This is a research question not a direct programming question.
I am working on a symbol recognition algorithm, What the software currently does, it takes an image, divide it into contours (blobs) and start matching each contour with a list of predefined templates. Then for each contour it takes the one that has the highest match rate.
The algorithm is doing fairely however I need to train it better. What I mean is this:
I want to use a machine learning algorithm that will train the algorithm to have better matching. So lets take an example:
I run the recognition on a symbol, the algorithm will run and find that this symbol is a car, then I have to confirm that result (maybe by clicking on "Yes" or "No") the algorithm should learn from that. So if I click on NO the algorithm should learn that this is not a car and will have better result next time (maybe try to match something else). while if i click on YES he will know that he was correct and next time he will perform better when searching for a car.
This is the concept I am trying to research. I need documents or algorithm that can achieve this sort of things. I am not looking for implementations or programming, just concept or researches.
I have done many researches and read a lot about machine learning, neural networks, decision trees.... but i was not able to know how can I use any in my scenarion.
I hope I was clear and this type of question is allowed on stack overflow. if not I'm sorry
Thanks a lot for any help or tip
Image recognition is still a challenge in the community. What you described in your process of manually clicking yes/no is just creating labeled data. Since this is a very broad area, I will just point you to a few links that might be useful.
To get start, you might want to use some existing image databases instead of creating your own, which saves you a lot of effort. e.g., this car dataset in UCIC image db.
Since you already have the background of machine learning, you can take a look at some survey paper that exactly match your project interests, e.g., search object recognition survey paper or feature extraction car in google.
Then you can dive into some good papers and see whether they are suitable for your project. For example, you can check the two papers below that linked with the UCIC image db.
Shivani Agarwal, Aatif Awan, and Dan Roth,
Learning to detect objects in images via a sparse, part-based representation.
IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(11):1475-1490, 2004.
Shivani Agarwal and Dan Roth,
Learning a sparse representation for object detection.
In Proceedings of the Seventh European Conference on Computer Vision, Part IV, pages 113-130, Copenhagen, Denmark, 2002.
Also check for some implemented softwares instead of starting from scratch, in your case, opencv should be good one to start with.
For image recognition, feature extraction is one of the most important step. You might want to check some stat-of-the-art algorithms in the community. (SIFT, mean-shift, harr features etc).
Boosting algorithm might also be useful when you reach the classification step. I see a lot of scholars mention this in image recognition community.
As #nickbar suggest, discuss more at https://stats.stackexchange.com/
Related
Recently, I'm studying about facial recognition with OpenCV, and I'm trying some simple example based on study.
I'm considering to use it at front door condition.
Nowadays some buildings or apartments use facial recognition for preventing intruders. When someone joins them (such as company or houses), they require the person's picture. As I know, they require just one picture.
I didn't care about that last time, but now, I'm very curious about it.
The famous algorithms such as PCA, LDA use machine learning, so they increase successful percentages(cases). To use machine learning, they need sample images as many as I can provide. That's why I'm curious about that. Buildings or companys require just one picture, but they can recognize each person. Moreover, their accuracy is very good. How can this happen? Is there any other algorithm besides PCA or LDA?
Thanks for reading!
As far as I know, this hasn't been achieved yet. So I don't think they can develop a software recognizing a person by using only one picture.
It is most likely that they teach the algorithm with the authorized person's pictures. So if that one picture does not match with the trained ones, the algorithm can say this is an intrusion.
Edit:
As linuxqwerty pointed out those commercial products are already trained with huge datasets.
As a result of this training, learning happens and the algorithm achieves feature extraction of all those sample faces.
Then the algorithm knows almost every kinds of features that an human face can have.
For example: thickness of eyebrows, distance between eyes, roundness of chin... These are only a human can say about faces. The algorithm can extract thousands of these features.
It can keep faces as a representation of those features.
So now we have this commercial software which can represent faces as binary codes with a lot of digits.
I am getting your question again.
The apartment or company bought this software.
They included the picture of authorized person.
What the software does is simply converting the picture as it was a thousand digits password.
So that person has this unique password which the system can only reproduce that password only from his face.
To sum up:
The learning part was achieved using big face databases.
Thanks to learning part, the recognition part can be done by using only one picture.
PS: Corrections are welcome.
I happened to read about facial recognition before, that time I wanted to do it as my semester project. And of course I have heard and thought of using OpenCV as well.
Your question is simple, those company or home that use facial recognition, they usually use very well-developed product, which normally includes well-programmed facial recognition. As we are talking about security here, normally companies will buy these security products, unless if they just want to use it as a tool to deter intruders which focus less on the practical usage, and recognition accuracy, they can opt for free facial recognition software.
So, when I'm talking about well-programmed facial recognition, it means that it was trained with huge amount of databases (the photos to be recognized that you mentioned), this means the training is done even before the software is officially launched, which is during the development stage. A good facial recognition software requires both good, complete and detailed programming coding, and also huge photo databases (taken at different ambient light intensity, different facial features like hair style, spectacles) to train it.
Therefore, the accuracy of the software does not depend solely on the amount of pictures given during the usage of the software provided that it is well-programmed in the first place. Thanks and hope I answered your question and wonder.
ps: recognize is spelled this way (US); recognise (UK) =)
I am new to clustering, just implemented a couple of algorithms before.
I need to cluster tweets according to their similarity.
One way is to use only hash tags, but I don't think it would be that informative. So complete tweets should be analyzed.
Moreover I was searching the web for the algorithms for clustering feeds.
One I encountered is TF-IDF. I want to know are there better algorithms which can be implemented in few hours and are better than TF-IDF.Also I would be intersetd in some informatics source about the clustering of twitter feeds.
PS: No. of tweets : 10^5
As Anony Mousse pointed out in his comment above, TF/IDF is only a normalization measure to make sure words that are overly popular among all documents don't gain too much important.
For data preparation, I'd recommend reading this and the second part of it too (linked via the above link), if you haven't already done so. It is very important to get a vector of numbers from each tweet. In general, in machine learning, it is important to get a feature vector because that way, you can apply mathematical algorithms to your data then.
Now that you have a feature vector for each tweet in your collection, things get a bit simple. There are two clustering algorithms that come to my mind that you can whip up in a couple of hours each, with maybe extensive testing taking a weekend.
K-Means Clustering
Hierarchical Clustering With Single Linkage
With 100,000 tweets only, you should actually be able to implement these algorithms on a single computer (i.e. this is not big data -- no need for cluster computing), using your favorite language (C++, Java, Python, MATLAB, etc.). Personally, I think it's easier to implement K-Means Clustering (which I have done before) compared to Hierarchical Clustering (which I have also done before).
EDIT: Please follow the below comments only if you have labeled training data, i.e. you have tweets say, with labeled sentiments (happy-user, ok-ok, bad product, angry-user, abusive-user) and the question you want to answer is: Given a new tweet, what is it's sentiment?
Here is one very good resource you should look at, to get a better understanding of K-Nearest Neighbors:
Laszlo Kozma's Slides
In general, for the other two algorithms, there are ample resources, with Wikipedia articles the best way to start. Personally, I feel K-Nearest Neighbors (shorthand k-NN) is the easiest of the three to implement and will give you quick results.
I work at an airport where we need to determine the visibility conditions of pilots.
To do this, we have signs placed every 200 meters along the runway that allow us to determine how far the visibility is. We have multiple runways, and the visibility needs to be checked every hour.
Right now the visibility check is done manually with a human being who looks at the photos from the cameras placed at the end of each runway. So it can be tedious.
I'm a programmer who has very little experience with machine learning, but this sounds like an easy problem to automate. How should I approach this problem? Which algorithms should I study? Would OpenCV help me?
Thanks!
I think this can be automated using computer vision techniques. openCV could make the implementation easier. If all the signs are similar then ,we can train our program to recognize the sign in a specific conditions(lights). Then, we can use the trained classifier to check for the visibility of signs every hours using a simple script.
There is harr-like feature extraction already in openCV. You can use to train classifier which will output a .xml file and use that .xml file for detecting the sign regularly.
I have done a similar project RTVTR(Real Time Vehicle Tracking and Recognition) using openCV and it worked great. http://www.youtube.com/watch?v=xJwBT76VEZ4
Answering to your questions:
How should I approach this problem?
It depends on the result you want/need to obtain. Is this an "hobby" project (even if job-related) or do you need to build a machine vision system to solve the problem and should it be compliant with some regulations or standard?
Which algorithms should I study?
I am very interested in your question but I am not an expert in the field of meteorology and so searching in the relative literature is, for me, a time consuming task... so I reserve to update this part of the answer in the future. I think there will be different algorithms involved in the solution of the problem, some are very general like for example algorithms for the image segmentation, some are very specific like for example how to measure the visibility.
Update: one of the keyword for searching in the literature is Meteorological Visibility, for example
HAUTIERE, Nicolas, et al. Automatic fog detection and estimation of visibility distance through use of an onboard camera. Machine Vision and Applications, 2006, 17.1: 8-20.
LENOR, Stephan, et al. An Improved Model for Estimating the Meteorological Visibility from a Road Surface Luminance Curve. In: Pattern Recognition. Springer Berlin Heidelberg, 2013. p. 184-193.
Would OpenCV help me?
Yes, I think OpenCV can help giving you a starting point.
An idea for a naïve algorithm:
Segment the image in order to get the pixel regions belonging to the signs and to the background.
Compute the measure of visibility according to some procedure, the measure is computed by a function that has as input the regions of all the signs and the background region.
The segmentation can be simplified a lot if the signs are always in the same fixed and known position inside the image.
The measure of visibility is obviously the core of the algorithm and it can be performed in a lot of ways...
You can follow a simple approach where you compute the visibility with a mathematical formula based on the average gray level of the signs and background regions.
You can follow a more sophisticated and machine-learning oriented approach where you implement an algorithm that mimics your current human being based procedure. In this case your problem can be framed as a supervised learning task: you have a set of training examples, each training example is a pair composed by a) the photo of the runway (the input) and b) the visibility related to that photo and computed by human (the desired output). Then the system is trained by means of the training set and when you give a new photo as input it will give you back the visibility measure. I think you have a log for past visibility measures (METAR?) and if you saved the related images too, you will already have a relevant amount of data in order to build a training set and a test set.
Update in the age of Convolutional Neural Networks:
YOU, Yang, et al. Relative CNN-RNN: Learning Relative Atmospheric Visibility from Images. IEEE Transactions on Image Processing, 2018.
Both Tensor and uvts_cvs 's replies are very helpful. While the opencv mainly aims to recognize the sign pattern or even segment it from the background, when you extract the core feature in your problem : visibility, you may still need to include the background signal in your training set. I assume manual check of visibility is based on image contrast, if so, the signal-to-noise ratio(SNR) or contrast-to-noise ratio(CNR) is a good feature in learning. A threshold is defined to classify 'visible-1' and 'invisible-0'. The SNR/CNR can be obtained automatically especially if your sign position and size are fixed in your camera images.
Gather whole bunch of photos and videos and propose it as a challenge on Kaggle. I am sure many people would like to try solve it, even if reward would not be very high.
You can use the template matching functionality of openCV:
http://docs.opencv.org/doc/tutorials/imgproc/histograms/template_matching/template_matching.html
Where the template is the sign. If you manage to find a correct match, then the sign is visible. I think you can also get a sense of the scale of the sign in the image from that code.
As this is a very controlled and static environment, you have perfect conditions to estimate the visibility with vision-based approaches. Nonetheless, it is not so easy to decide which approach to take. In my thesis, I am reviewing this topic in depth for the less well-controlled environment of road traffic. See: LENOR, Stephan. Model-Based Estimation of Meteorological Visibility in the Context of Automotive Camera Systems. 2016. Doktorarbeit. (https://archiv.ub.uni-heidelberg.de/volltextserver/20855/1/20160509_lenor_thesis_final_print.pdf).
I see two major directions you could follow up:
Model-based approaches: Advantages: Not so much dependent on your very specific setup. You do not need heavy collection of data.
Data-based approaches/ML: Advantages: Can hide the whole complexity of different light and weather conditions. You seem to have a good source of data if there are people doing the job right now. Very promising without much engineering effort (just use a light-weighted CNN with few layers or so).
You could also combine both, etc. etc. If you are still interested in a solution, you can contact me again and I am happy to consult in more depth.
I am somewhat of an amateur farmer and I have a precious cherry tomato plant growing in a pot. Lately, to my chagrin, I have discovered that my precious plant has been the victim of a scheme perpetrated by the evil Manduca Quinquemaculata - also known as the Tomato Hornworm (http://insects.tamu.edu/images/insects/common/images/cd-43-c-txt/cimg308.html).
While smashing the last worm I saw, I thought to myself, if I were to use a webcam connected to my computer with a program running, would it be possible to use some kind of an application to monitor my precious plant? These pests are supremely camouflaged and very difficult for my naive eyes to detect.
I've seen research using artificial neural networks (ANNs) for all sorts of things such as recognizing people's faces, etc., and so maybe it would be possible to locate the pest with an ANN.
I have several questions though that I would like some suggestions though.
1) Is there a ranking of the different ANNs in terms of how good they are at classifying? Are multilayer perceptrons known to be better than Hopfields? Or is this a question to which the answer is unknown?
2) Why do there exist several different activation functions that can be used in ANNs? Sigmoids, hyperbolic tangents, step functions, etc. How would one know which function to choose?
3) If I had an image of a plant w/ a worm on one of the branches, I think that I could train a neural network to look for branches that are thin, get fat for a short period, and then get thin again. I have a problem though with branches crossing all over the place. Is there a preprocessing step that could be applied on an image to distinguish between foreground and background elements? I would want to isolate individual branches to run through the network one at a time. Is there some kind of nice transformation algorithm?
Any good pointers on pattern recognition and image processing such as books or articles would be much appreciated too.
Sincerely,
mj
Tomato Hornworms were harmed during the writing of this email.
A good rule of thumb for machine learning is: better features beat better algorithms. I.e if you feed the raw image pixels directly into your classifier, the results will be poor, no matter what learning algorithm you use. If you preprocess the image and extract features that are highly correlated with "caterpillar presence", then most algorithms will do a decent job.
So don't focus on the network topology, start with the computer vision task.
Do these little suckers move around regularly? If so, and if the plant is quite static (meaning no wind or other forces that make it move), then a simple filter to find movement could be sufficient. That would bypass the need of any learning algorithm, which are often quite difficult to train and implement.
A developer I am working with is developing a program that analyzes images of pavement to find cracks in the pavement. For every crack his program finds, it produces an entry in a file that tells me which pixels make up that particular crack. There are two problems with his software though:
1) It produces several false positives
2) If he finds a crack, he only finds small sections of it and denotes those sections as being separate cracks.
My job is to write software that will read this data, analyze it, and tell the difference between false-positives and actual cracks. I also need to determine how to group together all the small sections of a crack as one.
I have tried various ways of filtering the data to eliminate false-positives, and have been using neural networks to a limited degree of success to group cracks together. I understand there will be error, but as of now, there is just too much error. Does anyone have any insight for a non-AI expert as to the best way to accomplish my task or learn more about it? What kinds of books should I read, or what kind of classes should I take?
EDIT My question is more about how to notice patterns in my coworker's data and identify those patterns as actual cracks. It's the higher-level logic that I'm concerned with, not so much the low-level logic.
EDIT In all actuality, it would take AT LEAST 20 sample images to give an accurate representation of the data I'm working with. It varies a lot. But I do have a sample here, here, and here. These images have already been processed by my coworker's process. The red, blue, and green data is what I have to classify (red stands for dark crack, blue stands for light crack, and green stands for a wide/sealed crack).
In addition to the useful comments about image processing, it also sounds like you're dealing with a clustering problem.
Clustering algorithms come from the machine learning literature, specifically unsupervised learning. As the name implies, the basic idea is to try to identify natural clusters of data points within some large set of data.
For example, the picture below shows how a clustering algorithm might group a bunch of points into 7 clusters (indicated by circles and color):
(source: natekohl.net)
In your case, a clustering algorithm would attempt to repeatedly merge small cracks to form larger cracks, until some stopping criteria is met. The end result would be a smaller set of joined cracks. Of course, cracks are a little different than two-dimensional points -- part of the trick in getting a clustering algorithm to work here will be defining a useful distance metric between two cracks.
Popular clustering algorithms include k-means clustering (demo) and hierarchical clustering. That second link also has a nice step-by-step explanation of how k-means works.
EDIT: This paper by some engineers at Phillips looks relevant to what you're trying to do:
Chenn-Jung Huang, Chua-Chin Wang, Chi-Feng Wu, "Image Processing Techniques for Wafer Defect Cluster Identification," IEEE Design and Test of Computers, vol. 19, no. 2, pp. 44-48, March/April, 2002.
They're doing a visual inspection for defects on silicon wafers, and use a median filter to remove noise before using a nearest-neighbor clustering algorithm to detect the defects.
Here are some related papers/books that they cite that might be useful:
M. Taubenlatt and J. Batchelder, “Patterned Wafer Inspection Using Spatial Filtering for Cluster Environment,” Applied Optics, vol. 31, no. 17, June 1992, pp. 3354-3362.
F.-L. Chen and S.-F. Liu, “A Neural-Network Approach to Recognize Defect Spatial Pattern in Semiconductor Fabrication.” IEEE Trans. Semiconductor Manufacturing, vol. 13, no. 3, Aug. 2000, pp. 366-373.
G. Earl, R. Johnsonbaugh, and S. Jost, Pattern Recognition and Image Analysis, Prentice Hall, Upper Saddle River, N.J., 1996.
Your problem falls in the very broad field of image classification. These types of problems can be notoriously difficult, and at the end of the day, solving them is an art. You must exploit every piece of knowledge you have about the problem domain to make it tractable.
One fundamental issue is normalization. You want to have similarly classified objects to be as similar as possible in their data representation. For example, if you have an image of the cracks, do all images have the same orientation? If not, then rotating the image may help in your classification. Similarly, scaling and translation (refer to this)
You also want to remove as much irrelevant data as possible from your training sets. Rather than directly working on the image, perhaps you could use edge extraction (for example Canny edge detection). This will remove all the 'noise' from the image, leaving only the edges. The exercise is then reduced to identifying which edges are the cracks and which are the natural pavement.
If you want to fast track to a solution then I suggest you first try the your luck with a Convolutional Neural Net, which can perform pretty good image classification with a minimum of preprocessing and noramlization. Its pretty well known in handwriting recognition, and might be just right for what you're doing.
I'm a bit confused by the way you've chosen to break down the problem. If your coworker isn't identifying complete cracks, and that's the spec, then that makes it your problem. But if you manage to stitch all the cracks together, and avoid his false positives, then haven't you just done his job?
That aside, I think this is an edge detection problem rather than a classification problem. If the edge detector is good, then your issues go away.
If you are still set on classification, then you are going to need a training set with known answers, since you need a way to quantify what differentiates a false positive from a real crack. However I still think it is unlikely that your classifier will be able to connect the cracks, since these are specific to each individual paving slab.
I have to agree with ire_and_curses, once you dive into the realm of edge detection to patch your co-developers crack detection, and remove his false positives, it seems as if you would be doing his job. If you can patch what his software did not detect, and remove his false positives around what he has given you. It seems like you would be able to do this for the full image.
If the spec is for him to detect the cracks, and you classify them, then it's his job to do the edge detection and remove false positives. And your job to take what he has given you and classify what type of crack it is. If you have to do edge detection to do that, then it sounds like you are not far from putting your co-developer out of work.
There are some very good answers here. But if you are unable to solve the problem, you may consider Mechanical Turk. In some cases it can be very cost-effective for stubborn problems. I know people who use it for all kinds of things like this (verification that a human can do easily but proves hard to code).
https://www.mturk.com/mturk/welcome
I am no expert by any means, but try looking at Haar Cascades. You may also wish to experiment with the OpenCV toolkit. These two things together do face detection and other object-detection tasks.
You may have to do "training" to develop a Haar Cascade for cracks in pavement.
What’s the best approach to recognize patterns in data, and what’s the best way to learn more on the topic?
The best approach is to study pattern recognition and machine learning. I would start with Duda's Pattern Classification and use Bishop's Pattern Recognition and Machine Learning as reference. It would take a good while for the material to sink in, but getting basic sense of pattern recognition and major approaches of classification problem should give you the direction. I can sit here and make some assumptions about your data, but honestly you probably have the best idea about the data set since you've been dealing with it more than anyone. Some of the useful technique for instance could be support vector machine and boosting.
Edit: An interesting application of boosting is real-time face detection. See Viola/Jones's Rapid Object Detection using a Boosted Cascade of Simple
Features (pdf). Also, looking at the sample images, I'd say you should try improving the edge detection a bit. Maybe smoothing the image with Gaussian and running more aggressive edge detection can increase detection of smaller cracks.
I suggest you pick up any image processing textbook and read on the subject.
Particularly, you might be interested in Morphological Operations like Dilation and Erosion, which complements the job of an edge detector. Plenty of materials on the net...
This is an image processing problem. There are lots of books written on the subject, and much of the material in these books will go beyond a line-detection problem like this. Here is the outline of one technique that would work for the problem.
When you find a crack, you find some pixels that make up the crack. Edge detection filters or other edge detection methods can be used for this.
Start with one (any) pixel in a crack, then "follow" it to make a multipoint line out of the crack -- save the points that make up the line. You can remove some intermediate points if they lie close to a straight line. Do this with all the crack pixels. If you have a star-shaped crack, don't worry about it. Just follow the pixels in one (or two) directions to make up a line, then remove these pixels from the set of crack pixels. The other legs of the star will recognized as separate lines (for now).
You might perform some thinning on the crack pixels before step 1. In other words, check the neighbors of the pixels, and if there are too many then ignore that pixel. (This is a simplification -- you can find several algorithms for this.) Another preprocessing step might be to remove all the lines that are too thin or two faint. This might help with the false positives.
Now you have a lot of short, multipoint lines. For the endpoints of each line, find the nearest line. If the lines are within a tolerance, then "connect" the lines -- link them or add them to the same structure or array. This way, you can connect the close cracks, which would likely be the same crack in the concrete.
It seems like no matter the algorithm, some parameter adjustment will be necessary for good performance. Write it so it's easy to make minor changes in things like intensity thresholds, minimum and maximum thickness, etc.
Depending on the usage environment, you might want to allow user judgement do determine the questionable cases, and/or allow a user to review the all the cracks and click to combine, split or remove detected cracks.
You got some very good answer, esp. #Nate's, and all the links and books suggested are worthwhile. However, I'm surprised nobody suggested the one book that would have been my top pick -- O'Reilly's Programming Collective Intelligence. The title may not seem germane to your question, but, believe me, the contents are: one of the most practical, programmer-oriented coverage of data mining and "machine learning" I've ever seen. Give it a spin!-)
It sounds a little like a problem there is in Rock Mechanics, where there are joints in a rock mass and these joints have to be grouped into 'sets' by orientation, length and other properties. In this instance one method that works well is clustering, although classical K-means does seem to have a few problems which I have addressed in the past using a genetic algorithm to run the interative solution.
In this instance I suspect it might not work quite the same way. In this case I suspect that you need to create your groups to start with i.e. longitudinal, transverse etc. and define exactly what the behviour of each group is i.e. can a single longitudinal crack branch part way along it's length, and if it does what does that do to it's classification.
Once you have that then for each crack, I would generate a random crack or pattern of cracks based on the classification you have created. You can then use something like a least squares approach to see how closely the crack you are checking fits against the random crack / cracks you have generated. You can repeat this analysis many times in the manner of a Monte-Carlo analysis to identify which of the randomly generated crack / cracks best fits the one you are checking.
To then deal with the false positives you will need to create a pattern for each of the different types of false positives i.e. the edge of a kerb is a straight line. You will then be able to run the analysis picking out which is the most likely group for each crack you analyse.
Finally, you will need to 'tweak' the definition of different crack types to try and get a better result. I guess this could either use an automated approach or a manual approach depending on how you define your different crack types.
One other modification that sometimes helps when I'm doing problems like this is to have a random group. By tweaking the sensitivity of a random group i.e. how more or less likely a crack is to be included in the random group, you can sometimes adjust the sensitivty of the model to complex patterns that don't really fit anywhere.
Good luck, looks to me like you have a real challenge.
You should read about data mining, specially pattern mining.
Data mining is the process of extracting patterns from data. As more data are gathered, with the amount of data doubling every three years, data mining is becoming an increasingly important tool to transform these data into information. It is commonly used in a wide range of profiling practices, such as marketing, surveillance, fraud detection and scientific discovery.
A good book on the subject is Data Mining: Practical Machine Learning Tools and Techniques
(source: waikato.ac.nz) ](http://www.amazon.com/Data-Mining-Ian-H-Witten/dp/3446215336 "ISBN 0-12-088407-0")
Basically what you have to do is apply statistical tools and methodologies to your datasets. The most used comparison methodologies are Student's t-test and the Chi squared test, to see if two unrelated variables are related with some confidence.