Non-linear hypotheses Machine Learning Non-linear Classification x - - PowerPoint PPT Presentation

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Non-linear hypotheses Machine Learning Non-linear Classification x - - PowerPoint PPT Presentation

May 20, 2023 50 likes •474 views

Neural Networks: Representation Non-linear hypotheses Machine Learning Non-linear Classification x 2 x 1 size # bedrooms # floors age Andrew Ng What is this? You see this: But the camera sees this: Andrew Ng Computer Vision: Car

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Neural Networks: Representation

Non-linear hypotheses

Machine Learning

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Andrew Ng

Non-linear Classification

x1 x2

size # bedrooms # floors age

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Andrew Ng

You see this:

But the camera sees this:

What is this?

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Andrew Ng

Computer Vision: Car detection Testing: What is this?

Not a car Cars

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Andrew Ng

Learning Algorithm

pixel 1 pixel 2 pixel 1 pixel 2 Raw image Cars “Non”-Cars

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Andrew Ng

pixel 1 pixel 2 Raw image Cars “Non”-Cars

Learning Algorithm

pixel 1 pixel 2

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Andrew Ng

pixel 1 pixel 2 Raw image Cars “Non”-Cars

50 x 50 pixel images→ 2500 pixels (7500 if RGB)

pixel 1 intensity pixel 2 intensity pixel 2500 intensity

Quadratic features ( ): ≈3 million features

Learning Algorithm

pixel 1 pixel 2

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Neural Networks: Representation

Neurons and the brain

Machine Learning

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Andrew Ng

Neural Networks Origins: Algorithms that try to mimic the brain. Was very widely used in 80s and early 90s; popularity diminished in late 90s. Recent resurgence: State-of-the-art technique for many applications

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Andrew Ng

Auditory cortex learns to see

Auditory Cortex

The “one learning algorithm” hypothesis

[Roe et al., 1992]

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Andrew Ng

Somatosensory cortex learns to see

Somatosensory Cortex

The “one learning algorithm” hypothesis

[Metin & Frost, 1989]

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Andrew Ng

Seeing with your tongue Human echolocation (sonar) Haptic belt: Direction sense Implanting a 3rd eye

Sensor representations in the brain

[BrainPort; Welsh & Blasch, 1997; Nagel et al., 2005; Constantine-Paton & Law, 2009]

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Neural Networks: Representation

Machine Learning

Model representation I

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Andrew Ng

Neuron in the brain

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Andrew Ng

Neurons in the brain

[Credit: US National Institutes of Health, National Institute on Aging]

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Neuron model: Logistic unit Sigmoid (logistic) activation function.

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Andrew Ng

Neural Network

Layer 3 Layer 1 Layer 2

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Andrew Ng

Neural Network

“activation” of unit in layer matrix of weights controlling function mapping from layer to layer If network has units in layer , units in layer , then will be of dimension .

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Neural Networks: Representation

Model representation II

Machine Learning

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Andrew Ng

Add . Forward propagation: Vectorized implementation

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Andrew Ng

Layer 3 Layer 1 Layer 2

Neural Network learning its own features

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Andrew Ng

Layer 3 Layer 1 Layer 2

Other network architectures

Layer 4

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Neural Networks: Representation

Examples and intuitions I

Machine Learning

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Andrew Ng

Non-linear classification example: XOR/XNOR , are binary (0 or 1).

x1 x2 x1 x2

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Andrew Ng

Simple example: AND

1 1 1 1

1.0

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Andrew Ng

Example: OR function

1 1 1 1

  • 10

20 20

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Neural Networks: Representation

Examples and intuitions II

Machine Learning

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Andrew Ng

Negation:

1

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Andrew Ng

Putting it together:

1 1 1 1

  • 30

20 20 10

  • 20
  • 20
  • 10

20 20

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Andrew Ng

Neural Network intuition

Layer 3 Layer 1 Layer 2 Layer 4

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Andrew Ng

Handwritten digit classification

[Courtesy of Yann LeCun]

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Andrew Ng

Handwritten digit classification

[Courtesy of Yann LeCun]

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Andrew Ng

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Andrew Ng

Neural Networks: Representation

Multi-class classification

Machine Learning

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Andrew Ng

Multiple output units: One-vs-all.

Pedestrian Car Motorcycle Truck

Want , , , etc.

when pedestrian when car when motorcycle

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Andrew Ng

Multiple output units: One-vs-all. Want , , , etc.

when pedestrian when car when motorcycle

Training set:

  • ne of ,

, ,

pedestrian car motorcycle truck

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Andrew Ng