I have two groups A and B of strings of the letters "AGTE" and I'd like to find some way of comparing these to see whether they are statistically similar. The first group A are real world observations, B are predictions. There are 400 or so in each group Eg
**A**
GTAATEGTTTEAAA
TTEAGE
...
**B**
AGTEAAAAGT
TAT
GGATEAATGGGTEAATG
....
I'd also like to be up to visualise these in some way really for presentation purposes. Do you have any ideas how I might be able to do that?
I'd suggest you compute the Levenshtein distance between the strings, then you can plot these inter string distances. Larger values indicate strings that are more dissimilar.
If you don't want to implement the Levenshtein distance calculation yourself, check out these submissions on file exchange.
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Levenshtein distance is a gauge of the distance between two strings. Is there a similar metric for assessing how similar a group of strings are to each other, a kind of mean or group distance?
EDIT: I realize now that my question above could be better worded. Let's say I have a list of strings:
['aaa','aab','aaaa','aacd']
Is there a way to compute the degree to which every string in the above list is similar to each other? Some sort of measurement?
I have several curves that contain many data points. The x-axis is time and let's say I have n curves with data points corresponding to times on the x-axis.
Is there a way to get an "average" of the n curves, despite the fact that the data points are located at different x-points?
I was thinking maybe something like using a histogram to bin the values, but I am not sure which code to start with that could accomplish something like this.
Can Excel or MATLAB do this?
I would also like to plot the standard deviation of the averaged curve.
One concern is: The distribution amongst the x-values is not uniform. There are many more values closer to t=0, but at t=5 (for example), the frequency of data points is much less.
Another concern. What happens if two values fall within 1 bin? I assume I would need the average of these values before calculating the averaged curve.
I hope this conveys what I would like to do.
Any ideas on what code I could use (MATLAB, EXCEL etc) to accomplish my goal?
Since your series' are not uniformly distributed, interpolating prior to computing the mean is one way to avoid biasing towards times where you have more frequent samples. Note that by definition, interpolation will likely reduce the range of your values, i.e. the interpolated points aren't likely to fall exactly at the times of your measured points. This has a greater effect on the extreme statistics (e.g. 5th and 95th percentiles) rather than the mean. If you plan on going this route, you'll need the interp1 and mean functions
An alternative is to do a weighted mean. This way you avoid truncating the range of your measured values. Assuming x is a vector of measured values and t is a vector of measurement times in seconds from some reference time then you can compute the weighted mean by:
timeStep = diff(t);
weightedMean = timeStep .* x(1:end-1) / sum(timeStep);
As mentioned in the comments above, a sample of your data would help a lot in suggesting the appropriate method for calculating the "average".
So I have multiple paths stored, each path would consist of data points x1,y1 | x2, y2 | x3, y3 ... etc
I would like to compare these paths with one another to work out if any similarities are present.
I could run through each point and see if it matched any of the points in the first path, then look to see if the next point matches the next point.
I think this would work if there were no anomalies, but could skip over if the next point did not match.
I would like to build in some level of tolerance eg 10, 10 may match 12, 12 or 8, 8
Is this a good way to compare the data, or is there a better approach?
As a second step I may want to consider time as a value too, so each point would have a time value associated with it.
Some possible approaches you can use:
handle booth paths as polygon and compare them as such
see: How to compare two shapes?
use OCR algorithms/approaches
see: OCR and character similarity
transform both paths to synchronized dataset and correlate
either extract significant points only and/or resample paths to the same point count. Then synchronize booth datasets (as in bullet 1) and use correlation coefficient
[notes]
Depending on the input data you can also exploit DCT/DFT transforms to remove unimportant data (like in JPG compression) And or compare in frequency domain instead of spatial/time domain.
You can also compare obvious things (invariant on rotation and translation) like
area
perimeter length
number of self-intersections
number of inflex points
u could compare the mean and variances of the two set of points. If they are on straight lines, as you hypothesize, you could fit straight lines through the two datasets and then compare the parameters of the two straight lines to infer about their distances. It would be more helpful if you could tell the behavour of the two datasets.
Given a range of numbers, say from [80,240], it is easy to determine how much of that range lies within [100,105]: (105-100)/(240-80) = 5/160 = .03125. Easy.
So now, how much of a Meriam Webster dictionary lies between umbrella and velvet? Even if we assume uniform distribution of text across the corpus, is there a standard metric for text?
I don't think there is a standard for that. If you had all entries from Meriam Webster in an array, you could use first and last positions as the bounds, so you would have a set going from 1 to n. Then you could pick the positions of "umbrella" and "velvet", call them x and y, and calculate your range as (y - x + 1) / (n).
That works if you are seeing words as elements of an ordered set, so as to have them behave as real numbers. You are basically dividing the distance between two numbers in a set by the distance between the boundaries of the set. Some forms of algebra deal with them differently - when calculating the Levenshtein distance between any two given words, for example, each words is seen as a vector with as many dimensions as they have characters.
You could define the boundaries of your n-dimensional space by using the biggest word in Meriam Webster (hint: it's "pneumonoultramicroscopicsilicovolcanoconiosis", so your space would have 45 dimensions). However, when considering any A-B pair of words, a third word C of intermediary length may or may not be between those, depending on the operations involved in the transformation from A to B.
You'd have to check every word with a length between that of A and B to check whether they are part of the range between A and B... So it's not a matter of simple calculus, and I don't know if this could be even feasible with a regular computer nowadays. And that's just considering Meriam's close to half a million entries.
I heard about clustering to group similar data. I want to know how it works in the specific case for String.
I have a table with more than different 100,000 words.
I want to identify the same word with some differences (eg.: house, house!!, hooouse, HoUse, #house, "house", etc...).
What is needed to identify the similarity and group each word in a cluster? What algorithm is more recommended for this?
To understand what clustering is imagine a geographical map. You can see many distinct objects (such as houses). Some of them are close to each other, and others are far. Based on this, you can split all objects into groups (such as cities). Clustering algorithms make exactly this thing - they allow you to split your data into groups without previous specifying groups borders.
All clustering algorithms are based on the distance (or likelihood) between 2 objects. On geographical map it is normal distance between 2 houses, in multidimensional space it may be Euclidean distance (in fact, distance between 2 houses on the map also is Euclidean distance). For string comparison you have to use something different. 2 good choices here are Hamming and Levenshtein distance. In your particular case Levenshtein distance if more preferable (Hamming distance works only with the strings of same size).
Now you can use one of existing clustering algorithms. There's plenty of them, but not all can fit your needs. For example, pure k-means, already mentioned here will hardly help you since it requires initial number of groups to find, and with large dictionary of strings it may be 100, 200, 500, 10000 - you just don't know the number. So other algorithms may be more appropriate.
One of them is expectation maximization algorithm. Its advantage is that it can find number of clusters automatically. However, in practice often it gives less precise results than other algorithms, so it is normal to use k-means on top of EM, that is, first find number of clusters and their centers with EM and then use k-means to adjust the result.
Another possible branch of algorithms, that may be suitable for your task, is hierarchical clustering. The result of cluster analysis in this case in not a set of independent groups, but rather tree (hierarchy), where several smaller clusters are grouped into one bigger, and all clusters are finally part of one big cluster. In your case it means that all words are similar to each other up to some degree.
There is a package called stringdist that allows for string comparison using several different methods. Copypasting from that page:
Hamming distance: Number of positions with same symbol in both strings. Only defined for strings of equal length.
Levenshtein distance: Minimal number of insertions, deletions and replacements needed for transforming string a into string b.
(Full) Damerau-Levenshtein distance: Like Levenshtein distance, but transposition of adjacent symbols is allowed.
Optimal String Alignment / restricted Damerau-Levenshtein distance: Like (full) Damerau-Levenshtein distance but each substring may only be edited once.
Longest Common Substring distance: Minimum number of symbols that have to be removed in both strings until resulting substrings are identical.
q-gram distance: Sum of absolute differences between N-gram vectors of both strings.
Cosine distance: 1 minus the cosine similarity of both N-gram vectors.
Jaccard distance: 1 minues the quotient of shared N-grams and all observed N-grams.
Jaro distance: The Jaro distance is a formula of 4 values and effectively a special case of the Jaro-Winkler distance with p = 0.
Jaro-Winkler distance: This distance is a formula of 5 parameters determined by the two compared strings (A,B,m,t,l) and p chosen from [0, 0.25].
That will give you the distance. You might not need to perform a cluster analysis, perhaps sorting by the string distance itself is sufficient. I have created a script to provide the basic functionality here... feel free to improve it as needed.
You can use an algorithm like the Levenshtein distance for the distance calculation and k-means for clustering.
the Levenshtein distance is a string metric for measuring the amount of difference between two sequences
Do some testing and find a similarity threshold per word that will decide your groups.
You can use a clustering algorithm called "Affinity Propagation". This algorithm takes in an input called similarity matrix which you can generate by taking negative of the either Levenstein distance or an harmonic mean of partial_ratio and token_set_ratio from fuzzywuzzy library if you are using Python.