I am designing a system for anomaly detection.
There are multiple approaches for building such system. I choose to implement one facet of such system by detection of features shared by the majority of samples. I acknowledge the possible insufficiencies of such method but for my specific use-case: (1) It suffices to know that a new sample contains (or lacks) features shared by the majority of past data to make a quick decision.(2) I'm interested in the insights such method will offer to the data.
So, here is the problem:
Consider a large data set with M data points, where each data point may include any number of {key:value} features. I choose to model a training dataset by grouping all the features observed in the data (the set of all unique keys) and setting it as the model's feature space. I define each sample by setting its values for existing keys and None for values in features it does not include.
Given this training data set I want to determine which features reoccur in the data; and for such reoccurring features, do they mostly share a single value.
My question:
A simple solution would be to count everything - for each of the N features calculate the distribution of values. However as M and N are potentially large, I wonder if there is a more compact way to represent the data or more sophisticated method to make claims about features' frequencies.
Am I reinventing an existing wheel? If there's an online approach for accomplishing such task it would be even better.
If I understand correctly your question,
you need to go over all the data anyway, so why not using hash?
Actually two hash tables:
Inner hash table for the distribution of feature values.
Outer hash table for feature existence.
In this way, the size of the inner hash table will indicate how is the feature common in your data, and the actual values will indicate how they differ one another. Another thing to notice is that you go over your data only once, and the time complexity for every operation (almost) on hash tables (if you allocate enough space from the beginning) is O(1).
Hope it helps
I'm trying to create a datamart for the healthcare application. The facts in the datamart are basically going to be measurements and findings related to heart, and we have 100s of them. Starting from 1000 and can go to as big as 20000 per exam type.
I'm wondering what my design choices for the fact tables are:
Grain: 1 row per patient per exam type.
Some of the choices that I can think of -
1) A big wide fact table with 1000 or more columns.
2) EAV based design - A separate Measure dimension table. This foreign key will go into the fact table and the measure value will be in fact table. So the grain of the fact table will be changed to 1 row per patient per exam type per measurement.
3) Create smaller multiple fact tables per exam type per some other criteria like subgroup. But the end user is going to query across subgroups for that exam type and fact-fact join is not recommended.
4) any other ideas?
Any inputs would be appreciated.
1. A big wide fact table with 1000 or more columns.
One very wide fact table gives end-user maximum flexibility if queries are executed directly in the data warehouse. However some considerations should be taken into account, as you might hit some limits depending on a platform.
SQL Server 2014 limits are as per below:
Bytes per row 8,060. A row-overflow storage might be a solution, however it supports only few column types typically not related to fact nature, i.e. varchar, nvarchar, varbinary, sql_variant. Also not supported in In-Memory OLTP. https://technet.microsoft.com/en-us/library/ms186981(v=sql.105).aspx
Columns per non-wide table 1024. Wide-tables and sparse columns are solution as columns per wide table limit is 30,000. However the same Bytes per row limit applies. https://technet.microsoft.com/en-us/library/cc280604(v=sql.120).aspx
Columns per SELECT/INSERT/UPDATE statement 4,096
Non-clustered indexes per table 999
https://technet.microsoft.com/en-us/library/ms143432(v=sql.120).aspx
2. EAV based design - A separate Measure dimension table. This foreign key will go into the fact table and the measure value will be in fact table. So the grain of the fact table will be changed to 1 row per patient per exam type per measurement.
According to Kimball, EAV design is called Fact Normalization. It may make sense when a number of measurements is extremely lengthy, but sparsely populated for a given fact and no computations are made between facts.
Because facts are normalized therefore:
Extensibility is very easy, i.e. it's easy to add new measurements without the need to amend the data structure.
It's good to extract all measurements for one exam and present measurements as rows on the screen.
It's hard to extract/aggregate/make computation between several measurements (e.g. average HDL to CHOL ration) and present measurements/aggregates/computations as columns, i.e. requires complex WHERE/PIVOTING or multi-joins. SQL makes it difficult to make computations between facts in different rows.
If primary end-user platform is an OLAP cube then Fact Normalization makes sense. The cubes allows to make computation across any dimension.
Data importing could be an issue if data format is in a flat style CSV.
This questions is also discussed here Should I use EAV model?.
3) Create smaller multiple fact tables per exam type per some other criteria like subgroup. But the end user is going to query across subgroups for that exam type and fact-fact join is not recommended.
In some scenarios multiple smaller fact tables perfectly makes sense. One of the reason is if you hit some physical limits set by platform, e.g. Bytes per row.
The facts could be grouped either by subject area, e.g. measurement group/subgroup, or by frequency of usage. Each table could be placed on a separate file group and drive to maximize I/O.
Further, you could duplicate measurements across different fact tables to reduce the need of fact tables join, i.e. put one measurement in a specific measurement subgroup fact table and in frequently used measurement fact table.
However some considerations should be taken into account if there are some specific requirements for data loading. For example, if a record errors out in your ETL to one fact table, you might want to make sure that the corresponding records in the other fact tables are deleted and staged to your error table so you don't end up with any bogus information. This is especially true if end users have their own calculations in the front end tool.
If you use OLAP cubes then multiple fact tables actually becomes a source of a measure group to a specific fact table.
In terms of fact-to-fact join, you (BI application) should never issue SQL that joins two fact tables together across the fact table’s foreign keys. Instead, the technique of Drilling Across two fact tables should be used, where the answer sets from two or more fact tables are separately created, and the results sort-merged on the common row header attribute values to produce the correct result.
More on this topic: http://www.kimballgroup.com/2003/04/the-soul-of-the-data-warehouse-part-two-drilling-across/
4) any other ideas?
SQL XML or some kind NoSQL could be an option, but the same querying / aggregation / computation / presentation issues exist.
I've a bunch of columns in my fact tables that have a very low cardinality (~8). Each of these columns store keys that refer to a master table. I'm wondering whether to import each of these individual master tables as dimension or do I store the values directly in the fact table. Master tables have no additional attributes except the value I'm trying to store. What are the pros and cons of each approach ?
This seems to be a classic example of a junk dimension that combines together a number of miscellaneous, low-cardinality flags and indicators (instead of putting each of them in a separate dimension table).
Disadvantages of other approaches:
Putting every low cardinality attribute in a separate, dedicated dimension could result in an overly complex model with excessive number of dimension tables (centipede fact tables).
Storing the attributes directly in the fact table is allowed but reserved only for degenerate dimensions, i.e. values like order or invoice numbers, retail point-of-sale transaction numbers - high-cardinality values that don't have any additional attributes describing them.
Low-cardinality flags are not DDs, because even though they may consist of a sole key now, they may easily have additional attributes in the future, e.g. multiple descriptive captions for reports - short for mobile users and long for desktop users.
Details: Design Tip #113 Creating, Using, and Maintaining Junk Dimensions
Given an HTML table with none of it's cells identified as "< th >" or "header" cells, I want to automatically detect whether the table is a "Vertical" table or "Horizontal" table.
For example:
This is a Horizontal table:
and this is a vertical table:
of course keep in mind that the "Bold" property along with the shading and any styling properties will not be available at the classification time.
I was thinking of approaching this by a statistical means, I can hand write couple of features like "if the first row has numbers, but the first column doesn't. That's probably a Vertical table" and give score for each feature and combine to decide the Class of the table orientation.
Is that how you approach such a problem? I haven't used any statistical-based algorithm before and I am not sure what would be optimal for such a problem
This is a bit confusing question. You are asking about ML method, but it seems you have not created training/crossvalidation/test sets yet. Without data preprocessing step any discussion about ML method is useless.
If I'm right and you didn't created datasets yet - give us more info on data (if you take a look on one example how do you know the table is vertical or horizontal?, how many data do you have, are you always sure whether s table is vertical/horizontal,...)
If you already created training/crossval/test sets - give us more details how the training set looks like (what are the features, number of examples, do you need white-box solution (you can see why a ML model give you this result),...)
How general is the domain for the tables? I know some Web table schema identification algorithms use types, properties, and instance data from a general knowledge schema such as Freebase to attempt to identify the property associated with a column. You might try leveraging that knowledge in an classifier.
If you want to do this without any external information, you'll need a bunch of hand labelled horizontal and vertical examples.
You say "of course" the font information isn't available, but I wouldn't be so quick to dismiss this since it's potentially a source of very useful information. Are you sure you can't get your data from a little bit further back in the pipeline so that you can get access to this info?
I have just read #PerformanceDBA's arguments re: 6NF and E-A-V. I am intrigued. I had previously been skeptical of 6NF as it was presented as "merely" sticking some timestamp columns on tables.
I have always worked with a data dictionary and do not need to be convinced to use one, or to generate SQL code. So I expect an answer that would require a dictionary (or catalog) that is used to generate code.
So I would like to know how 6NF would deal with an extremely simple example. A table of items, descriptions and prices. The prices change over time.
So anyway, what does the Items table look like when converted to 6NF? What is the "explosion of tables?" that happens here?
If the example does not work with a table this simple, feel free to add what is necessary to get the point across.
I actually started putting an answer together, but I ran into complications, because you (quite understandably) want a simple example. The problem is manifold.
First I don't have a good idea of your level of actual expertise re Relational Databases and 5NF; I don't have a starting point to take up and then discuss the specifics of 6NF,
Second, just like any of the other NFs, it is variegated. You can just barely step into it; you can implement 6NF for certan tables; you can go the full hog on every table, etc. Sure there is an explosion of tables, but then you Normalise that, and kill the explosion; that's an advanced or mature implementation of 6NF. No use providing the full or partial levels of 6NF, when you are asking for the simplest, most straight-forward example.
I trust you understand that some tables can be "in 5NF" while others are "in 6NF".
So I put one together for you. But even that needs explanation.
Now SQL barely supports 5NF, it does not support 6NF at all (I think dportas says the same thing in different words). Now I implement 6NF at a deep level, for performance reasons, simplified pivoting (of entire tables; any and all columns, not the silly PIVOT function in MS), columnar access, etc. For that you need a full catalogue, which is an extension to the SQL catalogue, to support the 6NF that SQL does not support, and maintain data Integrity and business Rules. So, you really do not want to implement 6NF for fun, you only do that if you have a need, because you have to implement a catalogue. (This is what the EAV crowd do not do, and this is why most EAV systems have data integrity problems. Most of them do not use the declarative Referential & Data Integrity that SQL does have.)
But most people who implement 6NF don't implement the deeper level, with a full catalogue. They have simpler needs, and thus implement a shallower level of 6NF. So, let's take that, to provide a simple example for you. Let's start with an ordinary Product table that is declared to be in 5NF (and let's not argue about what 5NF is). The company sells various different kinds of Products, half the columns are mandatory, and the other half are optional, meaning that, depending on the Product Type, certain columns may be Null. While they may have done a good job with the database, the Nulls are now a big problem: columns that should be Not Null for certain ProductTypes are Null, because the declaration states NULL, and their app code is only as good as the next guy's.
So they decide to go with 6NF to fix that problem, because the subtitle of 6NF states that it eliminates The Null Problem. Sixth Normal Form is the irreducible Normal Form, there will be no further NFs after this, because the data cannot be Normalised further. The rows have been Normalised to the utmost degree. The definition of 6NF is:
a table is in 6NF when the row contains the Primary Key, and at most one, attribute.
Notice that by that definition, millions of tables across the planet are already in 6NF, without having had that intent. Eg. typical Reference or Look-up tables, with just a PK and Description.
Right. Well, our friends look at their Product table, which has eight non-key attributes, so if they make the Product table 6NF, they will have eight sub-Product tables. Then there is the issue that some columns are Foreign Keys to other tables, and that leads to more complications. And they note the fact that SQL does not support what they are doing, and they have to build a small catalogue. Eight tables are correct, but not sensible. Their purpose was to get rid of Nulls, not to write a little subsytem around each table.
Simple 6NF Example
Readers who are unfamiliar with the Standard for Modelling Relational Databases may find IDEF1X Notation useful in order to interpret the symbols in the example.
So typically, the Product Table retains all the Mandatory columns, especially the FKs, and each Optional column, each Nullable column, is placed in a separate sub-Product table. That is the simplest form I have seen. Five tables instead of eight. In the Model, the four sub-Product tables are "in 6NF"; the main Product table is "in 5NF".
Now we really do not need every code segment that SELECTs from Product to have to figure out what columns it should construct, based on the ProductType, etc, so we supply a View, which essentially provides the 5NF "view" of the Product table cluster.
The next thing we need is the basic rudiments of an extension to the SQL catalog, so that we can ensure that the rules (data integrity) for the various ProductTypes are maintained in one place, in the database, and not dependent on app code. The simplest catalogue you can get away with. That is driven off ProductType, so ProductType now forms part of that Metadata. You can implement that simple structure without a catalogue, but I would not recommend it.
Update
It is important to note that I implement all Business Rules in the database. Otherwise it is not a database (the notion of implementing rules "in application code" is hilarious in the extreme, especially nowadays, when we have florists working as "developers"). Therefore all rules, etc are first and foremost implemented as SQL declarations, CHECK constraints, functions, etc. That preserves all Declarative Referential Integrity, and declarative Data Integrity. The extension to the SQL catalog covers the area that SQL does not have declarations for, and they are then implemented as SQL. Being a good data dictionary, it does much more. Eg. I do not write Views every time I change the tables or add or change columns or their characteristics, they are created directly from the catalog+extension using a simple code generator.
One more very important note. You cannot implement 6NF (or EAV properly, for that matter), without completing a full and faithful Normalisation exercise, to 5NF. The problem I see at every site is, they don't have a genuine 5NF state, they have a mish-mash of partial normalisation or no normalisation at all, but they are very attached to that. Creating either 6NF or EAV from that is a disaster. Creating EAV or 6NF from that without all business rules implemented in declarative SQL is a nuclear disaster, burning for years. You get what you pay for.
End update.
Finally, yes, there are at least four further levels of Normalisation (Normalisation is a Principle, not a mere reference to a Normal Form), that can be applied to that simple 6NF Product cluster, providing more control, less tables, etc. The deeper we go, the more extensive the catalogue. And higher levels of performance. When you are ready, just ask, I have already erected the models and posted details in other answers.
In a nutshell, 6NF means that every relation consists of a candidate key plus no more than one other (key or non-key) attribute. To take up your example, if an "item" is identified by a ProductCode and the other attributes are Description and Price then a 6NF schema would consist of two relations (* denotes the key in each):
ItemDesc {ProductCode*, Description}
ItemPrice {ProductCode*, Price}
This is potentially a very flexible approach because it minimises the dependencies. That's also its main disadvantage however, especially in a SQL database. SQL makes it hard or impossible to enforce many multi-table constraints. Using the above schema, in most cases it will not be possible to enforce a business rule that every product must always have a description AND a price. Similarly, you may not be able to enforce some compound keys that ought to apply (because their attributes could be split over multiple tables).
So in considering 6NF you have to weigh up which dependencies and integrity rules are important to you. In many cases you may find it more practical and useful to stick to 5NF and normalize no further than that.
I had previously been skeptical of 6NF
as it was presented as "merely"
sticking some timestamp columns on
tables.
I'm not quite sure where this apparent misconception comes from. Perhaps the fact that 6NF was introduced for the book "Temporal Data and The Relational Mode" by Date, Darwen and Lorentzos? Anyhow, I hope the other answers here have clarified that 6NF is not limited to temporal databases.
The point I wanted to make is, although 6NF is "academically respectable" and always achievable, it may not necessarily lead to the optimal design in every case (and not just when considering implementation using SQL either). Even the aforementioned discoverers and proponents of 6NF seem to agree e.g.
Chris Date: "For practical purposes, stick to 5NF (and 6NF)."
Hugh Darwen: "the 6NF decomposition around Date [not the person!] would be overkill... an optimal design for the soccer club is... 5-and-a-bit-NF!"
Hugh Darwen: "we are in 5NF but not in 6NF, and again 5NF is sufficient" (several similar examples).
Then again, I can also find evidence to the contrary:
Chris Date: "Darwen and I have both felt for some time that all base relvars should be in 6NF".
On a practical note, I recently extended the SQL schema of one of our products to add a minor feature. I adopted a 6NF to avoid nullable columns and ended up with six new tables where most (all?) of my colleagues would have used one table (or perhaps extended an existing table) with nullable columns. Despite me proving several 'helper' stored procs and a 'denormalized' VIEW with a INSTEAD OF triggers, every coder that has had to work with this feature at the SQL level has gone out of their way to curse me :)
These guys have it down: Anchor Modeling. Great academic papers on the subject, combined with practical examples. Their writings have finally pushed me over the edge to consider building a DW in 6nf on an upcoming project. The POC work I have done has validated (for me, at least) that the enormous benefits of 6nf don't outweigh the costs.