# Learning Similarity Metrics with Invariance Properties

Posted in Science on September 16, 2008

Lecture slides:

• Learning Similarity Metrics with Invariances
• Learning an Invariant Dissimilarity Metric
• Dissimilarity Metric for Face Recognition
• Siamese Architecture
• Dissimilarity Metric vs Traditional Classification
• Trainable Metric vs Other Dimensionality Reduction Methods
• Trainable Metrics vs handcrafted invariances
• Siamese Architecture for Comparing TimeSeries Data
• 1D Convolutional Net (TDNN)
• Examples
• Siamese Architecture
• Probabilistic Training: Maximum Likelihood
• Solution?
• Another Loss Function
• Loss Function
• Examples of Loss Functions
• Loss Function: SquareExponential
• Face Verification datasets: AT&T, FERET, and AR/Purdue
• Face Verification datasets: AT&T, FERET, and AR/Purdue
• Face Verification datasets: AT&T, FERET, and AR/Purdue
• Face Verification dataset: AR/Purdue
• Preprocessing
• Centering with a Gaussianblurred face template
• Alternated Convolutions and Subsampling
• Architecture for the Mapping Function Gw(X)
• Internal state for genuine and impostor pairs
• Gaussian Face Model in the output space
• Dataset for Verification - Verification Results
• Classification Examples
• lInternal State
• DrLim: Dimensionality; Reduction by Learning an Invariant Mapping
• Learning a FUNCTION from input to output
• Learning an INVARIANT FUNCTION from input to output
• Learning Invariant Manifolds with EBMs
• Step 1: Building a Neighborhood Graph
• Step 2: Pick a Parameterized Family of Function
• Step 3: Pick a Loss function and Minimize it w.r.t. W
• Architecture
• Architecture and loss function
• Loss function
• Mechanical Analogy
• MNIST Dataset
• MNIST Handwritten Digits. Sanity Check
• Architecture of the Gw(X) Function:
• Alternated Convolutions and Subsampling
• Learning a mapping that is invariant to shifts
• Simple Experiment with Shifted MNIST
• Shifted MNIST: LLE Result
• Shifted MNIST: Injecting Prior Knowledge
• Discovering the Viewpoint Manifold
• Generic Object Detection and Recognition with Invariance to Pose and Illumination
• Data Collection, Sample Generation
• NORB Dataset: LLE
• Automatic Discovery of the Viewpoint Manifold with Invariant to Illumination
• NORB Dataset: Learned Hidden Units

Author: Yann Le Cun, New York University