Beyond for Loops: Performing Group Means with PyTorch's scatter_ Function

While PyTorch doesn't have a built-in groupby function, you can achieve group-wise mean calculation using a combination of techniques:

Identifying Groups:

• You'll need a tensor called labels that assigns each element in your data tensor (data) to a specific group. This labels tensor can be of type torch.LongTensor or torch.int64.

Using scatter_ for Efficient Grouping:

• PyTorch's torch.scatter_ function provides a powerful way to calculate the mean for each group. Here's the core idea:
  1. Create a new tensor (means) to store the group means, initialized with ones (representing the weights for averaging).
  2. Use labels.unsqueeze(1).repeat((1, data.size(1))) to create a 2D index for each data element. The first dimension corresponds to the group, and the second to the data element's position within that group.
  3. Employ means.scatter_(dim=0, index=index, src=data, reduce='mean'). This efficiently calculates the mean for each group:
     • dim=0: Specifies that the scattering happens along the group dimension (rows).
     • index: The 2D index tensor created earlier.
     • src=data: The data tensor containing the values.
     • reduce='mean': Instructs the operation to calculate the mean within each group.

Code Example:

import torch

# Sample data and labels
data = torch.tensor([[0.1, 0.1], [0.2, 0.2], [0.4, 0.4], [0.0, 0.0]])
labels = torch.LongTensor([1, 2, 2, 0])

# Calculate group means using scatter_
label_size = labels.unique().size(0)  # Number of unique groups
means = torch.ones(label_size, data.size(1))  # Initialize with ones for weighting
index = labels.unsqueeze(1).repeat((1, data.size(1)))
means.scatter_(0, index, data, reduce='mean')

print(means)

This code will output the mean for each group in the means tensor.

Alternative Approaches (if applicable):

• torch.unique and Looping: If your dataset is small or you prefer a more explicit approach, you can use torch.unique to get the unique groups and iterate over them, calculating the mean for each group within the loop. However, scatter_ is generally more efficient for larger datasets.
• Third-Party Libraries: Libraries like torch-cluster offer functionalities for grouping and aggregation, but scatter_ often provides a more concise and performant solution.

Key Points:

• labels identifies group membership for each data element.
• scatter_ efficiently calculates the mean within each group based on the index and reduces using the 'mean' option.
• The code example demonstrates how to use scatter_ for group-wise mean calculation.

import torch

# Sample data and labels
data = torch.tensor([[0.1, 0.1], [0.2, 0.2], [0.4, 0.4], [0.0, 0.0]])
labels = torch.LongTensor([1, 2, 2, 0])

# Calculate group means using scatter_
label_size = labels.unique().size(0)  # Number of unique groups
means = torch.ones(label_size, data.size(1))  # Initialize with ones for weighting
index = labels.unsqueeze(1).repeat((1, data.size(1)))
means.scatter_(0, index, data, reduce='mean')

print(means)

Explanation:

• This code defines data and labels tensors representing the data and group membership, respectively.
• It calculates the number of unique groups using labels.unique().size(0).
• A tensor means is initialized with ones, which will be used for weighting during average calculation.
• index is created by expanding the labels tensor and repeating it for each data element dimension. This creates a 2D index for each data point, reflecting its group and position within the group.
• Finally, means.scatter_(0, index, data, reduce='mean') efficiently calculates the mean within each group along the group dimension (row 0). The index specifies where to accumulate the values, data is the source tensor, and reduce='mean' instructs the operation to calculate the average.

Using torch.unique and Looping (Less Efficient for Large Datasets):

import torch

# Sample data and labels
data = torch.tensor([[0.1, 0.1], [0.2, 0.2], [0.4, 0.4], [0.0, 0.0]])
labels = torch.LongTensor([1, 2, 2, 0])

# Calculate group means using loop
unique_groups, counts = labels.unique(return_counts=True)
means = torch.zeros(unique_groups.size(0), data.size(1))
for i, group in enumerate(unique_groups):
  group_indices = (labels == group).nonzero()[:, 0]  # Indices of elements in each group
  means[i] = data[group_indices].mean(dim=0)  # Calculate mean for each group

print(means)

• This code iterates through unique groups identified using torch.unique(return_counts=True).
• For each group, it finds the indices of elements belonging to that group using (labels == group).nonzero()[:, 0].
• It then calculates the mean of the data elements within those indices using data[group_indices].mean(dim=0).
• Finally, the calculated mean for each group is stored in the means tensor.

Which approach to choose?

• For larger datasets, scatter_ is generally more efficient due to its vectorized operations.
• If your dataset is small or you prefer a more explicit approach for understanding, the loop-based method can be used.
• Consider using third-party libraries like torch-cluster for more complex grouping and aggregation tasks if applicable.

While less efficient than scatter_, this method can be helpful for understanding the core logic:

import torch

def groupby_mean(data, labels):
  """
  Custom function for group-wise mean calculation.

  Args:
      data: Tensor containing the data to be grouped.
      labels: Tensor indicating group membership for each data element.

  Returns:
      means: Tensor containing the mean for each group.
  """
  unique_groups, _ = labels.unique(return_counts=True)
  means = torch.zeros(unique_groups.size(0), data.size(1))
  for i, group in enumerate(unique_groups):
    group_mask = labels == group  # Create a mask for the group
    means[i] = data[group_mask].mean(dim=0)  # Calculate mean using the mask
  return means

# Example usage
data = torch.tensor([[0.1, 0.1], [0.2, 0.2], [0.4, 0.4], [0.0, 0.0]])
labels = torch.LongTensor([1, 2, 2, 0])
group_means = groupby_mean(data, labels)
print(group_means)

• This defines a groupby_mean function that takes data and labels as input.
• It iterates through unique groups and creates a mask using labels == group.
• The mean is then calculated for the elements where the mask is True (belonging to the current group).

Third-Party Libraries (for Specific Needs):

Libraries like torch-cluster offer functionalities specifically designed for grouping and aggregation tasks. These can be advantageous for:

• More complex grouping: If your grouping criteria involve more than just group labels, these libraries can handle hierarchical or k-nearest neighbor-based groupings.
• Additional aggregation functions: They may support calculations beyond mean, such as sum, standard deviation, or more specialized functions.

Choosing the Right Method:

• For basic group-wise mean calculation, scatter_ is the recommended approach due to its efficiency.
• If you need to understand the underlying logic, the custom function with a loop can be used for educational purposes.
• Consider third-party libraries like torch-cluster when dealing with complex grouping criteria or requiring additional aggregation functions beyond mean.