PHATE: Fixing Incompatible Settings For Advanced Analysis
Introduction
In this comprehensive article, we will delve into a specific issue encountered when using the PHATE (Potential of Heat-diffusion for Affinity-based Transition Embedding) library, a powerful tool for visualizing and analyzing high-dimensional data. Specifically, we will address the incompatibility between random landmarking and precomputed affinities within PHATE. Understanding and resolving this issue is crucial for researchers and data scientists who rely on PHATE for their data analysis pipelines, particularly when dealing with large datasets and non-Euclidean distance metrics. We will explore the bug, its causes, and potential solutions, ensuring you can effectively leverage PHATE's capabilities for your projects.
Understanding the Issue: Random Landmarking and Precomputed Affinities
The core of the problem lies in the interaction between two key features of PHATE: random landmarking and the use of precomputed affinity matrices. To fully grasp the issue, it's essential to understand what these features do individually and how their combination leads to an error.
Random Landmarking
Random landmarking is a technique employed to scale dimensionality reduction methods, like PHATE, to very large datasets. Instead of considering all data points, a subset of points, known as landmarks, are randomly selected. The algorithm then focuses on computing relationships between these landmarks and the remaining data points. This significantly reduces the computational burden, making it feasible to analyze datasets with millions of data points. By strategically choosing landmarks, the essential structure of the data can be preserved while drastically cutting down on processing time. Random landmarking is particularly useful when memory constraints are a concern, as it allows the algorithm to operate on a smaller subset of the data at any given time.
Precomputed Affinities
Precomputed affinity matrices, on the other hand, offer a way to incorporate non-Euclidean distance metrics into PHATE. Typically, PHATE relies on Euclidean distances to measure the similarity between data points. However, in many real-world scenarios, Euclidean distance might not be the most appropriate measure. For instance, in gene expression analysis or social network analysis, other metrics like correlation or network connectivity might better capture the underlying relationships. By precomputing an affinity matrix – a matrix where each element represents the similarity between two data points based on a chosen metric – users can provide PHATE with a more tailored representation of their data. This allows PHATE to be applied in a wider range of contexts, capturing complex relationships that Euclidean distance alone would miss. The flexibility of using precomputed affinities enhances PHATE's applicability in various domains.
The Incompatibility
The problem arises when you try to use both random landmarking and precomputed affinities simultaneously. The current implementation of PHATE does not fully support this combination, leading to an error. The error message, as reported, is not particularly informative, making it challenging for users to diagnose the issue. The crux of the problem seems to be in how points are assigned to landmarks when using a precomputed affinity matrix. The assignment process, in the default implementation, appears to rely on Euclidean distances, which contradicts the very purpose of using precomputed affinities in the first place. This limitation prevents the use of powerful techniques like RF-PHATE and RF-AE, which depend on custom affinity matrices, in large-scale applications where random landmarking is essential. Addressing this incompatibility would significantly broaden PHATE's utility and accessibility.
Bug Report: A Deep Dive into the Error
To illustrate the issue, let's examine the bug report provided, which clearly outlines the problem and the steps to reproduce it. We'll break down the code and the resulting error message to gain a clearer understanding.
Code to Reproduce the Bug
The following Python code snippet, using the phate library, demonstrates the bug:
import scipy.sparse as sp
import numpy as np
from phate import PHATE
seed = 42
np.random.seed(seed)
# Generate a random 10k x 10k sparse affinity matrix
n = 10_000
density = 0.0005
# random non-negative affinities
A = sp.random(n, n, density=density, data_rvs=lambda k: np.random.rand(k))
# ensure strictly positive diagonal
A.setdiag(np.random.rand(n) + 1e-3)
print("Random affinity matrix:", A.shape, "nnz:", A.nnz)
# PHATE with precomputed affinity and random landmarking
phate_operator = PHATE(
n_jobs=-1,
random_state=seed,
random_landmarking=True,
knn_dist="precomputed_affinity"
)
emb_train = phate_operator.fit_transform(A)
This code first generates a random sparse affinity matrix A of size 10,000 x 10,000. It then attempts to use PHATE with random_landmarking=True and knn_dist="precomputed_affinity". This specific combination triggers the bug.
The Error Message
When the fit_transform method is called, the following error occurs:
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
File ~/Projects/RF-GAP-Python/.venv/lib/python3.12/site-packages/graphtools/graphs.py:1129, in LandmarkGraph.landmark_op(self)
1128 try:
-> 1129 return self._landmark_op
1130 except AttributeError:
AttributeError: 'TraditionalLandmarkGraph' object has no attribute '_landmark_op'
During handling of the above exception, another exception occurred:
ValueError Traceback (most recent call last)
Cell In[4], line 26
19 # PHATE with precomputed affinity and random landmarking
20 phate_operator = PHATE(
21 n_jobs=-1,
22 random_state=seed,
23 random_landmarking=True,
24 knn_dist="precomputed_affinity"
25 )
---> 26 emb_train = phate_operator.fit_transform(A)
File ~/Projects/RF-GAP-Python/.venv/lib/python3.12/site-packages/phate/phate.py:1033, in PHATE.fit_transform(self, X, **kwargs)
1012 """Computes the diffusion operator and the position of the cells in the
1013 embedding space
1014
(...) 1030 The cells embedded in a lower dimensional space using PHATE
1031 """
1032 with _logger.log_task("PHATE"):
-> 1033 self.fit(X)
1034 embedding = self.transform(**kwargs)
1035 return embedding
File ~/Projects/RF-GAP-Python/.venv/lib/python3.12/site-packages/phate/phate.py:929, in PHATE.fit(self, X)
919 warnings.warn(
920 f"Graph is disconnected with {self.graph.n_connected_components} "
921 f"connected components. This may indicate that your knn parameter "
(...) 925 RuntimeWarning,
926 )
928 # landmark op doesn't build unless forced
---> 929 self.diff_op
930 return self
File ~/Projects/RF-GAP-Python/.venv/lib/python3.12/site-packages/phate/phate.py:318, in PHATE.diff_op(self)
316 if self.graph is not None:
317 if isinstance(self.graph, graphtools.graphs.LandmarkGraph):
--> 318 diff_op = self.graph.landmark_op
319 else:
320 diff_op = self.graph.diff_op
File ~/Projects/RF-GAP-Python/.venv/lib/python3.12/site-packages/graphtools/graphs.py:1131, in LandmarkGraph.landmark_op(self)
1129 return self._landmark_op
1130 except AttributeError:
-> 1131 self.build_landmark_op()
1132 return self._landmark_op
File ~/Projects/RF-GAP-Python/.venv/lib/python3.12/site-packages/graphtools/graphs.py:1212, in LandmarkGraph.build_landmark_op(self)
1210 distances = euclidean_distances(data, data[landmark_indices])
1211 else:
--> 1212 distances = cdist(data, data[landmark_indices], metric=self.distance)
1213 self._clusters = np.argmin(distances, axis=1)
1215 else:
File ~/Projects/RF-GAP-Python/.venv/lib/python3.12/site-packages/scipy/spatial/distance.py:3111, in cdist(XA, XB, metric, out, **kwargs)
3108 sB = XB.shape
3110 if len(s) != 2:
-> 3111 raise ValueError('XA must be a 2-dimensional array.')
3112 if len(sB) != 2:
3113 raise ValueError('XB must be a 2-dimensional array.')
ValueError: XA must be a 2-dimensional array.
The traceback indicates a ValueError: XA must be a 2-dimensional array. within the scipy.spatial.distance.cdist function. This suggests that the input data XA is not being correctly processed as a 2-dimensional array when precomputed affinities are used in conjunction with random landmarking. The error occurs during the landmark operator construction, specifically when computing distances between data points and landmarks.
Root Cause Analysis
The error arises because the cdist function, used for computing distances, expects a 2-dimensional array as input. When precomputed affinities are provided, the internal logic for handling distance computations in the presence of random landmarking does not correctly process the affinity matrix. The algorithm attempts to compute distances using a metric that is incompatible with the precomputed affinity data structure. This highlights a disconnect in how PHATE manages landmark assignment when custom affinity measures are involved. The crucial step of assigning points to landmarks, which should respect the precomputed affinities, instead falls back on a distance calculation that is not appropriate for the input data.
Proposed Solution and Expected Behavior
To address this issue, a more robust approach to assigning points to landmarks when using precomputed affinities is needed. The ideal behavior would be for PHATE to leverage the precomputed affinity matrix directly when building the transition matrix from points to landmarks. This would ensure that the landmarking process respects the custom similarity metric encoded in the affinity matrix.
Building a Transition Matrix with Precomputed Affinities
The central question is: Given a set of randomly selected landmarks and a precomputed affinity matrix, how can we construct a transition matrix that reflects the affinities between points and landmarks? This involves devising a method to translate the affinity scores into probabilities of transitioning from a data point to a landmark.
One potential approach involves normalizing the affinity scores. For each data point, we can consider the affinity scores to all landmarks as a set of unnormalized probabilities. By normalizing these scores (e.g., dividing each score by the sum of scores for that data point), we obtain probabilities that can be used to build the transition matrix. This ensures that each data point has a probability distribution over the landmarks, reflecting its affinity to each landmark.
Expected Behavior
If the assignment step correctly uses the precomputed affinity matrix, the behavior should mirror that of the default spectral-clustering mode. In essence, the random landmarking should serve as a scalable approximation of the full affinity-based analysis. The resulting embedding should capture the essential structure of the data as defined by the precomputed affinities, even when dealing with millions of data points. This enhancement would make PHATE a more versatile tool for large-scale data analysis with non-Euclidean metrics. By aligning the landmark assignment with the precomputed affinities, the algorithm would maintain consistency and accuracy, regardless of the dataset size.
Addressing the Error Message
In addition to fixing the underlying incompatibility, it's crucial to provide users with more informative error messages. The current ValueError is not specific enough and doesn't clearly indicate the cause of the problem. A more helpful message would explicitly state that the combination of random_landmarking=True and knn_dist="precomputed_affinity" is not currently supported and potentially suggest alternative approaches or workarounds.
Improved Error/Warning Message
A better error or warning message could be structured as follows:
Warning: The combination of `random_landmarking=True` and `knn_dist="precomputed_affinity"` is not fully supported in the current version of PHATE. This may lead to unexpected behavior or errors.
Explanation: When using precomputed affinities, random landmarking requires a specialized method for assigning points to landmarks. The current implementation does not fully support this, potentially leading to incorrect distance computations.
Recommendation: Consider using one of the following alternatives:
1. If possible, disable `random_landmarking` for smaller datasets.
2. Explore alternative landmarking strategies or custom implementations that are compatible with precomputed affinities.
3. Check for updates to the PHATE library, as this issue may be addressed in future releases.
This message not only informs the user about the issue but also provides context and actionable recommendations. By clearly explaining the problem and offering potential solutions, users can better understand how to proceed with their analysis. Informative error messages are essential for a user-friendly experience, especially when dealing with complex algorithms like PHATE.
System Information and Software Versions
The bug report includes valuable system information and software versions, which can be crucial for debugging and ensuring consistent behavior across different environments. Let's review this information.
PHATE Version
The PHATE version reported is '2.0.0'. This is essential for identifying whether the bug is specific to a particular version or a more general issue. When reporting bugs or seeking help, including the software version is a standard practice that aids in troubleshooting.
Pandas and Related Libraries
The output of pd.show_versions() provides a comprehensive list of installed versions for pandas and its dependencies, including numpy, scipy, and others. These libraries play a critical role in data manipulation and numerical computations within PHATE. Any inconsistencies or version conflicts among these libraries could potentially lead to unexpected behavior. For instance, the versions reported are:
- pandas:
2.3.3 - numpy:
2.3.4 - scipy:
1.16.3
Ensuring that these libraries are compatible with the PHATE version is crucial for a stable and reliable analysis environment. Version information helps in replicating the bug and identifying potential dependencies that might be contributing to the issue. The detailed output from pd.show_versions() is a valuable resource for maintaining a consistent software environment.
Conclusion
In conclusion, the incompatibility between random landmarking and precomputed affinities in PHATE presents a significant challenge for large-scale data analysis with non-Euclidean metrics. The current error message is not sufficiently informative, and the underlying issue stems from how landmark assignments are handled when using precomputed affinities. To address this, PHATE needs a more robust method for building the transition matrix from points to landmarks, one that directly leverages the precomputed affinity matrix.
By implementing a solution that correctly incorporates precomputed affinities into the landmarking process and providing more informative error messages, PHATE can become an even more powerful and versatile tool for data scientists and researchers. This will enable the application of techniques like RF-PHATE and RF-AE to massive datasets, opening up new possibilities for data exploration and visualization. Fixing this issue will broaden PHATE's applicability and solidify its position as a leading dimensionality reduction technique. For more in-depth information on PHATE and related techniques, you can visit the official PHATE documentation.
