1. Example I: Predicting the Weather
How should we format the input patterns?
We need to represent the current weather conditions by an input vector whose elements range in magnitude between zero and one.
When we inspect the raw data, we find that there are two types of data that we have to account for:
Scaled, continuously variable values
n-ary representations of category values
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

2. Example I: Predicting the Weather
The following data can be scaled:
temperature (-10… 40 degrees Celsius)
atmospheric pressure (26… 34 inches of mercury)
relative humidity (0… 100 percent)
wind speed (0… 250 km/h)
cloud cover (0… 9)
We can just scale each of these values so that its lower limit is mapped to 0 and its upper value is mapped to 1.
These numbers will be the components of the input vector.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

3. Example I: Predicting the Weather
Usually, wind speeds vary between 0 and 40 km/h.
By scaling wind speed between 0 and 250 km/h, we can account for all possible wind speeds, but usually only make use of a small fraction of the scale.
Therefore, only the most extreme wind speeds will exert a substantial effect on the weather prediction.
Consequently, we will use two scaled input values:
wind speed ranging from 0 to 40 km/h
wind speed ranging from 40 to 250 km/h
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

4. Example I: Predicting the Weather
How about the non-scalable weather data?
Wind direction is represented by an eight- component vector, where only one element (or possibly two adjacent ones) is active, indicating one out of eight wind directions.
The subjective weather condition is represented by a nine-component vector with at least one, and possibly more, active elements.
With this scheme, we can encode the current conditions at a given weather station with 23 vector components:
one for each of the four scaled parameters
two for wind speed
eight for wind direction
nine for the subjective weather condition
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

5. Example I: Predicting the Weather
Since the input does not only include our station, but also the eight surrounding ones, the input layer of the network looks like this: …
our station …
north … …
northwest
The network has 207 input neurons, which accept 207-component input vectors.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

6. Example I: Predicting the Weather
What should the output patterns look like?
We want the network to produce a set of indicators that we can interpret as a prediction of the weather in 24 hours from now.
In analogy to the weather forecast on the evening news, we decide to demand the following four indicators:
a temperature prediction
a prediction of the chance of precipitation occurring
an indication of the expected cloud cover
a storm indicator (extreme conditions warning)
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

7. Example I: Predicting the Weather
Each of these four indicators can be represented by one scaled output value:
temperature (-10… 40 degrees Celsius)
chance of precipitation (0%… 100%)
cloud cover (0… 9)
storm warning: two possibilities:
0: no storm warning; 1: storm warning
probability of serious storm (0%… 100%)
Of course, the actual network outputs range from 0 to 1 (or from  to (1 - ) for sigmoidal neurons), and after their computation, if necessary, they are scaled to match the ranges specified above.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

8. Example I: Predicting the Weather
We decide (or experimentally determine) to use a hidden layer with 42 sigmoidal neurons.
In summary, our network has
207 input neurons
42 hidden neurons
4 output neurons
Because of the small output vectors, 42 hidden units may suffice for this application.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

9. Example I: Predicting the Weather
The next thing we need to do is collecting the training exemplars.
First we have to specify what our network is supposed to do:
In production mode, the network is fed with the current weather conditions, and its output will be interpreted as the weather forecast for tomorrow.
Therefore, in training mode, we have to present the network with exemplars that associate known past weather conditions at a time t with the conditions at t – 24 hrs.
So we have to collect a set of historical exemplars with known correct output for every input.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

10. Example I: Predicting the Weather
Obviously, if such data is unavailable, we have to start collecting them.
The selection of exemplars that we need depends, among other factors, on the amount of changes in weather at our location.
For example, in Honolulu, Hawaii, our exemplars may not have to cover all seasons, because there is little variation in the weather.
In Boston, however, we would need to include data from every calendar month because of dramatic changes in weather across seasons.
As we know, some winters in Boston are much harder than others, so it might be a good idea to collect data for several years.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

11. Example I: Predicting the Weather
And how about the granularity of our exemplar data, i.e., the frequency of measurement?
Using one sample per day would be a natural choice, but it would neglect rapid changes in weather.
If we use hourly instantaneous samples, however, we increase the likelihood of conflicts.
Therefore, we decide to do the following:
We will collect input data every hour, but the corresponding output pattern will be the average of the instantaneous patterns over a 12-hour period.
This way we reduce the possibility of errors while increasing the amount of training data.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

12. Example I: Predicting the Weather
Now we have to train our network.
If we use samples in one-hour intervals for one year, we have 8,760 exemplars.
Our network has 207 4 = 8862 weights, which means that data from ten years, i.e., 87,600 exemplars would be desirable.
Rule of thumb: There should be at least 5 to 10 times as many training exemplars as there are weights in the network.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

13. Example I: Predicting the Weather
Since with a large number of samples the hold-one-out training method is very time consuming, we decide to use partial-set training instead.
The best way to do this would be to acquire a test set (control set), that is, another set of input-output pairs measured on random days and at random times.
After training the network with the 87,600 exemplars, we could then use the test set to evaluate the performance of our network.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

14. Example I: Predicting the Weather
Neural network troubleshooting:
Plot the global error as a function of the training epoch. The error should decrease after every epoch. If it oscillates, do the following tests.
Try reducing the size of the training set. If then the network converges, a conflict may exist in the exemplars.
If the network still does not converge, continue pruning the training set until it does converge. Then add exemplars back gradually, thereby detecting the ones that cause conflicts.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

15. Example I: Predicting the Weather
If this still does not work, look for saturated neurons (extreme weights) in the hidden layer. If you find those, add more hidden-layer neurons, possibly an extra 20%.
If there are no saturated units and the problems still exist, try lowering the learning parameter  and training longer.
If the network converges but does not accurately learn the desired function, evaluate the coverage of the training set.
If the coverage is adequate and the network still does not learn the function precisely, you could refine the pattern representation. For example, you could include a season indicator to the input, helping the network to discriminate between similar inputs that produce very different outputs.
Then you can start predicting the weather!
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

16. Further Examples Online
TensorFlow Neural Network Playground:
… and if you are interested in Deep Learning:
ConvNetJS:
We will talk about convolutional networks once we have studied computer vision for a bit.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

17. Computer Vision November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

18. Computer Vision A simple two-stage model of computer vision:
Image processing
Scene analysis
Bitmap image
Scene description
Prepare image for scene analysis
Build an iconic model of the world
feedback (tuning)
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

19. Computer Vision
The image processing stage prepares the input image for the subsequent scene analysis.
Usually, image processing results in one or more new images that contain specific information on relevant features of the input image.
The information in the output images is arranged in the same way as in the input image. For example, in the upper left corner in the output images we find information about the upper left corner in the input image.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

20. Computer Vision
The scene analysis stage interprets the results from the image processing stage.
Its output completely depends on the problem that the computer vision system is supposed to solve.
For example, it could be the number of bacteria in a microscopic image, or the identity of a person whose retinal scan was input to the system.
In the following lectures we will focus on the lower-level, i.e., image processing techniques.
Later we will discuss a variety of scene analysis methods and algorithms.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

21. Computer Vision
How can we turn a visual scene into something that can be algorithmically processed?
Usually, we map the visual scene onto a two-dimensional array of intensities.
In the first step, we have to project the scene onto a plane.
This projection can be most easily understood by imagining a transparent plane between the observer (camera) and the visual scene.
The intensities from the scene are projected onto the plane by moving them along a straight line from their initial position to the observer.
The result will be a two-dimensional projection of the three-dimensional scene as it is seen by the observer.
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

22. Camera Geometry November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II

23. Color Imaging via Bayer Filter
November 20, 2018
Introduction to Artificial Intelligence Lecture 20: How to Apply Neural Networks II