identify where are the difficulties with both the processes or data. When you will code the C++ version, you will know how to better architect the software, and you will produce way cleaner and more stable code than you would have without the prototyping step (this is the “throw-away system” idea presented by Frederick Brooks in The Mythical Man-Month).

4.4 – Verify the results presented in the paper

Read the “Experiment” section of the paper carefully, and try to reproduce the experimental conditions as closely as possible, by using test data as similar as possible to the ones used by the authors. This increases your chances of reproducing the results obtained by the authors. Not using similar conditions can lead you to a behavior of your implementation that you might consider as an error, whereas you are just not feeding it with the correct data. As soon as you can reproduce the results based on similar data, then you can start testing it on different kinds of data.

5 – Choose the right language and libraries

At this stage, you must have a clear understanding of the algorithm and concepts presented in the publication, and you must have a running prototype which convinces that the algorithm is actually working on the input data you wish to use in production. It is now time to go into the next step, which consists in implementing the publication with the language and framework that you wish to use in production.

5.1 – Pre-existing systems

Many times, the production language and libraries are being dictated by pre-existing systems. For instance, you have a set of algorithm for illumination normalization in a picture, in a library coded in Java, and you want to add a new algorithm from a publication. In that case, obviously, you are not going to code this new algorithm in C++, but in Java.

5.2 – Predicted future uses of the implementation

In the case there is no pre-existing system imposing you a language, then the choice of the language should be done based upon the predicted uses of the algorithm. For example, if you believe that within four to six months, a possible port of your application will be done to the iPhone, then you should choose C/C++ over Java as it would be the only way to easily integrate the code into an Objective-C application without having to start everything from scratch.

5.3 – Available libraries that solve fully or partly the algorithm

The available libraries in different languages can also orient the choice of the production language. Let’s imagine that the algorithm you wish to implement makes use of well-known algebra techniques such as principal component analysis (PCA) and singular value decomposition (SVD). Then you could either code PCA and SVD from scratch, and if there is a bug could end up debugging for a week, or you could re-use a library that already implements these techniques and write the code of your implementation using the convention and Matrix class of this library. Ideally, you should be able to decompose your implementation into sub-tasks, and try to find libraries that already implement as many of these sub-tasks as possible. If you find the perfect set of libraries that are only available for a given language, then you should pick that language. Also, note that the choice of libraries should be a trade-off between re-using existing code and minimizing dependencies. Yes, it is good to have code for every sub-task needed for your implementation, but if that requires to create dependencies over 20 different libraries, then it might be not very practical and can even endanger the future stability of your implementation.

6 – Implementation

Here are some tips from my experience in implementing publications

6.1 – Choose the right precision

The type you will use for your computation should be chosen carefully. It is generally way better to use double instead of float. The memory usage can be larger, but the precision in the calculation will greatly improve, and is generally worth it. Also, you should be aware of the differences between 32-bit and 64-bit systems. Whenever you can, create your own type to encapsulate the underlying type (float or double, 32-bit or 64-bit), and use this type in your code. This can be done with a define is C/C++ or a class in Java.

6.2 – Document everything

Although it is true that over-documenting can slow down a project dramatically, in the case of the implementation of a complex technical paper, you want to comment everything. Even if you are the only person working on the project, you should document your files, classes and methods. Pick a convention like Doxygen or reStructuredText, and stick to it. Later in the development, there will be a moment where you will forget how some class works, or how you implemented some method, and you will thank yourself for documenting the code!

6.3 – Add references to the paper in your code

For every equation from the paper that you implement, you need to add a comment citing the paper (authors and year) and either the paragraph number or the equation number. That way, when later re-reading the code, you will be able to connect directly the code to precise locations in the paper. These comments should look like:

// See Cootes et al., 2001, Equation 2.3// See Matthews and Baker, 2004, Section 4.1.2

6.4 – Avoid mathematical notations in your variable names

Let’s say that some quantity in the algorithm is a matrix denoted A. Later, the algorithm requires the gradient of the matrix over the two dimensions, denoted dA = (dA/dx, dA/dy). Then the name of the the variables should not be “dA_dx” and “dA_dy”, but “gradient_x” and “gradient_y”. Similarly, if an equation system requires a convergence test, then the variables should not be “prev_dA_dx” and “dA_dx”, but “error_previous” and “error_current”. Always name things for what physical quantity they represent, not whatever letter notation the authors of the paper used (e.g. “gradient_x” and not “dA_dx”), and always express the more specific to the less specific from left to right (e.g. “gradient_x” and not “x_gradient”).

6.5 – Do not optimize during the first pass

Leave all the optimization for later. As you can never be absolutely certain which part of your code will require optimization. Every time you see a possible optimization, add a comment and explain in a couple of lines how the optimization should be implemented, such as:

// OPTIMIZE HERE: computing the matrix one column at a time// and multiplying them directly could save memory

That way, you can later find all the locations in your code at which optimizations are possible, and you get fresh tips on how to optimize. Once your implementation will be done, you will be able to find where to optimize by running a profiler such as Valgrind or whatever is available in the programming language you use.

6.6 – Planning on creating an API?

If you plan on using your current code as a basis for an API that will grow with time, then you should be aware of techniques to create interfaces that are actually usable. For this, I would recommend the “coding against the library” technique, summarized by Joshua Bloch in his presentation How to Design a Good API and Why it Matters.

7 – Debugging

Implementing a new algorithm is like cooking a dish you never ate before. Even if it tastes kind of good, you will never know if this is what it was supposed to taste. Now we are lucky, since unlike for cooking, software development has some helpful trick to increase the confidence we have in an implementation.

7.1 – Compare results with other implementations

A good way to wash out the bugs is to compare the results of your code with the results of an existing implementation of the same algorithm. As I assume that you did correctly all the tasks in the “But before you jump” section presented above, you did not find any available implementation of the algorithm (or else you would have used it instead of implementing the paper!). As a consequence, the only other implementation that you have at this stage is the prototype that you programmed earlier.

The idea is therefore to compare the results of the prototype and the production implementation at every step of the algorithm. If the results are different, then one of the two implementations is doing something wrong, and you must find which and why. Precision can change (the prototype can give you x = 1.8966 and the production code x = 1.8965), and the comparison should of course take this into account.

7.2 – Talk with people who have read the paper

Once all the steps for both implementations (prototype and production) are giving the exact same results, you can gain some confidence that your code is bug free. However, there is still a risk that you made a mistake in your understanding of the paper. In that case, both implementations will give the same results for each step, and you will think that your implementations are good, whereas this just proves that both implementations are equally wrong. Unfortunately, there is no way that I know of to detect this kind of problems. Your best option is to find someone who has read the paper, and ask that person questions regarding the parts of the algorithm you are not sure about. You could even try to ask the authors, but your chances to get an answer are very low.

7.3 – Visualize your variables

While developing, it is always good to keep an eye on the content of the variables used by the algorithm. I am not talking about merely printing all the values in the matrices and data you have, but finding the visualization trick adapted to any variable in your implementation. For instance, if a matrix is suppose to represent the gradient of an image, then during the coding and debugging, you should have a window popping up and showing that gradient image, not just the number values in the image matrix. That way, you will associate actual an image with the data you are handling, and you will be capable of detecting when there is a problem with one of the variables, which in turn will indicate a possible bug. Inventive visualization tricks include images, scatter plots, graphs, or anything that is not just a stupid list of 1,000 numbers and upon which you can associate a mental image.

7.4 – Testing dataset

Generating data to experiment with your implementation can be very time consuming. Whenever you can, try to find databases (face database, text extract databases, etc.) or tools for generating such data. If there are none, then do not lose time generating 1000 samples manually. Code a quick data generator in 20 lines and get done with it.


In this article, I have presented good practices for the implementation of a scientific publication. Remember that these are only based on my personal experience, and that they should not be blindly followed word for word. Always pay attention when you read and code, and use your judgement to determine which of the guidelines presented above fit your project. Maybe some of the practices will hurt your project more than it will help it, and that’s up to you to find out.

Now go implement some cool algorithm!