I have been learning the book "Computer Algebra and Materials Physics" during this period of time.
In the chapter 9 titled by "Final Remarks", the author wrote the following:
In my article, I have omitted several important application of the
group theory and the algebra. One of this is the treatment of magnetic
or color groups. Also I omitted the treatment of Lie algebra,
important in the spin system or the study of angular momentum. As for
the former, a package of color groups is implemented in GAP (The Gap
Group 2017).
Since there is no example, I am still confused about the magnetic space group creating in GAP. It's well known that there are 1651 types of
magnetic space groups in total, as shown below:
I'm not sure if all these groups can be created and manipulated in GAP currently. Any tips or examples
will be appreciated.
Regards,
HZ
Related
I am creating a machine learning model that essentially returns the correctness of one text to another.
For example; “the cat and a dog”, “a dog and the cat”. The model needs to be able to identify that some words (“cat”/“dog”) are more important/significant than others (“a”/“the”). I am not interested in conjunction words etc. I would like to be able to tell the model which words are the most “significant” and have it determine how correct text 1 is to text 2, with the “significant” words bearing more weight than others.
It also needs to be able to recognise that phrases don’t necessarily have to be in the same order. The two above sentences should be an extremely high match.
What is the basic algorithm I should use to go about this? Is there an alternative to just creating a dataset with thousands of example texts and a score of correctness?
I am only after a broad overview/flowchart/process/algorithm.
I think TF-IDF might be a good fit to your problem, because:
Emphasis on words occurring in many documents (say, 90% of your sentences/documents contain the conjuction word 'and') is much smaller, essentially giving more weight to the more document specific phrasing (this is the IDF part).
Ordering in Term Frequency (TF) does not matter, as opposed to methods using sliding windows etc.
It is very lightweight when compared to representation oriented methods like the one mentioned above.
Big drawback: Your data, depending on the size of corpus, may have too many dimensions (the same number of dimensions as unique words), you could use stemming/lemmatization in order to mitigate this problem to some degree.
You may calculate similiarity between two TF-IDF vector using cosine similiarity for example.
EDIT: Woops, this question is 8 months old, sorry for the bump, maybe it will be of use to someone else though.
May I know how to evaluate the semantic search (ontology search) and do the ranking for the retrieved document ?
since semantic search can retrieve the similar meaning of the document even if the document does not have the keyword of the query. it means that I cannot use TFIDF to compare the query and documents and do the ranking. as the precision and recall will not be accurate.
How to evaluate the ontology based semantic search and do the document ranking?
You should use data sets that are used as gold standards.
Relevance is assessed relative to an , not a query. For example, an information need might be:
Information on whether drinking red wine is more effective at reducing your risk of heart attacks than white wine.
This might be translated into a query such as:
wine and red and white and heart and attack and effective
A document is relevant if it addresses the stated information need, not because it just happens to contain all the words in the query.
Here is a list of the most standard test collections and evaluation series.
The Cranfield collection. This was the pioneering test collection in allowing precise quantitative measures of information retrieval effectiveness, but is nowadays too small for anything but the most elementary pilot experiments. Collected in the United Kingdom starting in the late 1950s, it contains 1398 abstracts of aerodynamics journal articles, a set of 225 queries, and exhaustive relevance judgments of all (query, document) pairs.
Text Retrieval Conference (TREC) . The U.S. National Institute of Standards and Technology (NIST) has run a large IR test bed evaluation series since 1992. Within this framework, there have been many tracks over a range of different test collections, but the best known test collections are the ones used for the TREC Ad Hoc track during the first 8 TREC evaluations between 1992 and 1999. In total, these test collections comprise 6 CDs containing 1.89 million documents (mainly, but not exclusively, newswire articles) and relevance judgments for 450 information needs, which are called topics and specified in detailed text passages. Individual test collections are defined over different subsets of this data. The early TRECs each consisted of 50 information needs, evaluated over different but overlapping sets of documents. TRECs 6-8 provide 150 information needs over about 528,000 newswire and Foreign Broadcast Information Service articles. This is probably the best subcollection to use in future work, because it is the largest and the topics are more consistent. Because the test document collections are so large, there are no exhaustive relevance judgments. Rather, NIST assessors' relevance judgments are available only for the documents that were among the top $k$ returned for some system which was entered in the TREC evaluation for which the information need was developed.
In more recent years, NIST has done evaluations on larger document collections, including the 25 million page GOV2 web page collection. From the beginning, the NIST test document collections were orders of magnitude larger than anything available to researchers previously and GOV2 is now the largest Web collection easily available for research purposes. Nevertheless, the size of GOV2 is still more than 2 orders of magnitude smaller than the current size of the document collections indexed by the large web search companies.
NII Test Collections for IR Systems ( NTCIR ). The NTCIR project has built various test collections of similar sizes to the TREC collections, focusing on East Asian language and cross-language information retrieval , where queries are made in one language over a document collection containing documents in one or more other languages. See: http://research.nii.ac.jp/ntcir/data/data-en.html
Cross Language Evaluation Forum ( CLEF ). This evaluation series has concentrated on European languages and cross-language information retrieval. See: http://www.clef-campaign.org/
and Reuters-RCV1. For text classification, the most used test collection has been the Reuters-21578 collection of 21578 newswire articles; see Chapter 13 , page 13.6 . More recently, Reuters released the much larger Reuters Corpus Volume 1 (RCV1), consisting of 806,791 documents; see Chapter 4 , page 4.2 . Its scale and rich annotation makes it a better basis for future research.
20 Newsgroups . This is another widely used text classification collection, collected by Ken Lang. It consists of 1000 articles from each of 20 Usenet newsgroups (the newsgroup name being regarded as the category). After the removal of duplicate articles, as it is usually used, it contains 18941 articles.
and thanks for reading my thread.
I have read some of the previous posts on formatting/normalising input data for a Neural Network, but cannot find something that addresses my queries specifically. I apologise for the long post.
I am attempting to build a radial basis function network for analysing horse racing data. I realise that this has been done before, but the data that I have is "special" and I have a keen interest in racing/sportsbetting/programming so would like to give it a shot!
Whilst I think I understand the principles for the RBFN itself, I am having some trouble understanding the normalisation/formatting/scaling of the input data so that it is presented in a "sensible manner" for the network, and I am not sure how I should formulate the output target values.
For example, in my data I look at the "Class change", which compares the class of race that the horse is running in now compared to the race before, and can have a value between -5 and +5. I expect that I need to rescale these to between -1 and +1 (right?!), but I have noticed that many more runners have a class change of 1, 0 or -1 than any other value, so I am worried about "over-representation". It is not possible to gather more data for the higher/lower class changes because thats just 'the way the data comes'. Would it be best to use the data as-is after scaling, or should I trim extreme values, or something else?
Similarly, there are "continuous" inputs - like the "Days Since Last Run". It can have a value between 1 and about 1000, but values in the range of 10-40 vastly dominate. I was going to scale these values to be between 0 and 1, but even if I trim the most extreme values before scaling, I am still going to have a huge representation of a certain range - is this going to cause me an issue? How are problems like this usually dealt with?
Finally, I am having trouble understanding how to present the "target" values for training to the network. My existing results data has the "win/lose" (0 or 1?) and the odds at which the runner won or lost. If I just use the "win/lose", it treats all wins and loses the same when really they're not - I would be quite happy with a network that ignored all the small winners but was highly profitable from picking 10-1 shots. Similarly, a network could be forgiven for "losing" on a 20-1 shot but losing a bet at 2/5 would be a bad loss. I considered making the results (+1 * odds) for a winner and (-1 / odds) for a loser to capture the issue above, but this will mean that my results are not a continuous function as there will be a "discontinuity" between short price winners and short price losers.
Should I have two outputs to cover this - one for bet/no bet, and another for "stake"?
I am sorry for the flood of questions and the long post, but this would really help me set off on the right track.
Thank you for any help anyone can offer me!
Kind regards,
Paul
The documentation that came with your RBFN is a good starting point to answer some of these questions.
Trimming data aka "clamping" or "winsorizing" is something I use for similar data. For example "days since last run" for a horse could be anything from just one day to several years but tends to centre in the region of 20 to 30 days. Some experts use a figure of say 63 days to indicate a "spell" so you could have an indicator variable like "> 63 =1 else 0" for example. One clue is to look at outliers say the upper or lower 5% of any variable and clamp these.
If you use odds/dividends anywhere make sure you use the probabilities ie 1/(odds+1) and a useful idea is to normalize these to 100%.
The odds or parimutual prices tend to swamp other predictors so one technique is to develop separate models, one for the market variables (the market model) and another for the non-market variables (often called the "fundamental" model).
I am optimizing algorithmic strategies. In the process of choosing from a pool of many optimized strategies, I am in the phase of searching (evaluating) for robustness of the strategy.
Following the guidelines of Dr. Pardo's book "The Evaluation of Trading Strategies" in page 231 Dr. Pardo recomends, in the Numeral 3 to apply the following ratio to the optimized data:
" 3. The ratio of the total profit of all profitable simulations divided by the
total profit of all simulationsis significantly positive"
The Question: from the optimization results, I am not being able to properly understand what does Mr. Pardo means by stating "...all simulationsis significantly positive"; what does Mr. Pardo means by 'significantly positive?
a.) with 95% confidence level?
b.) with a certain p value?
c.) the relation of the average net profit of each simulation minus it' standard deviation
Even though the sentence might seem 'simple' I would REALLY like to understand what Mr. Pardo means by the statement and HOW to calculate it, in order to filter the most robust algorithmic strategies.
The aim of analyzing the optimization profile of an algorithmic simulation is to be able to filter robust strategies.
Therefore the ratio should help us to uncover if the simulation results are on the right track or not.
So, we would like to impose some 'penalties' to our results, so we can select the robust cases from those of doubtful (not robust) result.
I came to the following penalizing measures (found in the book of Mr. Pardo and other sources).
a.) we can use a market return (yearly value) as a benchmark, so all the simulations whose result are below such level, can be excluded from our analysis,
b.) some other benchmark to divide those 'robust' results from those more 'doubtful' (for example, deducing to each result one standard deviation)
From (a) and (b), we can create the ratio:
the total sum of all profitable simulations divided by the profitable results considered robust
The ratio should be greater or equal than 1.
If the ratio is equal to 1 then it means that our simulation result has given interesting results (we are analyzing the positive values in this ratio, but profitable results should always be compared to the negative results also).
If the ratio is greater from 1, then we have not reach the possible scenario, and the result should be compared with the other tests for optimizations.
While simulating trading algorithms, no result is absolute but partial and it's value is taken in relationship to what we expect from the algorithm.
If someone has a better explanation or idea or concept you might find interesting please share, I would gladly read it.
Best regards to all.
Remark on the subject
With all due respect to the subject ( published in 2008 ) the term robustness has its own meaning if-and-only-if the statement also clarifies in which particular respect is the robustness measured and against what phenomena is it to be exposed & tested the Model-under-review's response ( against what perturbances -- type and scale -- shall the Model-under-test hold its robust behaviour, measures of which were both defined and quantified a-priori the test ).
In any case, where such context of the robustness is not defined, the material, be it printed by any bold name, sounds -- and forgive me to speak in plain English -- just like a PR-story, an over-hyped e-zine headline or like a paid advertorial.
Serious quantitative model evaluations, the more if one strives to perform an optimisation ( with respect to some defined quantitative goal ), requires a more thorough insight into the subject than to axiomatically post a trivial "must-have" imperative of
large-average && small-HiLo-range && small StDev.
Any serious Quant-Modelling effort, if it were not to just spoil the consumed hundreds-of-thousands CPU core hours of deep parametric-spaces' scans, shall incorporate a serious parametrisation decision in either dimension of the main TruTrading Strategy sub-spaces --
{ aSelectPOLICY, aDetectPOLICY, anActPOLICY, anAllocatePOLICY, aTerminatePOLICY }
A failure to do so, either cripples the model or leads to a blind-belief, where it is hard to guess, whether the former or the latter is a greater of the both Quant-sins.
Remark on the cited hypothesis
The book states, without any effort to proof the construction, that:
The more robust trading strategywill have an optimization profile with a: 1. Largeaverageprofit 2. Small maximum-minimumrange3. Small standarddeviation
Is it correct?
Now kindly spend a few moments and review this 4D-animated view of a Model-under-test ( visualisation of which is reduced into just four dimensions for easier visual perception ), where none of the above stands true.
<aMouseRightCLICK>.openPictureOnAnotherTab to see full HiRes picture details
Based on contemporary state-of-art adaptive money-management practice, that fails to be correct, be it due to a poor parametrisation ( thus artificially leading the model into a rather "flat-profits" sub-space of aParamSetVectorSPACE )
or due to a principal mis-concept or a poor practice ( including the lack thereof ) of the implementation of the most powerful profit-booster ever -- the very money-management model sub-space.
Item 1 becomes insignificant at all.
Item 2 works right on the contrary to the stated postulate.
Item 3 cannot yield anything but the opposite due to 1 & 2 above.
Im trying to analyse data from cycle accidents in the UK to find statistical black spots. Here is the example of the data from another website. http://www.cycleinjury.co.uk/map
I am currently using SQLite to ~100k store lat / lon locations. I want to group nearby locations together. This task is called cluster analysis.
I would like simplify the dataset by ignoring isolated incidents and instead only showing the origin of clusters where more than one accident have taken place in a small area.
There are 3 problems I need to overcome.
Performance - How do I ensure finding nearby points is quick. Should I use SQLite's implementation of an R-Tree for example?
Chains - How do I avoid picking up chains of nearby points?
Density - How to take cycle population density into account? There is a far greater population density of cyclist in london then say Bristol, therefore there appears to be a greater number of backstops in London.
I would like to avoid 'chain' scenarios like this:
Instead I would like to find clusters:
London screenshot (I hand drew some clusters)...
Bristol screenshot - Much lower density - the same program ran over this area might not find any blackspots if relative density was not taken into account.
Any pointers would be great!
Well, your problem description reads exactly like the DBSCAN clustering algorithm (Wikipedia). It avoids chain effects in the sense that it requires them to be at least minPts objects.
As for the differences in densities across, that is what OPTICS (Wikipedia) is supposed do solve. You may need to use a different way of extracting clusters though.
Well, ok, maybe not 100% - you maybe want to have single hotspots, not areas that are "density connected". When thinking of an OPTICS plot, I figure you are only interested in small but deep valleys, not in large valleys. You could probably use the OPTICS plot an scan for local minima of "at least 10 accidents".
Update: Thanks for the pointer to the data set. It's really interesting. So I did not filter it down to cyclists, but right now I'm using all 1.2 million records with coordinates. I've fed them into ELKI for analysis, because it's really fast, and it actually can use the geodetic distance (i.e. on latitude and longitude) instead of Euclidean distance, to avoid bias. I've enabled the R*-tree index with STR bulk loading, because that is supposed to help to get the runtime down a lot. I'm running OPTICS with Xi=.1, epsilon=1 (km) and minPts=100 (looking for large clusters only). Runtime was around 11 Minutes, not too bad. The OPTICS plot of course would be 1.2 million pixels wide, so it's not really good for full visualization anymore. Given the huge threshold, it identified 18 clusters with 100-200 instances each. I'll try to visualize these clusters next. But definitely try a lower minPts for your experiments.
So here are the major clusters found:
51.690713 -0.045545 a crossing on A10 north of London just past M25
51.477804 -0.404462 "Waggoners Roundabout"
51.690713 -0.045545 "Halton Cross Roundabout" or the crossing south of it
51.436707 -0.499702 Fork of A30 and A308 Staines By-Pass
53.556186 -2.489059 M61 exit to A58, North-West of Manchester
55.170139 -1.532917 A189, North Seaton Roundabout
55.067229 -1.577334 A189 and A19, just south of this, a four lane roundabout.
51.570594 -0.096159 Manour House, Picadilly Line
53.477601 -1.152863 M18 and A1(M)
53.091369 -0.789684 A1, A17 and A46, a complex construct with roundabouts on both sides of A1.
52.949281 -0.97896 A52 and A46
50.659544 -1.15251 Isle of Wight, Sandown.
...
Note, these are just random points taken from the clusters. It may be sensible to compute e.g. cluster center and radius instead, but I didn't do that. I just wanted to get a glimpse of that data set, and it looks interesting.
Here are some screenshots, with minPts=50, epsilon=0.1, xi=0.02:
Notice that with OPTICS, clusters can be hierarchical. Here is a detail:
First, your example is quite misleading. You have two different sets of data, and you don't control the data. If it appears in a chain, then you will get a chain out.
This problem is not exactly suitable for a database. You'll have to write code or find a package that implements this algorithm on your platform.
There are many different clustering algorithms. One, k-means, is an iterative algorithm where you look for a fixed number of clusters. k-means requires a few complete scans of the data, and voila, you have your clusters. Indexes are not particularly helpful.
Another, which is usually appropriate on slightly smaller data sets, is hierarchical clustering -- you put the two closest things together, and then build the clusters. An index might be helpful here.
I recommend though that you peruse a site such as kdnuggets in order to see what software -- free and otherwise -- is available.