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4.2 Data Input-Output Representation
1. Background ( Ref: Handbook of Neural Computation )
Saund: Key theme in AI is to discover good rep. for the problem at hand. A good rep. makes explicit
info. useful to the computation, it strips away obscuring clutter, it reduces info. to its essentials.
Output
Raw
Data
Input
Transf.
NN
Transf.
Final
Output
(1) Data Rep. is more important/critical than network topology
Goals of Data Rep. [Garbage In Garbage Out]
•
Feature Enhancement / Data Reduction for Separability
•
•
•
•
Similar (Diff) events  Similar (Diff) rep. for better interpolation
More elements for important features
Compactness without losing (or even enhancing) info. for fast learning
Preserve feature info. (clustering / metric info)
Ex. Binary coding could destroy metric
01111  10000 [Hamming metric]
Ex. Character Recognition
Raw data = 5 64bit binary vectors.
Representation ① raw data
② any code for five characters
③ shape features : horizontal and vertical spars, their ratio,
relative positions of the spars
Other extreme:
Wasserman : raw data may be more useful in cases where essential features are
unknown. NN can discover features in hidden neurons.
2. Data Preprocessing techniques
Data sets are plagued by Noise, Bias, Large variations in dynamic range . . .
(1) Normalize  Remove large dynamic variances over one or more
dimensions in data
Ex.
① Normalize gray scale image  invariant to light condition
② Normalize speech signal  invariant to absolute volume level
③ Normalize with respect to position and size - Character recognition
(2) Nomalization ① x'  x / l
Algorithms :
One Way to embed magnitude ( l ) info. :
( x1 ,, xD , l )  Normalize
② Row Norm. (2-D) : for each row, divide by the mean value
③ Column Norm. (2-D)
(3) Principal Component Analysis – Dim. Reduction
1
R
N
n
T
(
x

x
)(
x

x
)
 k
k
k 1
M
~
x   (e j  x)e j
j 1
M D
3. Case Study : Face Recognition
(profile)
Data Reduction
416 x 320

16x2
 23 (Discard High freq. components)
(= 133,120 pixels)
① Efficient tech. to extract high interest features.
② Method for data reduction with minimal info. loss
③ DCT applied to reduced vector descriptions enhances info. content, provides
invariance to small change and increased separability.
4. Actual Coding Schemes
(1) Local R O Y G B I V
(2) Distributed C2 C1 C0
1 0 0 0 0 0 0
0 0 1


1 1 1
0 0 0 0 0 0 1
In Local representation, each node may be [0 1] [-1 1] or even continuous when
more than one node can be active to indicate presence of two or more features.
(3) Coarse Distributed
Wider overlapping receptive fields
36 nodes
27 nodes
Students’ Questions from 2005:
While DCT in facial image processing helps data
reduction, does it also help face recognition ?
Since Human faces are all alike, its Fourier transform
will also be similar. Spatial features will be more
relevant to recognition.
Normalization or Coding will reduce data or help
classification. But, isn’t the process going to delay the
overall learning time ?
Coarse distributed coding will reduce the total number
of nodes. However, when a single node is represented
in overlapped fashion, isn’t the additional info. needed
such as the overlap position, etc. ?
When an NN technique is used for character or speech
recognition, how does its performance compare with
non-NN approaches ?
NN can be applied to many problems. Any application
where NN is hard to apply to ?
Is there any general measure to tell the importance of
information in feature extraction ?
If line search is used to find an optimal learning rate,
the number of steps may decrease but I am afraid the
overall processing time may increase.
Can better separation for classification result via data
representation ? Can the information content increase
via a good data rep. ?
5. Discrete Coding
(1) Simple Sum (fault tolerance, but requires many nodes for large numbers)
5 = 000011111 = 110000111 =
(2) Value Unit Encoding
1-3
4-6
7-9 10-12 13-15
1-3
4-6 7-9 10-12 13-15
2=
10 =
(3) Discrete Thermometer
x >0 x>3 x>6 x>9 x>12
2=
x >0 x>3 x>6 x>9 x>12
10 =
6. Continuous Coding
(1) Simple Analog
• For an activation ai range of [0,1] or [-1,1],
value in range [u, v] = (v - u) ai + u
• Logarithmic scale for data set with large dynamic range
(2) Continuous Thermometer
(3) Proportional Coarse Coding
- Pomerleau used a Gaussian Smearing function to represent steering directions in an
Autonomous Land Vehicle In a Neural Network (ALVINN)
Ref. “Neural Network Perception
For Mobile Robot Guidance,”
D. Pomerleau, Kluwer, 93.
Slight Right Turn