Data Mining 2 (ex Análisis Inteligente de Datos y Data Mining) Lluís A. Belanche.
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Transcript of Data Mining 2 (ex Análisis Inteligente de Datos y Data Mining) Lluís A. Belanche.
Contents of the course (hopefully)
1. Introduction & methodologies
2. Exploratory DM through visualization
3. Pattern recognition: introduction
4. Pattern recognition: the Gaussian case
5. Feature extraction
6. Feature selection & weighing
7. Error estimation
8. Linear methods are nice!
9. Probability in Data Mining
10. Latency, generativity, manifolds and all that
11. Application of GTM: from medicine to ecology
12. DM Case studies
Sorry guys! … no fuzzy systems …
Linear classifiers are nice! (II) Transformation
(x) = [ (x), (x), … m(x) ]
with x = [ x1, x2, …, xn ]
Useful for “ascending” (m>n) or “descending” (m>n)
with 0 < m,n < oo (integers) … an example?
Utility
• This is a very powerful setting• Let us suppose:
r>s increase in dimension
increase in expressive power, ease the task for almost any learning machine
r<s decrease in dimension
visualization, compactation, noise reduction, removal of useless information
Contradictory !?
On intelligence …
• What is Intelligence?• What is the function of Intelligence?
to ensure survival in nature
• What are the ingredients of intelligence?– Perceive in a changing world– Reason under partial truth– Plan & prioritize under uncertainty– Coordinate different simultaneous tasks– Learn under noisy experiences
“Generally, a car can be parked rather easily because the final position of the car is not specified exactly. It it were specified to within, say, a fraction of a millimeter and a few seconds of arc, it would take hours of maneuvering and precise measurements of distance and angular position to solve the problem.”
HighHigh precision carries a highhigh cost.
Parking a Car (difficult or easy?)
Soft Computing
Rough Sets
Fuzzy Logic
Neural Networks
Evolutionary Algorithms
Chaos & Fractals
Belief
Networks
The primordial soup
What could MACHINE LEARNING possibly be?
In the beginning, there was a set of examples …
• To exploit imprecision, uncertainty, robustness, data dependencies, learning and/or optimization ability, to achieve a working solution to a problem which is hard to solve.
• To find an exact (approximate) solution to an imprecisely (precisely) formulated problem.
The challenge is to put these capabilities into use by devising methods of computation which lead to an acceptable solution at the lowest possible cost.
This should be the guiding principle
So what is the aim?
Fuzzy Logic : the algorithms for dealing with imprecision and uncertainty Neural Networks : the machinery for learning and function approximation with noise Evolutionary Algorithms : the algorithms for adaptive search and optimization
RSRough Sets
uncertainty arising from the granularity in the domain of discourse
Different methods = different roles
Examples of soft computing
• TSP: 105 cities, – accuracy within 0.75%, 7 months– accuracy within 1%, 2 days
• Compare– “absoulute best for sure” with “very good with
very high probability”
Are you one of the top guns?
• Consider …– Search space of size s– Draw N random samples– What is the probability p that at least one of
them is in the top t ?
• Answer: p = 1 – (1-t/s)N
• Example: s= 1012, N=100.000, t=1.000 1 in 10.000 !
On Algorithms
• what is worth?
Problems
Eff
icie
ncy
P
Specialized algorithms: best performance for special problemsGeneric algorithms: good performance over a wide range of problems
Specialized Algo.
Generic Algorithms
Words are important !
• What is a theory ?
• What is an algorithm ?
• What is an implementation ?
• What is a model ?
• What does “non-linear” mean ?
• What does “non-parametric” mean ?
The problem of induction
• Classical problem in Philosophy
• Example: 1,2,3,4,5,?• A more through
example: JT
What are the conditions for successful learning?
• Training data (sufficiently) representative
• Principle of similarity
• Target function within capacity of the learner
• Non-dull learning algorithm
• Enough computational resources
• A correct (or close to) learning bias