Introduction; Geometric and topological perspective on data analysis; Data representations; Learning on point clouds and graphs; Joint data analysis.

Reading:

Lecture 1 Slides

Visual data sets: ImageNet and ShapeNet; Techniques for annotation and annotation transport.

Reading: ImageNet, ShapeNet, Annotation1, Annotation2

Lecture 2 Slides

Linear algebraic techniques: principal components analysis (PCA), Kernel PCA.

Reading: PCA Tutorial, KPCA

Lecture 3 Slides

Linear algebraic techniques: canonical correlation analysis (CCA).

Reading: CCA Tutorial, CCA2

Homework 1 out.

Lecture 4 Slides

Graph methods; spectral approaches, graph Laplacians, Laplacian embeddings, spectral clustering.

Reading: Spectral graph theory Yale course (first few lectures); spectral clustering tutorial

Lecture 5 Slides

Multidimensional scaling. Non-linear dimensionality reduction: locally linear embeddings, Laplacian eignemaps, Isomap, t-SNE.

Reading: MDS1, MDS2, Isomap, LE, LLE, t-SNE

Lecture 6 Slides

Computational topology: topology review, complexes, homology groups.

Reading: Topology and Data

Lecture 7 Slides

Persistent homology, barcodes and persistence diagrams.

Reading: Barcodes, Persistent Homology

Homework 1 due. Homework 2 out.

Lecture 8 Slides

Topological inference; the Mapper algorithm. Applications.

Reading: Shape barcodes, Mapper, persistence-based segmentation, scalar fields, ToMATo

Lecture 9 Slides

Representations of 3D Geometry: Voxel-Grids, Point Clouds, Meshes and Other Boundary Models, Solid Models

Reading: Old survey

Lecture 10 Slides

Geometry processing; Laplace-Beltrami and other operators on meshes;

Reading: LB1, LB2, ShapeDNA

Lecture 11 Slides

Shape alignment. Global and local shape descriptors; intrinsic descriptors, heat and wave kernel signatures.

Reading: ICP; RANSAC; Shape descriptors for retrieval; global point signatures; heat kernel signatures;

Homework 2 due. Homework 3 out.

Lecture 12 Slides

Non-rigid shape alignment; isometric matching, conformal maps, Möbius voting, blended intrinsic maps

Reading: one point isometric matching; Möbius maps; Möbius voting; blended intrinsic maps

Lecture 13 Slides

Deep learning; Volumetric and multi-view CNNs for 3D geometry

Reading: MVCNN1, MCCNN2, VoxelCNN1, VoxelCNN2

Lecture 14 Slides

Deep nets for pointclouds

Reading: PointNet, PointNet++

Lecture 15 Slides

Deep nets for graphs and meshes

Reading: spectral, graph, geodesic, sync, survey

Homework 3 due. Homework 4 out.

Lecture 16 Slides

Memorial day holiday -- no class

Functional spaces and functional maps, variations; map visualization

Reading: functional maps paper; map visualization; Siggraph 17 course notes

Lecture 17 Slides

Shape differences and shape variability.

Reading: shape differences, co-segmentation

Lecture 18 Slides

Networks of shapes and images; cycle consistency; map processing and latent spaces.

Reading: multi-latent space co-segmentation, 3D object co-segmentation

Lecture 19 Slides

Homework 4 due.