Paper analyzis + Roadmap

[balthazarneveu]

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Roadmap

• 4 @InesVATI

• 6 @ManalAkh

• 7 @balthazarneveu

• :gift: theory : #5 @InesVATI but all involved!

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• [x] read & summarize paper
• [x] list actions to be done

[balthazarneveu]

Questions

1. How to build the edges?

   • pairwise similarity between subjects = edges encode phenotypic information -> how to label?
   • data is acquired using different imaging protocols -> harmonization?

2. How to classify a new individual? do we need to insert it in the graph?

3. Spectral convolutions vs graph convolutions (without spectral)

Notations

Graph = {V, E, W} ,

• Vertex v in V , |V| = N , x(v) = features for vertex = patient v, dimension C . built from imaging data : resting-state fMRI or structural MRI :question:
• E : edge with phenotypic information
• W adjacency matrix
• l in L labels . M labelled samples, N-M to classify

Edges construction: non-imaging phenotypic data : age gender, acquisition site M = {Mh}

Adjacency matrix

• v & w 2 nodes/patients .
• Sum : 1 if same gender or same site else 0 , 1 if age difference under a threshold else 0 ... (total up to H if totally similar)
• Sim (Sv, Sw) measure of similarity between subjects . ( ADNI : same subject? , ABIDE: correlation on rs-fMRI :question: )

Vocabulary

ADNI (Alzheihmer)

Graph definition

• H=2 gender and age (highly correlates with brain volume)
• Same subject may have several acquisitions. Sim(Sv, Sw) = "lamdba" if same subject. 1 otherwise

  General description

• ADNI : Alzheihmer's disease neuroimaging initiative.
• 19 years public / private partnership.
• 206M$ investement
• 157 partners
• 12.7k MRI scans -> heterogeneous (multiple sites)
• 9.5k PET scans
• 1M biosamples Task : predicting the conversion from Mild Cognitive Impairment (MCI) to Alzheimer’s Disease (AD) Presentation video

Alzheimer's disease: neuro degeneracy

• plaques (beta amyloid sticky cluster)
• tangles. (tau stop supporting the microtobules inside the neurons = kills the neuron)

Preprocessing

ABIDE (Autism)

Graph definition

• H = 2 for graph connectivity : age & acquisition size
• We define Sim(Sv, Sw) as the correlation distance between the subjects’ rs-fMRI connectivity networks after feature selection, as a separation between ASD and controls can be observed within certain sites .

  General description

• 1112 subjects, 20 different sites.
• Task = classify : ASD (Autism Spectrum disorder) Preprocessing

Note - not straightforward to download proprocessed + download scripts

[balthazarneveu]

Graph neural networks

A simple idea for a proof of concept work:

• consider a regular grid image as a graph
• implement a spectral convolution, compare to convolution.
• extend

:gift: MUST READ :gift: Convolutions on graphs

Gold standard : **aggregation has to be node-order equivariant***

Polynoms of the Laplacian ...

in a nutshell: -in a local neighborhood of a node, there's no order (no left or right or up or down like in images).

• You can simply take the average of neighbor features.
• Boring you may say... you can also do the laplacian = D*identity - sum over neigbors operator.
• An you can compose these laplacians to extend the receptive field & perform operations over a much larger range of nodes (consider applying a filter on a downscaled image)
• Combine these with polynomials & you're basically able to perform a flexible amount of operations.

The polynom of Laplacian is a big square matrix |V|² containing the weight to apply to neighboring nodes. Just multiply by the features of the nodes (|V| stacked "feature vectors of size D" ), apply a Relu .. this is a single layer of a neural network.

Spectral "global" convolutions

How to attend the whole graph at once?

Important note: spectral convolutions have largely been superseded by ‘local’ convolutions for the reasons discussed above, there is still much merit to understanding the ideas behind them.

Spectral aspect of convolutions

One of Bart Wronky's blogpost Eigen values of circulant matrix = amplitude of the frequencies

Extra stuffs

:+1: Intro to graph neural networks