1. Analogies and Case-Based Reasoning

2. Analogy
Analogy is either the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), or a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from a particular to another particular, as opposed to deduction, induction, and abduction, where at least one of the premises or the conclusion is general.
-- Wikipedia
An analogy is a relationship between two or more entities which are similar in one or more respects. An analogy is present whenever [one or more of] the following descriptions are present: resemblance, similarity, correspondence, likeness, comparison, counterpart, resemblance of relations, and mapping.
-- philosophy.lander.edu

3. Analogy
Analogy plays a significant role in many cognitive tasks, including
Problem solving & decision making
Perception
Memory
Creativity
Emotion
Analogy is particularly important in ordinary language and common sense
E.g., the use of proverbs, idioms, metaphors
It lies behind basic tasks such as the identification of places, objects and people
E.g., face perception and facial recognition systems.
Hofstadter: Analogy is "the core of cognition" [Gentner et al ]

4. Non-Argumentative Use of Analogy
Literary uses
Metaphor: a word or phrase literally denoting one kind of object or idea is used in place of another to suggest a likeness or analogy between them
E.g., the ship plows the sea.
E.g., his fist was a knotty hammer
Similié: a figure of speech comparing two unlike things often introduced by the words, "like" or "as."
E.g., cheeks like roses
E.g., "And ice mast high came floating by as green as emerald"
Use in explanation
The atom is (like) a miniature solar system
A tree is (like) a factory

5. Analogical Inference
An analogical inference is drawn from a resemblance of relations.
J. S. Mill's example of a country which has sent out colonies is termed "the mother country."
The colonies stand in the same relation to her as parents do to their children
Reasoning by analogy, then, obedience or affection is due by the colonies to the mother country. parents → children mother country → colonies

6. Analogical Inference
The general form of an analogical argument is as follows
a, b, c, d stand for entities
P, Q, R stand for properties
Note that this essentially reduces analogy to a form of induction.
a, b, c, d all have the properties P and Q.
a, b, c all have the further property R
_________________________________
therefore, d probably has the property R

7. Structured Mapping (Gentner)
Analogy depends on the mapping or alignment of the elements of source and target
The mapping takes place not only between objects, but also between relations of objects and between relations of relations
The whole mapping yields the assignment of a predicate or a relation to the target
When used in a computational framework, analogy would require the computation of similarities between the source and the target

8. High-Level Perception
Douglas Hofstadter challenged the shared structure theory and mostly its applications in computer science
Argued that there is no line between perception, including high-level perception, and analogical thought.
Analogy occurs not only after, but also before and at the same time as high-level perception
In high-level perception, humans make representations selecting relevant information from low-level stimuli.
Perception is necessary for analogy, but analogy is also necessary for high-level perception.
Chalmers (a student of Hofstadter) concluded that analogy is high-level perception.
Other claims
Analogy is only a metaphor (Forbus, 1998).
Hofstadter and Gentner do not defend opposite views, but are instead dealing with different aspects of analogy (Morrison and Dietrich 1995)

9. Case-Based Reasoning
The computational view of analogy has led to an approach called Case-based reasoning (CBR) with many applications in Computer Science and Artificial Intelligence
CBR is the process of solving new problems based on the solutions of similar past problems
E.g., an auto mechanic who fixes an engine by recalling another car that exhibited similar symptoms
E.g., a judge who makes a ruling in a trial based on legal precedents
An example of computations CBR: Collaborative Filtering Recommender Systems.

10. Case-Based Reasoning To solve a current problem
The problem is matched against the cases in the case base
Similar cases are retrieved
The retrieved cases are used to suggest a solution which is tested for success
If necessary, the solution is then revised
Finally the current problem and the final solution are retained as part of a new case.

11. Case-Based Reasoning
All case-based reasoning methods have in common the following process:
retrieve the most similar case (or cases) comparing the case to the library of past cases;
reuse the retrieved case to try to solve the current problem;
revise and adapt the proposed solution if necessary;
retain the final solution as part of a new case.
Retrieving a case starts with a (possibly partial) problem description and ends when a best matching case has been found. The subtasks involve:
identifying a set of relevant problem descriptors;
matching the case and returning a set of sufficiently similar cases (given a similarity threshold of some kind); and
selecting the best case from the set of cases returned.

12. Collaborative Filtering
Applies the basic CBR process to user profile data to predict a new user’s preferences
Predictions are computed based the other users’ with similar interests scores on items in the new user’s profile
i.e. users with similar tastes (aka “nearest neighbors”)
requires computing correlations between user u and other users according to interest scores or ratings

13. Basic Collaborative Filtering Process
Current User Record
<user, item1, item2, …>
Neighborhood
Formation
Nearest
Neighbors
Recommendation
Engine
Combination
Function
Historical
User Records
user
item
rating
Recommendations
Neighborhood Formation Phase
Recommendation Phase
Both of the Neighborhood formation and the
recommendation phases are real-time components

14. Collaborative Filtering: Measuring Similarities
Pearson Correlation
weight by degree of correlation between user U and user J
1 means very similar, 0 means no correlation, -1 means dissimilar
Works well in case of user ratings (where there is at least a range of 1-5)
Not always possible (in some situations we may only have implicit binary values, e.g., whether a user did or did not select an item)
Average rating of user J
on all items.

15. Example Collaborative System
Item1
Item 2
Item 3
Item 4
Item 5
Item 6
Correlation with Alice
Alice 5 2 3 ?
User 1 4 1
-1.00
User 2
0.33
User 3
.90
User 4
0.19
User 5
User 6
0.65
User 7
Prediction 
Best match
Using k-nearest neighbor with k = 1

16. Item-based Collaborative Filtering
Find similarities among the items based on ratings across users
Prediction of item i for user a is based on the past ratings of user a on items similar to i.
Suppose:
Predicted rating for Karen on Indep. Day will be 7, because she rated Star Wars 7 (using only the most similar item)
sim(Star Wars, Indep. Day) > sim(Jur. Park, Indep. Day) > sim(Termin., Indep. Day)

17. Item-Based Collaborative Filtering
Prediction 
Item1
Item 2
Item 3
Item 4
Item 5
Item 6
Alice 5 2 3 ?
User 1 4 1
User 2
User 3
User 4
User 5
User 6
User 7
Item similarity
0.76
0.79
0.60
0.71
0.75
Best match

18. Problem with Collaborative Filtering
Can be attacked using profile injection attacks
consist of a number of "attack profiles"
added to the system by providing ratings for various items
engineered to bias the system's recommendations
Two basic types:
“Push attack” (“Shilling”): designed to promote an item
“Nuke attack”: designed to demote a item

19. A Successful Push Attack
Item1
Item 2
Item 3
Item 4
Item 5
Item 6
Correlation with Alice
Alice 5 2 3 ?
User 1 4 1
-1.00
User 2
0.33
User 3
.90
User 4
0.19
User 5
User 6
0.65
User 7
Attack 1
Attack 2
0.76
Attack 3
0.93
Prediction 
Best Match
“user-based” algorithm using k-nearest neighbor with k = 1

20. Movielens Recommender System