A Python Toolkit for Evaluating the Reliability of Dimensionality Reduction Embeddings
Project description
ZADU: A Python Library for Evaluating the Reliability of Dimensionality Reduction Embeddings
ZADU is a Python library that provides distortion measures for evaluating and analyzing dimensionality reduction (DR) embeddings. The library supports a diverse set of local, cluster-level, and global distortion measures, allowing users to assess DR techniques from various structural perspectives. By offering an optimized execution and pointwise local distortions, ZADU enables efficient and in-depth analysis of DR embeddings.
Installation
You can install ZADU via pip
:
pip install zadu
Supported Distortion Measures
ZADU currently supports a total of 17 distortion measures, including:
- 7 local measures
- 4 cluster-level measures
- 6 global measures
For a complete list of supported measures, refer to measures.
How To Use ZADU
ZADU provides two different interfaces for executing distortion measures. You can either use the main class that wraps the measures, or directly access and invoke the functions that define each distortion measure.
Using the Main Class
Use the main class of ZADU to compute distortion measures. This approach benefits from the optimization, providing faster performance when executing multiple measures.
from zadu import zadu
hd, ld = load_datasets()
spec = [{
"id" : "tnc",
"params": { "k": 20 },
}, {
"id" : "snc",
"params": { "k": 30, "clustering": "hdbscan" }
}]
scores = zadu.ZADU(spec, hd).measure(ld)
print("T&C:", scores[0])
print("S&C:", scores[1])
hd
represents high-dimensional data, ld
represents low-dimensional data
ZADU Class
The ZADU class provides the main interface for the Zadu library, allowing users to evaluate and analyze dimensionality reduction (DR) embeddings effectively and reliably.
Class Constructor
The ZADU class constructor has the following signature:
class ZADU(spec: List[Dict[str, Union[str, dict]]], hd: np.ndarray, return_local: bool = False)
Parameters:
spec
A list of dictionaries that define the distortion measures to execute and their hyperparameters. Each dictionary must contain the following keys:
-
"id"
: The identifier of the distortion measure, such as"tnc"
or"snc"
. -
"params"
: A dictionary containing hyperparameters specific to the chosen distortion measure.
List of ID/Parameters for Each Function
Local Measures
Measure | ID | Parameters | Range | Optimum |
---|---|---|---|---|
Trustworthiness & Continuity | tnc | k=20 |
[0.5, 1] | 1 |
Mean Relative Rank Errors | mrre | k=20 |
[0, 1] | 1 |
Local Continuity Meta-Criteria | lcmc | k=20 |
[0, 1] | 1 |
Neighborhood hit | nh | k=20 |
[0, 1] | 1 |
Neighbor Dissimilarity | nd | k=20 |
R+ | 0 |
Class-Aware Trustworthiness & Continuity | ca_tnc | k=20 |
[0.5, 1] | 1 |
Procrustes Measure | proc | k=20 |
R+ | 0 |
Cluster-level
Measure | ID | Parameters | Range | Optimum |
---|---|---|---|---|
Steadiness & Cohesiveness | snc | iteration=150, walk_num_ratio=0.3, alpha=0.1, k=50, clustering_strategy="dbscan" |
[0, 1] | 1 |
Distance Consistency | dsc | [0.5, 1] | 0.5 | |
Internal Validation Measures | ivm | measure="silhouette" |
Depends on IVM | Depends on IVM |
Clustering + External Clustering Validation Measures | c_evm | measure="arand", clustering="kmeans", clustering_args=None |
Depends on EVM | Depends on EVM |
Global
Measure | ID | Parameters | Range | Optimum |
---|---|---|---|---|
Stress | stress | R+ | 0 | |
Kullback-Leibler Divergence | kl_div | sigma=0.1 |
R+ | 0 |
Distance-to-Measure | dtm | sigma=0.1 |
R+ | 0 |
Topographic Product | topo | k=20 |
R | 0 |
Pearson’s correlation coefficient | pr | [-1, 1] | 1 | |
Spearman’s rank correlation coefficient | srho | [-1, 1] | 1 |
hd
A high-dimensional dataset (numpy array) to register and reuse during the evaluation process.
return_local
A boolean flag that, when set to True
, enables the computation of local pointwise distortions for each data point. The default value is False
.
Directly Accessing Functions
You can also directly access and invoke the functions defining each distortion measure for greater flexibility.
from zadu.measures import *
mrre = mean_relative_rank_error.measure(hd, ld, k=20)
pr = pearson_r.measure(hd, ld)
nh = neighborhood_hit.measure(ld, label, k=20)
Advanced Features
Optimizing the Execution
ZADU automatically optimizes the execution of multiple distortion measures. It minimizes the computational overhead associated with preprocessing stages such as pairwise distance calculation, pointwise distance ranking determination, and k-nearest neighbor identification.
Computing Pointwise Local Distortions
Users can obtain local pointwise distortions by setting the return_local flag. If a specified distortion measure produces local pointwise distortion as intermediate results, it returns a list of pointwise distortions when the flag is raised.
from zadu import zadu
spec = [{
"id" : "dtm",
"params": {}
}, {
"id" : "mrre",
"params": { "k": 30 }
}]
zadu_obj = zadu.ZADU(spec, hd, return_local=True)
global_, local_ = zadu_obj.measure(ld)
print("MRRE local distortions:", local_[1])
Visualizing Local Distortions
With the pointwise local distortions obtained from ZADU, users can visualize the distortions using various distortion visualizations. We provide ZADUVis, a python library that enables the rendering of two disotortion visualizations: CheckViz and the Reliability Map.
from zadu import zadu
from zaduvis import zaduvis
import matplotlib.pyplot as plt
from sklearn.manifold import TSNE
from sklearn.datasets import fetch_openml
## load datasets and generate an embedding
hd = fetch_openml('mnist_784', version=1, cache=True).target.astype(int)[::7]
ld = TSNE.fit_transform(hd)
## Computing local pointwise distortions
specs = [{"id": "snc", "params": {"k": 50}}]
zadu_obj = zadu.ZADU(spec, hd, return_local=True)
global_, local_ = zadu_obj.measure(ld)
l_s = local_[0]["local_steadiness"]
l_c = local_[0]["local_cohesiveness"]
## Visualizing local distortions
fig, ax = plt.subplots(1, 2, figsize=(20, 10))
zaduvis.checkviz(ld, l_s, l_c, ax=ax[0])
zaduvis.reliability_map(ld, l_s, l_c, ax=ax[1])
The above code snippet demonstrates how to visualize local pointwise distortions using CheckViz and Reliability Map plots.
Documentation
For more information about the available distortion measures, their use cases, and examples, please refer to our paper [TBD].
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