I have the following problem I would like to tackle.
I have a list of elements 'Ei' (element i), each with several parameters.
The parameters are similar and each is assigned with a weight 'Wx' (Weight for parameter x).
The weight can be changed according to preference.
I need to rank/prioritize the elements according to the parameters and their weights.
Are you familiar with any approach/technique/solution for a similar system?
Thanks
Are you storing those elements in a Colletions-type structure? If so, you can use sorting by weight, making so the element with the most weight stays at the top. Search for sorting algorithms.
Related
I have a dataset where we are bringing in a dataframe of values, and assigning each of the values a number 1-5. We're then sorting these values according to this column using dplyr::arrange.
In looking through the resulting data, it's clear that, aside from being ordered by the numbers in the 1-5 column, the original order the rows came in impacts the final order. However, I can't figure out what's impacting the order of rows within each group.
To this end, I've been trying to find the sorting algorithm that dplyr's arrange function uses - however, I can't find it anywhere here or in the documentation. Any help would be appreciated
The documentation doesn't tell you, and doesn't guarantee that order is preserved within ties. That means you shouldn't assume anything about the behaviour within ties.
All you should assume is that things are ordered as the documentation says they will be. If that is violated, it's a bug. If the documentation doesn't say what will happen, then you should assume that whatever happens today may be different tomorrow.
It's easy enough to make any sort into a stable sort (that maintains the original ordering within ties). Just add an extra column containing the original position, and include it as the final column for breaking ties. For example,
dplyr::arrange(mtcars, carb)
doesn't say anything about the order within rows that have the same value of carb. But
dplyr::arrange(data.frame(i = 1:nrow(mtcars), mtcars), carb, i)[-1]
guarantees that the original order is kept within carb values.
The code shows it eventually calls base::order with the default method, so:
method: the method to be used: partial matches are allowed. The
default (‘"auto"’) implies ‘"radix"’ for short numeric
vectors, integer vectors, logical vectors and factors.
Otherwise, it implies ‘"shell"’. For details of methods
‘"shell"’, ‘"quick"’, and ‘"radix"’, see the help for ‘sort’.
Though, it does pass through vctrs::vec_proxy_order first - not sure it that matters.
I am using BsplinesComp for a sample problem.
The objective is to maximize the area under the line.
My problem arises when I want to set a constraint for one of the values in the output array that bspline gives. So a value such that the spline goes through that no matter what configuration it is in.
I tried this in two ways and I have uploaded the codes. They are both very badly coded so i think there is a neater way to do so. Links to codes:
https://gist.github.com/stackoverflow38/5eae1e86c5802a4df91becdf580d28c5
1- Using an extra explicit component in which the middle array value is imposed to be a selected value
2- Tried to use an execcomp but I get an error. Target shapes do not match.
I vaguely remember reading such a question but could not find it.
Overall I am trying to set a constraint for either the first, middle or last value of the bspline and some range that it should be in.
Similar to the plots here
So, I think you want to know the best way to do this, and the best way is to not use any extra components at all. You can directly constrain a single point in the output of the BsplinesComp by using the "indices" argument in the add_constraint call. Here, I constrain the first point in the spline to lie on the interval [-1, 1].
model.add_constraint('interp.h', lower=-1, upper=1, indices=[0])
Running the model gives me a shape that looks more like one of the ones you included.
Just for reference, for the errors you got with 1 and 2:
Not sure what is wrong here, but maybe the version you uploaded isn't the latest. You never used the AeraComp in a constraint, so it didn't do anything.
The exception was due to a size mismatch in connecting the vector output of the Bsplines comp to a scaler expression. You can do this by specifying the "src_indices", giving it a list of which indices in the array to connect to the target. model.connect('interp.h', 'execcomp.x', src_indices=[0])
I am trying to figure out the meaning of RescaleType = 'LOG_E REL' in a DICOM file. To be more specific, I need to know how to process the raw pixel values to get the image displayed in a proper way. Up to now I have only seen files with RescaleType = 'P-VALUES', which seemed to be correctly processed when applying formula:
pixVal = rescaleIntercept + rescaleSlope * pixRaw.
What would be the rescaling formula to apply when RescaleType = 'LOG_E REL'?
I am not sure if this value is part of the Dicom standard or it is just a specific value for a given manufacturer.
I am telling that because I only have seen these values for the images generated by an old (currently out of service) Agfa ADC compact CR
In the documentation you can read this:
LOG_E REL: pixel values are linearly related to the Log Exposure on
the image plate; the maximum pixel value corresponds to a delta LogE
of 3.2767 above the LogE for the minimum pixel value; in this case, a
VOI module (sequenced item) is present, also containing a lookup
table. Only 12 bit is supported.
I do not know if you should apply a rescaling formula or this is just a note related to some kind of postprocessing algorithm having been applied to the original image.
I assume you should just apply the given VOI LUT instead of trying to apply a rescale equation.
It would help if you could share an example of such dataset. In any way, I believe this is a Type 3 tag in which case, the information is not really required. Just apply the Rescale Slope/Intercept as usual and see what it does.
I have a site that has multiple Project objects. Each project has (for example):
multiple tags
multiple categories
a size
multiple types
etc.
I would like to write a method to grab all 'similar' projects based on the above criteria. I can easily retrieve similar projects for each of the above singularly (i.e. projects of a similar size or projects that share a category etc.) but I would like it to be more intelligent then just choosing projects that either have all the above in common, or projects that have at least one of the above in common.
Ideally, I would like to weight each of the criteria, i.e. a project that has a tag in common is less 'similar' then a project that is close in size etc. A project that has two tags in common is more similar than a project that has one tag in common etc.
What approach (practically and mathimatically) can I take to do this?
The common way to handle this (in machine learning at least) is to create a metric which measures the similarity -- A Jaccard metric seems like a good match here, given that you have types, categories, tags, etc, which are not really numbers.
Once you have a metric, you can speed up searching for similar items by using a KD tree, vp-tree or another metric tree structure, provided your metric obeys the triangle inequality( d(a,b) < d(a,c) + d(c, b) )
The problem is, that there are obviously an infinite number of ways of solving this.
First of all, define a similarity measure for each of your attributes (tag similarity, category similarity, description similarity, ...)
Then try to normalize all these similarities to use a common scale, e.g. 0 to 1, with 0 being most similar, and the values having a similar distribution.
Next, assign each feature a weight. E.g. tag similarity is more important than description similarity.
Finally, compute a combined similarity as weighted sum of the individual similarities.
There is an infinite number of ways, as you can obviously assign arbitrary weights, have various choices for the single-attribute similarities already, infinite number of ways of normalizing the individual values. And so on.
There are methods for learning the weights. See ensemble methods. However, to learn the weights you need to have user input on what is a good result and what not. Do you have such training data?
Start with a value of 100 in each category.
Apply penalties. Like, -1 for each kB difference in size, or -2 for each tag not found in the other project. You end up with a value of 0..100 in each category.
Multiply each category's value with the "weight" of the category (i.e., similarity in size is multiplied with 1, similarity in tags with 3, similarity in types with 2).
Add up the weighted values.
Divide by the sum of weight factors (in my example, 1 + 3 + 2 = 6) to get an overall similarity of 0..100.
Possibilities to reduce the comparing of projects below the initial O(n^2) (i.e. comparing each project with each other) is heavily depending on context. It might be the real crux of your software, or it might not be necessary at all if n is low.
I need to automatically match product names (cameras, laptops, tv-s etc) that come from different sources to a canonical name in the database.
For example "Canon PowerShot a20IS", "NEW powershot A20 IS from Canon" and "Digital Camera Canon PS A20IS"
should all match "Canon PowerShot A20 IS". I've worked with levenshtein distance with some added heuristics (removing obvious common words, assigning higher cost to number changes etc), which works to some extent, but not well enough unfortunately.
The main problem is that even single-letter changes in relevant keywords can make a huge difference, but it's not easy to detect which are the relevant keywords. Consider for example three product names:
Lenovo T400
Lenovo R400
New Lenovo T-400, Core 2 Duo
The first two are ridiculously similar strings by any standard (ok, soundex might help to disinguish the T and R in this case, but the names might as well be 400T and 400R), the first and the third are quite far from each other as strings, but are the same product.
Obviously, the matching algorithm cannot be a 100% precise, my goal is to automatically match around 80% of the names with a high confidence.
Any ideas or references is much appreciated
I think this will boil down to distinguishing key words such as Lenovo from chaff such as New.
I would run some analysis over the database of names to identify key words. You could use code similar to that used to generate a word cloud.
Then I would hand-edit the list to remove anything obviously chaff, like maybe New is actually common but not key.
Then you will have a list of key words that can be used to help identify similarities. You would associate the "raw" name with its keywords, and use those keywords when comparing two or more raw names for similarities (literally, percentage of shared keywords).
Not a perfect solution by any stretch, but I don't think you are expecting one?
The key understanding here is that you do have a proper distance metric. That is in fact not your problem at all. Your problem is in classification.
Let me give you an example. Say you have 20 entries for the Foo X1 and 20 for the Foo Y1. You can safely assume they are two groups. On the other hand, if you have 39 entries for the Bar X1 and 1 for the Bar Y1, you should treat them as a single group.
Now, the distance X1 <-> Y1 is the same in both examples, so why is there a difference in the classification? That is because Bar Y1 is an outlier, whereas Foo Y1 isn't.
The funny part is that you do not actually need to do a whole lot of work to determine these groups up front. You simply do an recursive classification. You start out with node per group, and then add the a supernode for the two closest nodes. In the supernode, store the best assumption, the size of its subtree and the variation in it. As many of your strings will be identical, you'll soon get large subtrees with identical entries. Recursion ends with the supernode containing at the root of the tree.
Now map the canonical names against this tree. You'll quickly see that each will match an entire subtree. Now, use the distances between these trees to pick the distance cutoff for that entry. If you have both Foo X1 and Foo Y1 products in the database, the cut-off distance will need to be lower to reflect that.
edg's answer is in the right direction, I think - you need to distinguish key words from fluff.
Context matters. To take your example, Core 2 Duo is fluff when looking at two instances of a T400, but not when looking at a a CPU OEM package.
If you can mark in your database which parts of the canonical form of a product name are more important and must appear in one form or another to identify a product, you should do that. Maybe through the use of some sort of semantic markup? Can you afford to have a human mark up the database?
You can try to define equivalency classes for things like "T-400", "T400", "T 400" etc. Maybe a set of rules that say "numbers bind more strongly than letters attached to those numbers."
Breaking down into cases based on manufacturer, model number, etc. might be a good approach. I would recommend that you look at techniques for term spotting to try and accomplish that: http://www.worldcat.org/isbn/9780262100854
Designing everything in a flexible framework that's mostly rule driven, where the rules can be modified based on your needs and emerging bad patterns (read: things that break your algorithm) would be a good idea, as well. This way you'd be able to improve the system's performance based on real world data.
You might be able to make use of a trigram search for this. I must admit I've never seen the algorithm to implement an index, but have seen it working in pharmaceutical applications, where it copes very well indeed with badly misspelt drug names. You might be able to apply the same kind of logic to this problem.
This is a problem of record linkage. The dedupe python library provides a complete implementation, but even if you don't use python, the documentation has a good overview of how to approach this problem.
Briefly, within the standard paradigm, this task is broken into three stages
Compare the fields, in this case just the name. You can use one or more comparator for this, for example an edit distance like the Levenshtein distance or something like the cosine distance that compares the number of common words.
Turn an array fo distance scores into a probability that a pair of records are truly about the same thing
Cluster those pairwise probability scores into groups of records that likely all refer to the same thing.
You might want to create logic that ignores the letter/number combination of model numbers (since they're nigh always extremely similar).
Not having any experience with this type of problem, but I think a very naive implementation would be to tokenize the search term, and search for matches that happen to contain any of the tokens.
"Canon PowerShot A20 IS", for example, tokenizes into:
Canon
Powershot
A20
IS
which would match each of the other items you want to show up in the results. Of course, this strategy will likely produce a whole lot of false matches as well.
Another strategy would be to store "keywords" with each item, such as "camera", "canon", "digital camera", and searching based on items that have matching keywords. In addition, if you stored other attributes such as Maker, Brand, etc., you could search on each of these.
Spell checking algorithms come to mind.
Although I could not find a good sample implementation, I believe you can modify a basic spell checking algorithm to comes up with satisfactory results. i.e. working with words as a unit instead of a character.
The bits and pieces left in my memory:
Strip out all common words (a, an, the, new). What is "common" depends on context.
Take the first letter of each word and its length and make that an word key.
When a suspect word comes up, looks for words with the same or similar word key.
It might not solve your problems directly... but you say you were looking for ideas, right?
:-)
That is exactly the problem I'm working on in my spare time. What I came up with is:
based on keywords narrow down the scope of search:
in this case you could have some hierarchy:
type --> company --> model
so that you'd match
"Digital Camera" for a type
"Canon" for company and there you'd be left with much narrower scope to search.
You could work this down even further by introducing product lines etc.
But the main point is, this probably has to be done iteratively.
We can use the Datadecision service for matching products.
It will allow you to automatically match your product data using statistical algorithms. This operation is done after defining a threshold score of confidence.
All data that cannot be automatically matched will have to be manually reviewed through a dedicated user interface.
The online service uses lookup tables to store synonyms as well as your manual matching history. This allows you to improve the data matching automation next time you import new data.
I worked on the exact same thing in the past. What I have done is using an NLP method; TF-IDF Vectorizer to assign weights to each word. For example in your case:
Canon PowerShot a20IS
Canon --> weight = 0.05 (not a very distinguishing word)
PowerShot --> weight = 0.37 (can be distinguishing)
a20IS --> weight = 0.96 (very distinguishing)
This will tell your model which words to care and which words to not. I had quite good matches thanks to TF-IDF.
But note this: a20IS cannot be recognized as a20 IS, you may consider to use some kind of regex to filter such cases.
After that, you can use a numeric calculation like cosine similarity.