tsl is meant to deal with discrete-time spatiotemporal data, i.e., signals that evolve over discrete points in time and space. Common input examples are data coming from sensor networks. In principle, data of this kind can be represented by 3-dimensional tensors, with:
The Time (
t) dimension, accounting for the temporal evolution of the signal within a node (i.e., a sensor).
The Node (
n) dimension, accounting for simultaneous observations measured at the different nodes in the network in a given time step.
The Features (
f) or Channels dimension, allowing for multiple (heterogeneous) measurements at the same spatio-temporal point.
We call a spatiotemporal graph a tensor with finite
f dimensions, paired with the underlying topology. In tsl, we use the
tsl.data.Data to represent and store the attributes of
a single spatiotemporal graph.
tsl.data.Data object contains attributes related to a single spatiotemporal graph.
This object extends
torch_geometric.data.Data, preserving all its functionalities and
adding utilities for spatiotemporal data processing. The main APIs of
Data.input: view on the tensors stored in
Datathat are meant to serve as input to the model. In the simplest case of a single node-attribute matrix, we could just have
Data.target: view on the tensors stored in
Dataused as labels to train the model. In the common case of a single label, we could just have
Data.edge_index: graph connectivity. Can be in COO format (i.e., a
[2, E]) or in form of a
[N, N]. For dynamic graphs – with time-varying topology –
edge_indexis a Python list of
Data.edge_weight: weights of the graph connectivity, if
Data.edge_indexis not a
torch_sparse.SparseTensor. For dynamic graphs,
edge_weightis a Python list of
Data.mask: binary mask indicating the data in
Data.target.yto be used as ground-truth for the loss (default is
Data.transform: mapping of
ScalerModule, whose keys must be transformable (or transformed) tensors in
Data.pattern: mapping containing the pattern for each tensor in
None of these attributes are required and custom attributes can be seamlessly added.
Data.target – of type
provide a view on the unique (shared) storage in
Data, such that
the same key in
Data.target cannot reference different
If the graph connectivity changes over time, you can pass Python lists as
We now consider a simple fully-connected, undirected graph with 3 nodes as the
underlying topology. We assume to have a univariate signal – uniformly sampled
and synchronized across nodes – on each node, plus a graph-wise exogenous
variable (may be, for instance, an encoding of time, equal for all nodes). If we
now want to forecast the next step given a sequence of 12 observations, our
Data object would look like this:
import torch from tsl.data import Data edge_index = torch.tensor([[0, 0, 1, 1, 2, 2], [1, 2, 0, 2, 0, 1]], dtype=torch.long) input = dict( x=torch.randn(12, 3, 1), # t=12 n=3 f=1 u=torch.randn(12, 4) # t=12 f=4 ) target = dict( y=torch.randn(1, 3, 1) # t=1 n=3 f=1 ) data = Data(input=input, target=target, edge_index=edge_index) >>> Data( input=(x=[12, 3, 1], u=[12, 4]), target=(y=[1, 3, 1]), has_mask=False )
Since we know also to which dimension each axis refers to in the tensors, it is
a best practice to explicit them in the
Data object through patterns.
pattern = dict(x='t n f', u='t f', y='t n f') data = Data(input=input, target=target, edge_index=edge_index, pattern=pattern) >>> Data( input=(x=[t=12, n=3, f=1], u=[t=12, f=4]), target=(y=[t=1, n=3, f=1]), has_mask=False )
The usage of patterns is not mandatory, although they clarify the dimensions of each tensor in a spatiotemporal graph object and are used internally by tsl for operations on graphs (e.g., reduction to subgraph, temporal resampling, tensors collation).
tsl.data.StaticBatch object models a temporal graph signal over a
static graph: while data change over time, the topology does not. This object
tsl.data.Data, and has two additional methods for collating
Data objects into
The class method
from_data_list() creates a new
tsl.data.StaticBatch object from a list of
objects. The implicit assumption is that all objects in the list share the
same topology, and only the graph in the first object is kept. Accordingly,
all the tensors in the
Data objects having a static signal (i.e., without
temporal dimension) are not collated – only one copy of them is kept. Instead,
all time-varying data are stacked along the first dimension, as usually done
in mini-batch collations. Also,
objects are collated or copied in a similar fashion. Consider also that the
changes made in the tensors are then reflected in the
Conversely, the method
idx-th sample in the batch. This can be equally
achieved through the
__get_item__ function as
supports also slices. Note that you can use this function also on
StaticBatch that have been directly instantiated, without the use of the
More generally, data at hand come from a possibly dynamic setting, in which also the underlying topology changes over time. We supports two different types of discrete-time dynamic graph signals:
Disjoint Graph Signals, where the topology is static within the temporal window of a sample, but may change from a sample to another. This is a common scenario when we put together multiple temporal graph signals, each on a different (static) graph.
Dynamic Graph Signals, where the topology may change not only from sample to sample, but also from a time step to another in the same temporal window.