A list of topics

• Dynamic programming
  • Dynamic time warping
• Dijkstra, Minimum ratio cycles
• Graph cuts (s-t-min-cut/max-flow)
• Integral tricks (integral image)
• using hardware : parallel, GPU
• basics: simplex, linear programming, etc.

• gradient descents (basic, Newton, conjugate, etc.)
• stochastic methods
  • simulated annealing, swarm optimization...
  • genetic algorithms
  • Gibbs sampling, Monte Carlo Markov Chain, birth & death
• L0/L1 optimization
  • Lasso
• primal/dual
• on graphs
  • Loopy Belief Propagation
  • TRW-S
• iterative approaches : convergence ?
  • Expectation-Maximization (EM)

• discretization
  • sampling vs bases (numerical analysis)
  • derivatives (in space or time)
  • explicit/implicit schemes
• features
  • points of interest (SIFT...)
  • patch descriptors : HOG, co-variance, ...
  • bags of words, histograms
  • detectors
• geometry
  • shape, shape statistics
  • geometrical descriptors / analysis
    • local differential geometry of surfaces (mean and Gauss curvatures)
    • connected components, homology groups, Euler characteristic
    • persistence (size) theory
    • spatial tesselations (Delaunay and Voronoi diagrams for points, spheres, etc.)
• energy, criterion to optimize (L2, sparse, smoothness, ...)
  • Markov Random Fields
  • graphical models (Dirichlet...)
  • Gaussian processes
  • multi-resolution, multi-scale
  • sparsity with L0-L1 norms, compressed sensing
• metrics (norms, inner products), similarity measures
  • kernel methods
  • optimal transport, Earth Mover Distance, Wasserstein metrics
  • the sphere trick (explicit geodesic distance on a sphere with uniform metric)

• learning schemes
  • reinforcement learning
  • features --> bags of words --> clustering --> classification --> detection
  • offline / online, adaptative, etc.
  • bottom-up / top-down / feedbacks
  • No free lunch theorem
  • Occam's razor
• clustering
  • k means
  • mean shift
  • spectral clustering
  • region merging (hierarchical approaches)
• classification, prediction
  • k-NN, kernels, SVM
  • decision trees (adaboost, random forests)
  • capacity of a classifier : Vapnik-Chervonenkis
  • prediction of time series : the example of electricity management
• statistics from data
  • PCA, low-dimensional embeddings
  • density estimators, Parzen window
  • curse of dimensionality
• parameter estimation, cross-validation
• neural nets
  • structure, initialization, weight update and convergence...

• entropy, mutual information, Kullback-Leibler divergence
• compression, entropy coding (Hufmann/arithmetic coding), prediction
• Minimum Description Length (MDL) approaches, Bayesian information criterion (BIC), model selection

• Data structure
  • KD-tree, approximate nearest neighbors
• Temporal structure
  • automata
  • dynamical systems (periodic)
• Syntax
  • grammars
  • "patterns"

• Probabilities and statistics
  • distributions (Dirichlet...)
  • Bayes rule
  • likelihood
• Transforms : Fourier, Radon, wavelets...
  • time-frequency representations with Fourier
• Differential equations
• Differential geometry
  • manifold, metrics

• datasets and evaluation
  • beware lack of common ground truth / evaluation metrics (ex: tracking)
• software
  • good libraries
  • basics in programming, in C++, debugging...
  • scripts, environment (Linux, shell,...)
  • installing software
  • sharing software (svn, git...)
• hardware
  • GPU, parallelisation
  • using the Cluster
• tutorials on the web
• writing a paper
• making a presentation