FAQ: How Many Clusters Did You Use?

Luis Pedro Coelho, Joshua D. Kangas, Armaghan Naik, Elvira Osuna-Highley, Estelle Glory-Afshar, Margaret Fuhrman, Ramanuja Simha, Peter B. Berget, Jonathan W. Jarvik, and Robert F. Murphy, Determining the subcellular location of new proteins from microscope images using local features in Bioinformatics, 2013 [Advanced Access]  [Previous discussion on this blog]

Coelho, Luis Pedro, Tao Peng, and Robert F. Murphy. “Quantifying the Distribution of Probes Between Subcellular Locations Using Unsupervised Pattern Unmixing.” Bioinformatics 26.12 (2010): i7–i12. DOI: 10.1093/bioinformatics/btq220  [Previous discussion on this blog]

Both of my Bioinformatics papers above use the concept of bag of visual words. The first for classification, the second for pattern unmixing.

Visual words are formed by clustering local appearance descriptors. The descriptors may have different origins (see the papers above and the references below) and the visual words are used differently, but the clustering is a common intermediate step.

A common question when I present this work is how many clusters do I use? Here’s the answer: it does not matter too much.

I used to just pick a round number like 256 or 512, but for the local features paper, I decided to look at the issue a bit closer. This is one of the panels from the paper, showing accuracy (y-axis) as a function of the number of clusters (x-axis):

profile-field-dna+-RT-widefield-gs

As you can see, if you use enough clusters, you’ll do fine. If I had extended the results rightwards, then you’d see a plateau (read the full paper & supplements for these results) and then a drop-off. The vertical line shows N/4, where N is the number of images in the study. This seems like a good heuristic across several datasets.

One very interesting result is that choosing clusters by minimising AIC can be counter-productive! Here is the killer data (remember, we would be minimizing the AIC):

accuracy-aic-rt-widefield-gs

Minimizing the AIC leads to lower accuracy! AIC was never intended to be used in this context, of course, but it is often used as a criterion to select the number of clusters. I’ve done it myself.

Punchline: If doing classification using visual words, minimsing AIC may be detrimental, try using N/4 (N=nr of images).

Other References

This paper (reviewed before on this blog) presents supporting data too:

Noa Liscovitch, Uri Shalit, & Gal Chechik (2013). FuncISH: learning a functional representation of neural ISH images Bioinformatics DOI: 10.1093/bioinformatics/btt207

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Unsupervised subcellular pattern unmixing. Part II

On Friday, I presented the pattern unmixing problem. Today, I’ll discuss how we solved it.

Coelho, Luis Pedro, Tao Peng, and Robert F. Murphy. “Quantifying the Distribution of Probes Between Subcellular Locations Using Unsupervised Pattern Unmixing.” Bioinformatics 26.12 (2010): i7–i12. DOI: 10.1093/bioinformatics/btq220

The first step is to extract objects. For this, we use a combination of global & local thresholding: this means that a pixel is on if it is both above a global threshold which identifies the cells from the background and a local threshold (which identifies subcellular objects [1]).

We then group the objects found using k-means clustering. Here is what we obtain for a lysosomal picture (different colours mean different clusters) [2].

unmixing-colours-1

and the equivalent for the mitochondrial image:

unmixing-colours-0

You will see that the mitochondrial image has many green things and less dark purple objects, but both mitochondrial and lysosomal images have all of the groups. Now (and this is an important point): we do not attempt to classify each individual object, only to estimate the mixture.

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Of course, if we had the identity of each object, the mixture would be trivially estimated. But we do not need to identify each object. In fact, to attempt to do so would be a gross violation of Vapnik’s Dictum (which says do not solve, as an intermediate step, a harder problem than the one you are trying to solve). It is easier to just estimate the mixtures [3].

In this formulation it might not even matter much that some of the objects we detect correspond to multiple biological objects!

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How do we solve the mixture problem? Latent Dirichlet allocation or basis pursuit. The details are in the paper, but I will jump to the punchline.

We tested the method using a dataset where we had manipulated the cell tagging so we know the ground truth (but the algorithm, naturally, does not see it). On the graph below, the x-axis is the (hidden) truth and the y-axis is the automated estimate. In green, the perfect diagonal; and each dot represents one condition:

unmixing_corrcoef_lda

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I will note that each individual dot in the above plot represents several images from each condition. On a single image (or single cell) level the prediction is not so accurate. Only by aggregating a large number of objects can the model predict well.

This also points out why it may be very difficult for humans to perform this task (nobody has tried to do it, actually).

[1] A global threshold did not appear to be sufficient for this because there is a lot of in-cell background light (auto-fluorescence and auto-focus light).
[2] For this picture, I used 5 clusters to get 5 different colours. The real process used a larger number, obtained by minimising BIC.
[3] Sure, we can then reverse engineer and obtain a probability distribution for each individual object, but that is not the goal.

Old Work: Unsupervised Subcellular Pattern Unmixing

Continuing down nostalgia lane, here is another old paper of mine:

Coelho, Luis Pedro, Tao Peng, and Robert F. Murphy. “Quantifying the Distribution of Probes Between Subcellular Locations Using Unsupervised Pattern Unmixing.” Bioinformatics 26.12 (2010): i7–i12. DOI: 10.1093/bioinformatics/btq220

I have already discussed the subcellular location determination problem. This is Given images of a protein, can we assign it to an organelle?

This is, however, a simplified version of the world: many proteins are present in multiple organelles. They may move between organelles in response to a stimulus or as part of the cell cycle. For example, here is an image of mitochondria in green (nuclei in red):

img17

Here is one of lysosomes:

img71

And here is a mix of both!:

img77-2

This is a dataset constructed for the purpose of this work, so we know what is happening, but it simulates the situation where a protein is present in two locations simultaneously.

Thus, we can move beyond simple assignment of a protein to an organelle to assigning it to multiple organelles. In fact, some work (both from the Murphy group and others) has looked at subcellular location classification using multiple labels per image. This, however, is still not enough: we want to quantify this.

This is the pattern unmixing problem. The goal is to go from an image (or a set of images) to something like the following: This is 30% nuclear and 70% cytoplasmic, which is very different from 70% nuclear and 30% cytoplasmic. The basic organelles can serve as the base patterns [1].

Before our paper, there was some work in approaching this problem from a supervised perspective: Given examples of different organelles (ie, of markers that locate to a single organelle), can we automatically build a system which when given images of a protein which is distributed in multiple organelles, can figure out which fraction comes from each organelle?

Our paper extended this to work to the unsupervised case: can you learn a mixture when you do not know which are the basic patterns?

References

Determining the distribution of probes between different subcellular locations through automated unmixing of subcellular patterns Tao Peng, Ghislain M. C. Bonamy, Estelle Glory-Afshar, Daniel R. Rines, Sumit K. Chanda, and Robert F. Murphy PNAS 2010 107 (7) 2944-2949; published ahead of print February 1, 2010, doi:10.1073/pnas.0912090107

Object type recognition for automated analysis of protein subcellular location T Zhao, M Velliste, MV Boland, RF Murphy Image Processing, IEEE Transactions on 14 (9), 1351-1359

[1] This is still a limited model because we are not sure even how many base patterns we should consider, but it will do for now.

Old papers: Structured Literature Image Finder (SLIF)

Still going down memory lane, I am presenting a couple of papers:

Structured literature image finder: extracting information from text and images in biomedical literature LP Coelho, A Ahmed, A Arnold, J Kangas, AS Sheikh, EP Xing, WW Cohen, RF Murphy Linking Literature, Information, and Knowledge for Biology, 23-32 [DOI] [Murphylab PDF]

Structured literature image finder: Parsing text and figures in biomedical literature A Ahmed, A Arnold, LP Coelho, J Kangas, AS Sheikh, E Xing, W Cohen, RF Murphy Web Semantics: Science, Services and Agents on the World Wide Web 8 (2), 151-154 [DOI]

These papers refer to SLIF, which was the Subcellular Location Image Finder and later the Structured Literature Image Finder.

The initial goals of this project were to develop a system which parsed the scientific literature and extracted figures (including the caption). Using text-processing, the system attempted to guess what the image depicted and using computer vision, the system attempted to interpret the image.

In particular, the focus was on subcellular image analysis for different proteins from fluorescent micrographs in published literature.

slif-overview

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Additionally, there was a topic-model based navigation based on both images and the caption-text. This allowed for latent model based navigation. Unfortunately, the site is currently offline, but our user-study showed that it was a meaningful navigation model.

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The final result was a proof-of-concept system. Most of the subsystems worked at reasonably high accuracy, but it was not sufficient for the overall inferrences to be of very high accuracy (if there are six steps in an inferene step and each has 90% accuracy, then you are just about 50/50, which is much better than random guessing in large inference spaces, but still not directly trustable).

I think the vision is still valid and eventually the technology will be good enough. There is a lot of information inside the biological literature which is not always so obvious to get at and that much of this is in the form of image. SLIF was a first stab at getting at this data in addition to the text-based approaches that are more well known.

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More information about SLIF (including references to the initial SLIF papers, of which I was not a part).

Paper review: Assessing the efficacy of low-level image content descriptors for computer-based fluorescence microscopy image analysis

Paper review:

Assessing the efficacy of low-level image content descriptors for computer-based fluorescence microscopy image analysis by L. Shamir in Journal of Microscopy, 2011 [DOI]

This is an excellent simple paper [1]. I will jump to the punchline (slightly edited by me for brevity):

This paper demonstrates that microscopy images that were previously used for developing and assessing the performance of bioimage classification algorithms can be classified even when the biological content is removed from the images [by replacing them with white squares], showing that previously reported results might be biased, and that the computer analysis could be driven by artefacts rather than by the actual biological content.

Here is an example of what the author means:

white_squares

Basically, the author shows that even after modifying the images by drawing white boxes where the cells are, classifiers still manage to do apparently well. Thus, they are probably picking up on artefacts instead of signal.

This is (and this analogy is from the paper, although not exactly in this form) like a face recognition system which seems to work very well because all of the images it has of me have me wearing the same shirt. It can perform very well on the training data, but will be fooled by anyone who wears the same shirt.

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This is a very important work as it points to the fact that many previous results were probably overinflated. Looking at the dates when this work was done, this was probably at the same time that I was working on my own paper on evaluation of subcellular location determination (just that it took a while for that one to appear in print).

I expect that my proposed stricter protocol for evaluation (train and test on separate images) would be more protected against this sort of effect [2]: we are now modeling the real problem instead of a proxy problem.

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I believe two things about image analysis of biological samples:

  1. Computers can be much better than humans at this task.
  2. Some (most? much of?) published literature overestimates how well computers do with the method being presented.

Note that there is no contradiction between the two, except that point 2, if widely believed, can make it harder to convince people of point 1.

(There is also a third point which is most people overestimate how well humans do.)

[1] Normally, I’d review recent papers only, but this not only had this one escaped my attention when it came out (in my defense, it came out just when I was trying to finish my PhD thesis), but it deals with themes I have blogged about before.
[2] I tried a bit of testing around here, but it is hard to automate the blocking of the cells. Automatic thresholding does not work because it depends on the shape of the signal! This is why the author of this paper drew squares by hand.

Is Cell Segmentation Needed for Cell Analysis?

Having just spent some posts discussing a paper on nuclear segmentation (all tagged posts), let me ask the question:

Is cell segmentation needed? Is this a necessary step in an analysis pipeline dealing with fluorescent cell images?

This is a common FAQ whenever I give a talk on my work which does not use segmentation, for example, using local features for classification (see the video). It is a FAQ because, for many people, it seems obvious that the answer is that Yes, you need cell segmentation. So, when they see me skip that step, they ask: shouldn’t you have segmented the cell regions?

Here is my answer:

Remember Vapnik‘s dictum [1]do not solve, as an intermediate step, a harder problem than the problem you really need to solve.

Thus the question becomes: is your scientific problem dependent on cell segmentation? In the case, for example, of subcellular location determination, it is not: all the cells in the same field display the same phenotype, your goal being the find out what it is. Therefore, you do not need to have an answer for each cell, only for the whole field.

In other problems, you may need to have a per-cell answer: for example in some kinds of RNAi experiment only a fraction of the cells in a field display the RNAi phenotype and the others did not take up the RNAi. Therefore, segmentation may be necessary. Similarly, if a measurement such as distance of fluorescent bodies to cell membrane is meaningful, by itself (as opposed to being used as a feature for classification), then you need segmentation.

However, sometimes you can get away without segmentation.

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An important point to note is the following: while it may be good to have access to perfect classification, imperfect classification (i.e., the type you actually get), may not help as much as the perfect kind.

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Just to be sure, I was not the first person to notice that you do not need segmentation for subcellular location determination. I think this is the first reference:

Huang, Kai, and Robert F. Murphy. “Automated classification of subcellular patterns in multicell images without segmentation into single cells.” Biomedical Imaging: Nano to Macro, 2004. IEEE International Symposium on. IEEE, 2004. [Google scholar link]

[1] I’m quoting from memory. It may a bit off. It sounds obvious when you put it this way, but it is still often not respected in practice.

Video Abstract for Our Paper

Available on figshare. Check it out!

Can’t embed because WordPress would require me to pay a bit too much right now [it will probably be the only video I’ll post this year].

I did this on Linux and was surprised at how much the open source video editing software has grown. Everything worked well and the interfaces were good. It only took a few hours (which seems a lot, but this might reach as many people as if I gave a talk and I’d certainly spend as much time preparing for a talk).

I wish I had a better microphone than my laptop microphone, though.