Scientist Stories: Mengjia Xu, Neuro-inspired Algorithms and Theory

Today I'm going to talk about exploring neuroimaging signatures where tabloid graph representation learning— actually, there is some overlap with the previous speaker. How about now?

Can you project? Like, we now see both slides. That's, that's the problem. How do you project that? I'm not sure.

I don't know.

I never use that. So you see what's going on, right? So you have both, all of that.

So can you put online?

Online is good. So, okay, let's, let's do it. It's okay.

Okay, so yeah, so there is some actually overlap with the previous speaker, Ricky Chen. So today my talk will include 4 parts. The first, I will give a little bit of introduction and background. And second, I will introduce the different graph embedding techniques. Including two different Bayesian-based embedding methods. Basically, embedding the graph into vectors and also embedding high-dimensional graph into density Gaussian distributions. And also the third section, I will give a presentation on hyperbolic graph embedding for human brain network analysis, mainly for two different applications, subjective cognitive decline prediction and also the normal brain aging trajectory detection. And lastly, I'll give a conclusion. So first, because I want to give you a little bit some background about the human brain disease, like Alzheimer's disease has all of these. So AD is a progressive brain network disease with very complex etiology and multiple pathogenesis. So by 2050, there will be 152 million dementia patients and also $1.1 trillion healthcare cost in the world. And if you look at this figure, actually, sorry, this is so small here. If you look at this figure, you can see that actually before the onset of AD, we can see actually before the detection of the AD, actually there is almost 2 decades earlier already the people already developed AD, Alzheimer's disease. So starting from 40 years old, actually when they're 70 years old, actually they were detected as the Alzheimer's disease patients. So there are 3 major biomarkers for Alzheimer's disease. So 2 different proteins, alphalate and also tau protein. And the other one is a very important one, is the brain connectivity alterations. Basically, we can use very advanced neuroimaging modality. This is a machine we call magnetoencephalography. We call MEG neuroimaging modality. So we can use this to monitor the brain activity directly from different patients. So another topic application we are working on is called the normal brain aging trajectory detection. As we know, our brain is a very core part of the human body, and it also is the seat of the intelligence and the interpreter of the senses and also initiator of the body movement and also controller of behaviors. And our brain are affected at both the structural and functional levels by normal healthy aging. And also, we can see that the National Institute on Aging, they announced actually they'll continue to support the research to identify age-related neurotendrils and mechanisms that older people use to maintain optimal learning, memory, and other cognitive functions.. But currently, the studies about the trajectories of functional network brain connectivity alterations in the healthy brain aging are still not fully understood. It's very limited. And in our project, the aim is to study normal brain aging trajectory by examining alterations in the hierarchical structure of the brain networks, including both the brain regional level and also subnetwork level changes over around 600 subjects between 18 years old and 99 years old. So these are actually different imaging modalities like T1 structural MRI and also MEG functional neuroimaging data. So this is a brief introduction about neuroimaging. Actually, modalities fall into two broad categories, structural neuroimaging and functional neuroimaging. So it is really Now we're focusing on the functional neuroimaging data, MEG data. Basically, the MEG and functional MRI and also EEG are all functional imaging modalities. So they can measure the brain activity from source. And also for the diffusion MRI, also is a functional neuroimaging. They can measure the molecular diffusion in the biological tissues. However, the structural neuroimaging will describe the shape and the size and the integrity of the gray and white matter structures in our human brain. So based on both the structural and functional neuroimaging, we can actually build the brain network. Basically, we call brain connectome based on the collected data. So we can— but we need to use some brain atlas We also call it the brain template. So this actually has some predefined brain regions. So we can actually, based on the brain atlas, to extract the brain regional lag time series, and then we can compute the brain connectivity matrix based on the adjacency matrix for the graph. And here we can, because our main focus is on the MEG neuroimaging data, actually we can compare with other functional neuroimaging modality, we can see that it has a very good temporal resolution, actually very excellent. It's in milliseconds compared to the functional MRI, and it was invented by a professor at MIT in the 1970s. So, and another very important property of imaging, neuroimaging, is they can measure the absolute neural activity directly compared to functional MRI. Actually, they can only measure the relative neural activity where the oxygen of multiple near-active neurons. So this is indirectly apparent. And also, MEG, when they collect the data, it can be recorded in sleeping subjects, and it contains less noise compared to functional MRI. So that's some background. Now we are talking about what's human brain network. So human brain network, basically based on the collected neuroimaging data, we compute the human brain network. Different brain regions as different nodes in the graph. And also we have the connections between different regions. So in the human brain networks, actually they include several modules and also hierarchical structure nature. So it's different from the unstructured, the 2D images and also the language data. So each graph node has a different number of neighbors and also has actually a varied graph structure and sizes, there's different number of unordered nodes. So another important is that you're in space and there's complex interactions between the different nodes. And so how do we calculate the activation on a large high-dimensional representation for the very complex human brain networks and for early detection of Alzheimer's disease? And so next, I introduce some different graph embedding techniques so we can use these techniques for human brain network embedding. So the first one actually is existing some graphical representation learning starting from 2016. The node2vec method actually is motivated from the Word2Vec proposed from Stanford group. And they can project the graph node representation as low-dimensional vectors in the embedding space. And the other type of approach is Graphical Gauss, is published in 2018. And also there are other similar works. They can encode the high-dimensional graph into density function space with Gaussian distributions. So they can actually quantify the uncertainty in the latent space for each graph node. And recently, years— I started from 2017, I created Graph Neural Network, Graph Convolution Neural Network, one more popular than the attention networks. However, this is also a learning environment of the representation of every representation as a vector in the UTV space. And now due to the large language models becomes very popular, the graph transformers model also, there are quite a lot of works on that. They can address the two main issues of the graph neural networks. Always speaking on the long-term dependency, but with the computational cost due to the self-attention mechanism. However, there are actually very limited methods that can capture the non-linear hierarchical property in the latent space. But this is very important for different downstream tasks, especially in healthcare and finance and transportation and many other domains. So this is a summary of my previous work on self-text-to-word embedding for static graph and temporal graphs. So we have done some static functional brain network embedding into Euclidean space before, basically to encode the brain network into a lower-dimensional Gaussian distribution. So to quantify the uncertainty information, basically how many subnetworks in the prefrontal cortex using the variance of the Gaussian values. So we saw our two previous papers published in 2020 and 2021 2021. And on the right panel, it shows the dynamic brain anatomy with recent works, 2022 and 2024. This year, January, we published around 2 papers on dynamic brain anatomy. And so this slide will introduce the static brain anatomy into the continuous space for the early stage Alzheimer's disease detection. Basically, this is not in hydrologic space, but in Euclidean space. But so this is for the real data set. We have 76 allocognitive impairment patients. They're actually 48 stable MCI patients and also 28 progressive patients. Basically, they will convert to dementia after 2 years. And we also have some normal control subjects, 53, for the classification tasks. And the imaging data is MEG data, is 5 minutes and 306 channels. So basically, based on the collected 5-minute resting state MEG data, we use the brain atlas including 68 brain regions. This is the regional texture data. And we can compute the information to generate the adjacency matrix for the brain connectivity. And then they actually developed an approach based on Gaussian embeddings. They can embed this brain connectivity into lower-dimensional Gaussian distribution in terms of mean and variance. And based on this embedding, we can actually do different downstream tasks. First one, we actually do the classification for AD progression prediction. And second one, we actually want to detect, as shown in this slide, we want to show which— we want to detect which brain regions with significant FTG network alterations between the different subgroups. For example, the very important two subgroups is the stable MCI and progressive MCI. Why those people converted to dementia after 2 years? So this is a significant brain region with significant alterations detected based on the embeddings we learned from the neural networks. And it's largely included in the temporal and frontal regions of the cortex. And the concept is previous study using other different neuroimaging data, especially the temporal lobe. We have the hippocampus, which is very important for the memory. Release, and we can actually store our memory. So basically, it means in the temporal low X-ray, they have a big alterations between the two different subgroups. And on the right side, it shows the classification results based on the different groups for the classification. We do the normal controls and the cerebral FCI and progressive And here in the next following slides, I will start to talk about why we want to choose a model space as an embedding space, because a lot of contexts in the real world actually exhibit underlying hierarchical structure property. For example, brain connectome and genetic state of protein network and ontology networks and so on. And U-Plane space has already introduced this for embedding vector. Like graph data has very high running time and memory issue. However, the model space that is shown here is connected code word, this one. Compared to the Euclidean space with a zero code word, you can see that actually, it can actually preserve both graph distances and the complex hierarchy extremely efficiently in very few dimensions. So on the right side, it shows the Poincaré disk. Actually, Ricky Chen just already presented the Poincaré disk and also the many-body manifold. So they can actually already kind of calculate that. So those scale-free graphs. So into at least a very high, like exponential growth gross space actually from the radius. We can see that this is the parent node of the binary tree and the XY are the children nodes. We can see that actually the red curve shows the Haveli distance and the pink curve shows the geodesic distances and the blue curve shows the Euclidean distances. So we can see that Haveli distance kind of actually approximate the geodesic distance in the hyperbolic space. And also, so here in this slide, we can show that more clear. So this is the Euclidean space to embed a tree-like graph. And also this is the hyperbolic space to embed the tree-like graph into the hyperbolic space. We can see that in the Euclidean space, actually nodes will overlap and also clustered together. So it requires higher dimensions in the embedding space to embed more nodes. However, in the hyperbolic space, it grows exponentially with hyperbolic radius and much close to the boundary of the Poincaré disk, we can see there are more space to embed those children nodes. And also it has a lower, much lower distortion actually is all the nodes can be separable in the latent space and require very small embedding size. So the important thing for us to study neural network is the hierarchical property. So this is some of the fundamental mathematical formulas for the hyperbolic space representation models. There are two very typical models for the hyperbolic manifold representation, this Poincaré model actually proposed in Meta company in 2017 and 2018, Dr. Minkow. I think, yeah. So you can see that compared to Conqueror, they have a very different distance formulas here. This is the DPxy, this is the DL in the Lorenzo model. So the distance is much simpler. So it's remarkably more stable and simpler formulas. And more efficiently running optimization, and it's scalable to larger datasets. And here the key is a co-referee. And who co-referes you? And here in the high-voltage space, we cannot use the stochastic gradient descent optimization easily. We need to use another optimizer. It is called remaining SGD optimizer. Basically, we need to operate maps the features from the— based on the exponential map from the tangent space to manifold and also manifold— from manifold to tangent space, use a log map. So this is how to compute the gradient of the parameter C(t), and this theta is the learning rate. And here, this is all our running SGD optimization, how to update these parameters.. And this is our objective function in the remaining manifold space. And here shows the Hebbotic embedding compared to the Gaussian embedding I used to work on for the brain networks. So Hebbotic embedding, we can see that this is from Dr. Nichols' paper in 2017 for the word, the language WordNet dataset. So we can see that in the center of the point cloud, we can see the word is more generic and has a high hierarchy. Also, go through towards the boundary, we can see to the location and to the city and to New York, it's more and more specific and has a lower hierarchy. So this is a very important property for us. To study brain networks. That's why we want to choose this approach to study the brain disease and also the aging trajectory detection over time. So next, I will present two recent projects. First one is using the hypergraph convolutional neural network. Actually, the first initial paper is published in 2019 from the Sapporo group. So here we work on the MEG data using the AAL brain atlas, including 90 brain regions, to learn the brain node embeddings for different brain cortical regions. And here is the output. And we can see that actually the triangle basically indicates the left hemisphere regions. And the circle represents the regions in the right hemisphere. So we can see actually it is split to different sides in the point cloud. So this is symmetric actually. This is a good validation for brain network because we have a left hemisphere and a right hemisphere. So this is very unusual because not many papers are using hypotony mapping for brain connectivity. So in the very beginning, we need to validate this approach works for brain connectome. And so in our project, we have 49 subjects who come into 5 patients. So basically those patients will have 5 times likely converted to Alzheimer's disease. And we also have another conversion group is 41 clinical normal subjects. So this paper is now under revision. So it's already on the preprint, it's on the bioRxiv. Yeah, we got very good comments recently from the IEEE workgroup journal. And here is a comparison for the experimental results for the link prediction task with 3 different baselines. Basically, it's a standard graph convolutional network in the Euclidean space and also temporary embedding. And another is a Heterograph HJCM model with a fixed curvature. And also, we also study the curvature as the learned parameters. We can see that based on the learned curvature settings, the C, capital C here, is a learned and active curvature. You can see that actually with a fixed curvature, actually the learned curvature can get actually better results, better performance. And also in another finding based on this result is also consistent with their very initial paper from 2017 is that in morpheme embeddings, we can only need fewer embedding dimensions compared to the Euclidean space adjacent. And we can see that they need embedding dimension 8 to achieve 82% accuracy. And here we can only use actually dimension 3 to obtain 95% accuracy for the interpolation task. So finally, we choose the 3 dimensions of this learned character C to generate the brain regional embeddings for the downstream task that we want to study. What's the difference between the hierarchical changes in different subnetworks. So here, this is the dorsal attention network. So this is the ventral attention network, and this is a sensor-motor network. So the blue bars show the healthy control, and also the red one shows the subject with cognitive decline. We can see that actually the SCD subjects has a very Decreased hierarchical radius, metabolic radius in the left-hand space basically means when the radius decreases, basically it means they lose more connections and the brain connections, basically the node degree will reduce. And so for the healthy normal control people, we have more stronger connectivity because maybe due to some dead neurons and so on. And also, this is some relations based on hierarchical operation to cognition based on some other literatures. So the three subnetworks with pronounced operations between the two subgroups actually correlated to some higher scores on the depression scale. So, and the central motor network also has greater impairment in completing daily function activities. And also, those with attention have a higher subjectivity of reading or memory failures. So this is our important detection for studying the SCD prediction. And this is what we study because if you want to ask, actually, the brain network is not the largest viewgraph, why you don't need when you just compute based on the original adjacency matrix is a small matrix. Based on that paper, this is the blue, this is a histogram, and the blue histogram, the bars show based on the original adjacency matrix, then the classification result. However, the green and red marks show based on the embedding paper and also combine the embedding paper with the original adjacency matrix papers. We can see actually that the bottleneck features capture partially unique features and improve the classification scores over the original adjacent features. And the second project that we want to talk— I want to talk about is about the very recent work, actually very recent in the next week, is on the human brain aging trajectory on 600 healthy patients across 7 decades. Age decades. So from 18-year-old to 89-year-old. So we have the MEG neuroimaging data, and also we want to detect the changes in regional level and also subject level across time. So this is our dataset from the CONCOM dataset. So we have 7 different decades from very like teenager to like more older people, 80 to 90 years old. And we have— and this is how many female subjects. Basically 50% are female and 50% male, approximately. So in total, we have 587 subjects. And the imaging data is still the functional FDG neuroimaging data computed based on the brain atlas HCP. It's a very public one, including 368 brain cortical regions in brain. And so this is a physical value, basically is a metric for the brain connectivity estimation. So this dataset is from our collaborators in Italy, University of Trento, actually. They have an MEG center there. And so in this dataset, we also have other multi-modal features like cortical thickness, basically based on the structural MRI dataset. Mirror the thickness of the cortical. And also we have another melanation. This is also very, as demonstrated, is a very nice indicator for aging, human brain aging. So we have two different modality features and also the imaging, neuroimaging brain networks. And we input these novel features and also the brain asymmetries to the embodied graph convolutional neural network generates a human brain network embeddings. And this is, we want to quantify the heterogeneity changes over age decades, 7 different age decades. And every age decade, we have around, I think, 100 subjects, less than 100, 80 subjects around 85. So this is for the right-to-ear visual forecast, we can see that actually the hippocampal regions are increasing over aging decades. So this is basically reduced hierarchy of right area visual cortex during aging among these 587 subjects. And this is more detailed results based on the MRI, basically the region of interest, so that hierarchical changes across aging decades. For 6 different subnetworks, we can see actually the interesting finding in this project is some sensory and motor subnetworks, we can see actually they maintain the hierarchical radius, actually maintain until 60 years old and after 60, 70 years old, it exponentially grows. Basically the connection lose after 60 or 70 years old. However, like this one is the primary, so basically it's a very important area in our brain. And it's like a linear increase, basically the hierarchical decrease linearly. So it's like a heterogeneous changes over time. And this is a cortex hypotrophic radius for different cell network level. And the different color bars show the different 7 different age decades. So the blue, the purple show the teenagers, 18 to 30 years old. And then we can see actually some basically we compute the slope for this each subnetwork. And this is the final result based on subnetwork-level hierarchical gradient slope. So this way, the subnetwork with the larger slope value have more pronounced hierarchical changes during aging. We can see the primary visual, early visual cortex has higher hierarchical changes over aging. However, the early auditory and posterior operocular has relatively unchanged hierarchical So this is more studies about in the hyperbolic space, basically the embedding space. We study the different— we compare the first decade, basically the 18 years old to 30 years old. And for the early visual, basically we find that we have increased average hyperbolic gradient. Basically decrease the hierarchical loss more connections over aging. And this is the 7 decades. When the people are between 80 years old and 90 years old, we can see this is a— the hippocampus really increase after the 7th decade. So when you get aging, overaging, so the early visual cortex basically decrease the hierarchy, lose more connections. Due to some dead neurons. And this is an early auditory. We can see in the hyperbolic space, they didn't change that much. This way, it remained unchanged between the first age decade and the sixth age decade. And this is a visualization in the 3D human brain for the left hemisphere, this side, and right hemisphere. So this is an early visual subnetwork region basically is in the occipital lobe. They can process some images and is a very important area. And here the sensory and motor is a second subnetwork. It found has increasing load here. The largest load is the decrease hierarchy. So these are the very important regions, basically the subnetwork-level hierarchical changes for the aging, human brain aging trajectories. And lastly, I want to thank all my great collaborators at MIT. This way, I work with two master's students for their master's thesis in 2021, 2022, and 2023. They are graduating now. Working in the Amazon Robotics and some startup. And also thank you my collaborator from Madrid to provide the dataset called ICD, the first project. And the second project, the dataset provided from the University of Genoa in Italy. And also thank you other collaborator from the Johns Hopkins and the Houston, the University of Texas at Houston Center. And my DOE grant. And these are all the references about this embedding work for brain networks and two for the embedding networks. Okay, thank you very much. Thanks. Exhale. Also, there is some fresh copies, if you want to grab some.