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

Lecture Slides: Intro

Reading:

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

Lecture Slides: PCA

Reading: PCA Tutorial, KPCA

Linear algebraic techniques: canonical correlation analysis (CCA). Multidimensional scaling (MDS).

Lecture Slides: CCA+MDS

Reading: CCA Tutorial, CCA2, MDS1, MDS2, MDS3

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

Lecture Slides: SpectralGraph

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

Homework 1 out.

Computational topology: topology review, complexes, homology groups.

Lecture Slides: CompTop

Reading: Topology and Data

Persistent homology, barcodes and persistence diagrams.

Lecture Slides: Persistence

Reading: Barcodes, Persistent Homology, Computung Persistence I, Computing Persistence II, Ripser

Topological inference; the Mapper algorithm. Persistence Applications.

Lecture Slides: PersistenceApps

Reading: Shape barcodes, Mapper, Segmentation, scalar fields, ToMATo

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

Lecture Slides: 3DReps

Reading: Old survey

Homework 1 due. Homework 2 out.

Geometric deep learning; Volumetric and mesh CNNs for 3D geometry. Graph CNNs.

Lecture Slides: GeometricDL

Reading: MVCNN1, MCCNN2, VoxelCNN1, VoxelCNN2, geodesic, survey

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

Visual data sets: from ImageNet and ShapeNet to LAION-5B and ObjaverseXL; Techniques for annotation and annotation transport.

Lecture Slides: NLDR

Reading: Isomap, LE, LLE, t-SNE, SAE, VAE, https://scikit-learn.org/stable/auto_examples/#manifold-learning, ShapeNet, PartNet

Class Midterm.

Rigid and non-rigid shape alignment. Global and local shape descriptors; intrinsic descriptors, heat and wave kernel signatures.

Lecture Slides: AlignmentsCorrespondences

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

Homework 2 due. Homework 3 out.

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

Lecture Slides: GeomLB

Reading: LB1, LB2, ShapeDNA

Deep nets for pointclouds and applications to classification and segmentation.

Lecture Slides: PointNet

Reading: PointNet, PointNet++, VoteNet, FrustumPointnet, FlowNet3D

Symmetries and Regularities.

Lecture Slides: Symmetries

Reading: approx_symm_detection, Langevin, symmetries_and_regularites, relating_shapes_by_symmetries

Functional spaces and functional maps, variations; map visualization.

Lecture Slides: FunMaps

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

Homework 3 due. Homework 4 out.

Google Cloud Tutorial

Memorial Day Holiday

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

Lecture Slides: MapNets

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

Encoding geometry differences and shape variability.

Lecture Slides: ShapeDiffs

Reading: shape differences, StructureNet, DeformSyncNet

Semantics and geometry. Class wrap up.

Lecture Slides: Priors

Reading: Vector Neurons, JacobiNeRF

Homework 4 due.