# Are there any well-known ways to fuzzy-cluster (variable length) sequences of trajectories?

I have this issue where I need to create 'soft' clusters for different trajectories. The data is sequences of integers where each integer means a specific point; so I have sequences like $$s=(1,47,9)$$ or $$s=(23,50,47,9)$$. Here is what I found on the Internet:

• When I'm searching 'sequence clustering' I find a lot of biology papers on the topic but the proposed approaches don't suit my issue. Sometimes they rely on Chaos Game Representation which I read is a method developed specifically for the DNA sequences, sometimes they rely on some statistics based on the base-pairs etc.
• I also searched about Graph Neural Networks (GNNs), thinking about each sequence as visiting a node from the graph, but I saw that there GNNs aren't used in any way that'll help with that goal.
• I also read many papers on trajectories clustering but since those papers used the position and velocity' data which I don't have (and I'm only interested in the visits of specific points).
• I also saw attempts of using Convolutional Neural Networks (CNNs) on images generated from mouse movements or similar trajectories but I don't think it'll work for me since my data is so sparse, for example $$s_{1}=(1,2,3,4)$$ should be in the same clsuter as $$s_{2}=(1,2,3,50)$$ but since point $$50$$ may be really far from the others, it may cause the CNNs extracting features that won't help regrouping them in the same cluster (or at least both they have a high probability of being in the same cluster).

And I thought of doing the following:

• Considering only how many times an integers figure in the sequence dividede by how many times he figures in all of the sequences, but this will not take the order of visits.
• I also thought using an embedding layer with 0-padding and then apply fuzzy clustering algorithm on the results of the embedding layer, but I'm not sure if this approach works.