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I have no idea if I wrote that correctly. I want to start learning higher end data mining techniques and I'm currently using SQL server and Access 2016.
I have a system that tracks ID cards. Each ID is tagged to one particular level of a security hierarchy, which has many branches.
For example
Root
-Maintenance
- Management
- Supervisory
- Manager
- Executive
- Vendors
- Secure
- Per Diem
- Inside Trades
There are many other departments like Maintenance, some simple, some with much more convoluted, hierarchies.
Each ID card is tagged to a level so in the Maintenance example, - Per Diem:Vendors:Maintenance:Root. Others may be just tagged to Vendors, Some to general Maintenance itself (No one has root, thank god).
So lets say I have 20 ID Cards selected, these are available personnel I can task to a job but since they have different area's of security I want to find a commonalities they can all work on together as a 20 person group or whatever other groupings I can make.
So the intended output would be
CommonMatch = - Per Diem
CardID = 1
CardID = 3
CommonMatch = Vendors
CardID = 1
CardID = 3
CardID = 20
So in the example above, while I could have 2 people working on -Per Diem work, because that is their lowest common security similarity, there is also card holder #20 who has rights to the predecessor group (Vendors), that 1 and 3 share, so I could have three of them work at that level.
I'm not looking for anyone to do the work for me (Although examples always welcome), more to point me in the right direction on what I should be studying, what I'm trying to do is called, etc. I know CTE's are a way to go but that seems like only a tool in a much bigger process that needs to be done.
Thank you all in advance
Well, it is not so much a graph-theory or data-mining problem but rather a data-structure problem and one that has almost solved itself.
The objective is to be able to partition the set of card IDs into disjoint subsets given a security clearance level.
So, the main idea here would be to layout the hierarchy tree and then assign each card ID to the path implied by its security level clearance. For this purpose, each node of the hierarchy tree now becomes a container of card IDs (e.g. each node of the hierarchy tree holds a) its own name (as unique identification) b) pointers to other nodes c) a list of card IDs assigned to its "name".)
Then, retrieving the set of cards with clearance UP TO a specific security level is simply a case of traversing the tree from that specific level downwards until the tree's leafs, all along collecting the card IDs from the node containers as they are encountered.
Suppose that we have access tree:
A
+-B
+-C
D
+-E
And card ID assignments:
B:[1,2,3]
C:[4,8]
E:[10,12]
At the moment, B,C,E only make sense as tags, there is no structural information associated with them. We therefore need to first "build" the tree. The following example uses Networkx but the same thing can be achieved with a multitude of ways:
import networkx
G = networkx.DiGraph() #Establish a directed graph
G.add_edge("A","B")
G.add_edge("A","C")
G.add_edge("A","D")
G.add_edge("D","E")
Now, assign the card IDs to the node containers (in Networkx, nodes can be any valid Python object so I am going to go with a very simple list)
G.node["B"]=[1,2,3]
G.node["C"]=[4,8]
G.node["E"]=[10,12]
So, now, to get everybody working under "A" (the root of the tree), you can traverse the tree from that level downwards either via Depth First Search (DFS) or Breadth First Search (BFS) and collect the card IDs from the containers. I am going to use DFS here, purely because Networkx has a function that returns the visited nodes depending on visiting order, directly.
#dfs_preorder_nodes returns a generator, this is an efficient way of iterating very large collections in Python but I am casting it to a "list" here, so that we get the actual list of nodes back.
vis_nodes = list(networkx.dfs_preorder_nodes(G,"A")); #Start from node "A" and DFS downwards
cardIDs = []
#I could do the following with a one-line reduce but it might be clearer this way
for aNodeID in vis_nodes:
if G.node[aNodeID]:
cardIDs.extend(G.node[aNodeID])
In the end of the above iteration, cardIDs will contain all card IDs from branch "A" downwards in one convenient list.
Of course, this example is ultra simple, but since we are talking about trees, the tree can be as large as you like and you are still traversing it in the same way requiring only a single point of entry (the top level branch).
Finally, just as a note, the fact that you are using Access as your backend is not necessarily an impediment but relational databases do not handle graph type data with great ease. You might get away easily for something like a simple tree (like what you have here for example), but the hassle of supporting this probably justifies undertaking this process outside of the database (e.g, use the database just for retrieving the data and carry out the graph type data processing in a different environment. Doing a DFS on SQL is the sort of hassle I am referring to above.)
Hope this helps.
I have products with different details in different attributes and I need to develop an algorithm to find the most similar to the one I'm trying to find.
For example, if a product has:
Weight: 100lb
Color: Black, Brown, White
Height: 10in
Conditions: new
Others can have different colors, weight, etc. Then I need to do a search where the most similar return first. For example, if everything matches but the color is only Black and White but not Brown, it's a better match than another product that is only Black but not White or Brown.
I'm open to suggestions as the project is just starting.
One approach, for example, I could do is restrict each attribute (weight, color, size) a limited set of option, so I can build a binary representation. So I have something like this for each product:
Colors Weight Height Condition
00011011000 10110110 10001100 01
Then if I do an XOR between the product's binary representation and my search, I can calculate the number of set bits to see how similar they are (all zeros would mean exact match).
The problem with this approach is that I cannot index that on a database, so I would need to read all the products to make the comparison.
Any suggestions on how I can approach this? Ideally I would like to have something I can index on a database so it's fast to query.
Further question: also if I could use different weights for each attribute, it would be awesome.
You basically need to come up with a distance metric to define the distance between two objects. Calculate the distance from the object in question to each other object, then you can either sort by minimum distance or just select the best.
Without some highly specialized algorithm based on the full data set, the best you can do is a linear time distance comparison with every other item.
You can estimate the nearest by keeping sorted lists of certain fields such as Height and Weight and cap the distance at a threshold (like in broad phase collision detection), then limit full distance comparisons to only those items that meet the thresholds.
What you want to do is a perfect use case for elasticsearch and other similar search oriented databases. I don't think you need to hack with bitmasks/etc.
You would typically maintain your primary data in your existing database (sql/cassandra/mongo/etc..anything works), and copy things that need searching to elasticsearch.
What are you talking about very similar to BK-trees. BK-tree constructs search tree with some metric associated with keys of this tree. Most common use of this tree is string corrections with Levenshtein or Damerau-Levenshtein distances. This is not static data structure, so it supports future insertions of elements.
When you search exact element (or insert element), you need to look through nodes of this tree and go to links with weight equal to distance between key of this node and your element. if you want to find similar objects, you need to go to several nodes simultaneously that supports your wishes of constrains of distances. (Maybe it can be even done with A* to fast finding one most similar object).
Simple example of BK-tree (from the second link)
BOOK
/ \
/(1) \(4)
/ \
BOOKS CAKE
/ / \
/(2) /(1) \(2)
/ | |
BOO CAPE CART
Your metric should be Hamming distance (count of differences between bit representations of two objects).
BUT! is it good to compare two integers as count of different bits in their representation? With Hamming distance HD(10000, 00000) == HD(10000, 10001). I.e. difference between numbers 16 and 0, and 16 and 17 is equal. Is it really what you need?
BK-tree with details:
https://hamberg.no/erlend/posts/2012-01-17-BK-trees.html
https://nullwords.wordpress.com/2013/03/13/the-bk-tree-a-data-structure-for-spell-checking/
What's an efficient way to find all nodes within N hops of a given node? My particular graph isn't highly connected, i.e. most nodes have only degree 2, so for example the following query returns only 27 nodes (as expected), but it takes about a minute of runtime and the CPU is pegged:
MATCH (a {id:"36380_A"})-[*1..20]-(b) RETURN a,b;
All the engine's time is spent in traversals, because if I just find that starting node by itself, the result returns instantly.
I really only want the set of unique nodes and relationships (for visualization), so I also tried adding DISTINCT to try to stop it from re-visiting nodes it's seen before, but I see no change in run time.
As you said, matching the start node alone is really fast and faster if your property is indexed.
However what you are trying to do now is matching the whole pattern in the graph.
Keep your idea of your fast starting point:
MATCH (a:Label {id:"1234-a"})
once you got it pass it to the rest of the query with WITH
WITH a
then match the relationships from your fast starting point :
MATCH (a)-[:Rel*1..20]->(b)
Question after BIG edition :
I need to built a ranking using genetic algorithm, I have data like this :
P(a>b)=0.9
P(b>c)=0.7
P(c>d)=0.8
P(b>d)=0.3
now, lets interpret a,b,c,d as names of football teams, and P(x>y) is probability that x wins with y. We want to build ranking of teams, we lack some observations P(a>d),P(a>c) are missing due to lack of matches between a vs d and a vs c.
Goal is to find ordering of team names, which the best describes current situation in that four team league.
If we have only 4 teams than solution is straightforward, first we compute probabilities for all 4!=24 orderings of four teams, while ignoring missing values we have :
P(abcd)=P(a>b)P(b>c)P(c>d)P(b>d)
P(abdc)=P(a>b)P(b>c)(1-P(c>d))P(b>d)
...
P(dcba)=(1-P(a>b))(1-P(b>c))(1-P(c>d))(1-P(b>d))
and we choose the ranking with highest probability. I don't want to use any other fitness function.
My question :
As numbers of permutations of n elements is n! calculation of probabilities for all
orderings is impossible for large n (my n is about 40). I want to use genetic algorithm for that problem.
Mutation operator is simple switching of places of two (or more) elements of ranking.
But how to make crossover of two orderings ?
Could P(abcd) be interpreted as cost function of path 'abcd' in assymetric TSP problem but cost of travelling from x to y is different than cost of travelling from y to x, P(x>y)=1-P(y<x) ? There are so many crossover operators for TSP problem, but I think I have to design my own crossover operator, because my problem is slightly different from TSP. Do you have any ideas for solution or frame for conceptual analysis ?
The easiest way, on conceptual and implementation level, is to use crossover operator which make exchange of suborderings between two solutions :
CrossOver(ABcD,AcDB) = AcBD
for random subset of elements (in this case 'a,b,d' in capital letters) we copy and paste first subordering - sequence of elements 'a,b,d' to second ordering.
Edition : asymetric TSP could be turned into symmetric TSP, but with forbidden suborderings, which make GA approach unsuitable.
It's definitely an interesting problem, and it seems most of the answers and comments have focused on the semantic aspects of the problem (i.e., the meaning of the fitness function, etc.).
I'll chip in some information about the syntactic elements -- how do you do crossover and/or mutation in ways that make sense. Obviously, as you noted with the parallel to the TSP, you have a permutation problem. So if you want to use a GA, the natural representation of candidate solutions is simply an ordered list of your points, careful to avoid repitition -- that is, a permutation.
TSP is one such permutation problem, and there are a number of crossover operators (e.g., Edge Assembly Crossover) that you can take from TSP algorithms and use directly. However, I think you'll have problems with that approach. Basically, the problem is this: in TSP, the important quality of solutions is adjacency. That is, abcd has the same fitness as cdab, because it's the same tour, just starting and ending at a different city. In your example, absolute position is much more important that this notion of relative position. abcd means in a sense that a is the best point -- it's important that it came first in the list.
The key thing you have to do to get an effective crossover operator is to account for what the properties are in the parents that make them good, and try to extract and combine exactly those properties. Nick Radcliffe called this "respectful recombination" (note that paper is quite old, and the theory is now understood a bit differently, but the principle is sound). Taking a TSP-designed operator and applying it to your problem will end up producing offspring that try to conserve irrelevant information from the parents.
You ideally need an operator that attempts to preserve absolute position in the string. The best one I know of offhand is known as Cycle Crossover (CX). I'm missing a good reference off the top of my head, but I can point you to some code where I implemented it as part of my graduate work. The basic idea of CX is fairly complicated to describe, and much easier to see in action. Take the following two points:
abcdefgh
cfhgedba
Pick a starting point in parent 1 at random. For simplicity, I'll just start at position 0 with the "a".
Now drop straight down into parent 2, and observe the value there (in this case, "c").
Now search for "c" in parent 1. We find it at position 2.
Now drop straight down again, and observe the "h" in parent 2, position 2.
Again, search for this "h" in parent 1, found at position 7.
Drop straight down and observe the "a" in parent 2.
At this point note that if we search for "a" in parent one, we reach a position where we've already been. Continuing past that will just cycle. In fact, we call the sequence of positions we visited (0, 2, 7) a "cycle". Note that we can simply exchange the values at these positions between the parents as a group and both parents will retain the permutation property, because we have the same three values at each position in the cycle for both parents, just in different orders.
Make the swap of the positions included in the cycle.
Note that this is only one cycle. You then repeat this process starting from a new (unvisited) position each time until all positions have been included in a cycle. After the one iteration described in the above steps, you get the following strings (where an "X" denotes a position in the cycle where the values were swapped between the parents.
cbhdefga
afcgedbh
X X X
Just keep finding and swapping cycles until you're done.
The code I linked from my github account is going to be tightly bound to my own metaheuristics framework, but I think it's a reasonably easy task to pull the basic algorithm out from the code and adapt it for your own system.
Note that you can potentially gain quite a lot from doing something more customized to your particular domain. I think something like CX will make a better black box algorithm than something based on a TSP operator, but black boxes are usually a last resort. Other people's suggestions might lead you to a better overall algorithm.
I've worked on a somewhat similar ranking problem and followed a technique similar to what I describe below. Does this work for you:
Assume the unknown value of an object diverges from your estimate via some distribution, say, the normal distribution. Interpret your ranking statements such as a > b, 0.9 as the statement "The value a lies at the 90% percentile of the distribution centered on b".
For every statement:
def realArrival = calculate a's location on a distribution centered on b
def arrivalGap = | realArrival - expectedArrival |
def fitness = Σ arrivalGap
Fitness function is MIN(fitness)
FWIW, my problem was actually a bin-packing problem, where the equivalent of your "rank" statements were user-provided rankings (1, 2, 3, etc.). So not quite TSP, but NP-Hard. OTOH, bin-packing has a pseudo-polynomial solution proportional to accepted error, which is what I eventually used. I'm not quite sure that would work with your probabilistic ranking statements.
What an interesting problem! If I understand it, what you're really asking is:
"Given a weighted, directed graph, with each edge-weight in the graph representing the probability that the arc is drawn in the correct direction, return the complete sequence of nodes with maximum probability of being a topological sort of the graph."
So if your graph has N edges, there are 2^N graphs of varying likelihood, with some orderings appearing in more than one graph.
I don't know if this will help (very brief Google searches did not enlighten me, but maybe you'll have more success with more perseverance) but my thoughts are that looking for "topological sort" in conjunction with any of "probabilistic", "random", "noise," or "error" (because the edge weights can be considered as a reliability factor) might be helpful.
I strongly question your assertion, in your example, that P(a>c) is not needed, though. You know your application space best, but it seems to me that specifying P(a>c) = 0.99 will give a different fitness for f(abc) than specifying P(a>c) = 0.01.
You might want to throw in "Bayesian" as well, since you might be able to start to infer values for (in your example) P(a>c) given your conditions and hypothetical solutions. The problem is, "topological sort" and "bayesian" is going to give you a whole bunch of hits related to markov chains and markov decision problems, which may or may not be helpful.
I have a number of large sorted sets (5m-25m) in Redis and I want to get the first element that appears in a combination of those sets.
e.g I have 20 sets and wanted to take set 1, 5, 7 and 12 and get only the first intersection of only those sets.
It would seem that a ZINTERSTORE followed by a "ZRANGE foo 0 0" would be doing a lot more work that I require as it would calculate all the intersections then return the first one. Is there an alternative solution that does not need to calculate all the intersections?
There is no direct, native alternative, although I'd suggest this:
Create a hash which its members are your elements. Upon each addition to one of your sorted sets, increment the relevant member (using HINCRBY). Of course, you'll make the increment only after you check that the element does not exist already in the sorted set you are attempting to add to.
That way, you can quickly know which elements appear in 4 sets.
UPDATE: Now that I rethink about it, it might be too expensive to query your hash to find items with value of 4 (O(n)). Another option would be creating another Sorted Set, which its members are your elements, and their score gets incremented (as I described before, but using ZINCRBY), and you can quickly pull all elements with score 4 (using ZRANGEBYSCORE).