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September 17, 2011
Likeness Matrix
Okay, so I'm building a collaborative filtering system. This means that I am trying to take 1 person and be able to say to them, "here are some good choices for you. I found these by looking at other people in the system who are similar to you and picking some of the things that they liked."
However, in order for a computer to do this, you need a find a way to get the "who are similar to you" part.
This is called a likeness matrix. It is a set of numbers telling you how much "alike" each person is to every other person. So you create an N by N chart where N is the number of people. You X out the diagonal because it isn't useful to say how much a person is like themselves.
For example, we have suppose we have Anna, Bruce, Christy, and Derek. The likeness matrix might look something like the image, below. Anna and Bruce have a lot in common so they are 9. Anna and Christy have quite a lot in common, also, so they are an 8. Anna and Derek are nothing alike so they are 1. And so on.

Image created with LucidChart.com.
Computationally, you only need one half of the diagonal because they are mirrored. What would be a better data structure than a matrix? Maybe a database? A whole bunch of triples. (persona_id, personb_id, likeness_value).
Yeah, I think I'm going to use a database. Thanks for talking this through with me!
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Posted by Frozone Permalink on September 17, 2011 12:21 PM
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Depending on your use, a hashtable of hashtables would be quick and you could use all in memory objects if your use case didn't demand a DB.
Space wise it's a killer, but if that's not the concern and just something simple is needed I use this method all of the time for data processing.
If you don't want to see the relationship between Christy and Derek (two hashtable lookups) but want to see the top three people like Christy you could use a hashtable of ordered lists (one hashtable lookup and one list slice). Much faster than a DB storing things as triples, as you have to do a sort for each query and return the whole list of persons where you might only want the top three folks.
Depends on your language too; all of the above is easy in Java, but in Python there is no ordered list, so you have to implement bisecting yourself which isn't so hot (productivity wise anyways).
Productivity, space, time, and scalability trade offs. Who would have thought?
Posted by: Chris Brooks at September 29, 2011 07:51 PM
Thanks Chris! I truly appreciate your sharing your experience here.
I am using Java because that's what works best with AnyLogic (the simulation modelling tool I am using). Also, Java = very familliar. ;)
I am not exactly sure how the likeness matrix will inform my recommender algorithm. Somewhere in the mix, I think I will have to do some clustering to try to find the groups of "people like Christy" and "people like Derek". Your suggestions are very relevant here.
Posted by: Steph (a.k.a. Frozone) at October 1, 2011 11:54 AM
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Index to Steph's Notes
Feb. 24th 2007 - Weee! This new part of my website is not an entry, but rather a permanent fixture whose purpose is to "Look Down on All Those Notes With Some Grand Vision of Organization". Wish me luck. LOL- Representing meta-data (fuel) & the different kinds of "hooks" that intelligent systems can use (how fuel is injected into the motor of the engine)
- Motivation: Semantic net / Rationalizable to a machine
- Semantic network
- Genetic graph
- Prerequisite AND/OR graph
- Constraint Satisfaction Problems
- Bayesian networks / causal graphs
- Technology & Philosophy: RDF, modus ponens,
- Predicates, Logic & situation calculus
- What kinds of data? - What kinds of meta-data would an AIEd system possibly need, and how is it represented?
- task domain knowledge
- "is-prerequisite-to"-type knowledge
- interactions with learning objects & other learners - (location, composition is-a/part-of, sequencing by restricting navigation, personalization, ontologies for LO context)
- lesson plans, curriculum plans, practicing sessions (What is stored, what is generated on the fly? What is remembered?)
- How to organize it - When is it stored in a database? Meta-data? Agent memory banks? Protocols? Repositories? XML files? Home-servers? WSDL services? Frameworks? Portable banks? P2P access?
- Database of object-agent interactions
- Concept of "Home" on a P2P network -- maybe the bulk of a learning object's usage data is on its home server and can be queried using WSDL or something ? Similar homes for each student's usage history, etc. Baggage problem.
- Links to the ontologies
- referring to a concept/relationship - ex. AgentOwl?
- Generation of this data
- Rationalization: For use by other AIEd systems
- What is generated - discuss items under part I.C.
- When it's generated - describe procedural model, which parts of the engine generate what (isa-part-of data, XML feeds, web services, meta data bout groups and collaboration, protocols, examples Friend of A Friend FOAF project)
- Technical notes of HOW it's generated: JENA, issues of implementation demo, my Hermione & Ron agent examples, lol
- Usage of this generated data - see part IV. A.
- Given the engine, who uses it?
- Students / Learners / "Me"
- instructional planning, student model, pre-requisites, tutoring, coaching, collaboration,constructivism
- Teachers / Educators / "Me"
- putting together lessons
- be able to browse through task domain knowledge in an objective / encyclopaedia format, then be able to pick-and-choose what you need for your students
- compose examples, design explanations, pull together diagrams, learning objects, etc. Haystack Relo?
- Administration / Governement / Structure / Crowd Control
- as restrictions/obstacles/sand pit to the robot in agent environment
- can't just have a swarm of students and teachers out there -- need structure of courses, curriculum, objectives, requirements (at least, we do in this day and age!) - Report cards, evaluation, feedback
- government, marks, certificates, requirements, funding, curriclum, attendance, delinquent, non-attending, motivation
- school''s images, goals, strengths, payroll, HR, security, accounts, permissions, privacy
- registration, failed courses
- User Environment -- How does this engine work? What does the user see on the screen?
- Introduction - Given a background in educational psychology, how does the system present itself -- what does the user see, and were does this data come from? Links to thoughts from part I.)
- Task Domain Browsing - Suppose you're you're just idly browsing through the "raw" content. How would it look when it's not wrapped around a learning-context or lesson or tutorial or anything. 'Cross between browsing a raw task domain ontology and browsing a learning object repository.
- Cleaning up the data -- Visualizing the data for humans to pick through the task domain and work on it. Suppose the "Subject Expert" discovers an advancement in science and needs to update the "world's" domain knowledge. (I used the "Subject Expert" terminology from Ontologies to Support Learning Design Context - Thanks Chris) How would they make corrections to ontologies and learning objects, or at least point the users of "old" objects towards adopting the newer ones.
- "Modes" - Learning & Lessons / Checklist - Homework, Assignments, Courses being taken / Collaborative mode / Teaching mode / Calendar- email -adminisrative mode -- See also the different kinds of scenarios in the ActiveMath system
- Evolution of this engine
- target some key implementation hooks discussed in part I - design an experiment/demo
- scrape a page - (Note, scraping can only give objective data, not in-context dat)
- LO repository - related to browsing the task domain?
- a learners "To Do" list - where does it come from? Assignments, courses.
- sample group scenario
- sample teacher lesson planning
- sample data "left behind"
- sample use of that data
- Data mining (for what? lol )
- discovery / generation of ontologies - when do you need to hunt for them, and when do you have to have a solidly-known & predictable ontology?
- I/O - where it happens, which languages, protocols, which agents perform i/o and when, precepts, actuators
- Role Assignments
- My Environment Adapts to me
- Displaying feedback from the server on JSP pages (Software engineering considerations)
- Sketching out a design (Content planning vs. Delivery planning)
- agent negotiations / social structures / ummm... Web 2.0 ?
- garbage collection of meta data
- Artificial Intelligence & Evolution
- Memory Culling: Necessary part of intelligence? (artificial or human)
- Applications for the Genetic/Evolutionary algorithm
- open learning environments
- Agents, pets, grouping, Community modelling
- Protocols - finding groups, cyber dollars, state diagrams (?)
- "Community Studies" - graphs & communication hubs, types of communities (free-for-all, hierarchy of authority, etc.)
- implications of joining a community - what do you share, which parts of your student model are relevant
- Walls & sand traps -- deliberate restrictions as problem-solving for learning
- Communication channels - individual-to-individual, individual-to-community, chat channels, agent-only "administrative" communications, ex. requests for related learning objects in a particular community, etc.
- Educational/Pedagogical focus (this part probably shouldn't be its own section but rather incorporated into the whole picture, but it's separate for me right now because I'm still only just starting to learn about it.)
- Semantics - what there is to talk about in Education
- ex. Merril's First Principles of Instruction, linking educational terms to AI terms
- Pedagogical skills for tutors -- supporting human *and* artifical tutors
- Student modelling - what the machine needs to know about the student, pedagogically-speaking, about learning history/preferences
- Roles - Simulated students, Coaches, Tutors, Teachers,
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