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ZADU

A-to-Z python library for evalUating Dimensionality reduction

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 20 distortion measures, including:

  • 7 local measures
  • 5 cluster-level measures
  • 8 global measures

For a complete list of supported measures, refer to measures. The library initially provided 17 measures when it was first introduced by our academic paper. We added three more measures (label trustworthiness & continuity, non-metric stress, and scale-normalized stress) to the library.

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_strategy": "dbscan" }
}]

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

Warning: While using dsc, ivm, c_evm, nh, and ca_tnc, please be aware that these measures assume that class labels are well-separated in the original high-dimensional space. If the class labels are not well-separated, the measures may produce unreliable results. Use the measure only if you are confident that the class labels are well-separated. Please refer to the related academic paper for more detail.

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 Measures
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
Label Trustworthiness & Continuity l_tnc cvm="dsc" [0, 1] 1
Global Measures
Measure ID Parameters Range Optimum
Stress stress R+ 0
Non-metric stress R+ 0
Scale-normalized 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.

img

from zadu import zadu
from zaduvis import zaduvis
import matplotlib.pyplot as plt
from sklearn.manifold import TSNE
from sklearn.datasets import fetch_openml


hd = fetch_openml('mnist_784', version=1, cache=True).data.to_numpy()[::7]
ld = TSNE().fit_transform(hd)

## Computing local pointwise distortions
spec = [{
    "id": "tnc",
    "params": {"k": 25}
},{
    "id": "snc",
    "params": {"k": 50}
}]
zadu_obj = zadu.ZADU(spec, hd, return_local=True)
scores, local_list = zadu_obj.measure(ld)

tnc_local = local_list[0]
snc_local = local_list[1]

local_trustworthiness = tnc_local["local_trustworthiness"]
local_continuity = tnc_local["local_continuity"]
local_steadiness = snc_local["local_steadiness"]
local_cohesiveness = snc_local["local_cohesiveness"]

fig, ax = plt.subplots(1, 4, figsize=(50, 12.5))
zaduvis.checkviz(ld, local_trustworthiness, local_continuity, ax=ax[0])
zaduvis.reliability_map(ld, local_trustworthiness, local_continuity, k=10, ax=ax[1])
zaduvis.checkviz(ld, local_steadiness, local_cohesiveness, ax=ax[2])
zaduvis.reliability_map(ld, local_steadiness, local_cohesiveness, k=10, ax=ax[3])

The above code snippet demonstrates how to visualize local pointwise distortions using CheckViz and Reliability Map plots.

mnist_1:7

Documentation

For more information about the available distortion measures, their use cases, and examples, please refer to our paper (IEEE VIS 2023 Short).

Citation

Hyeon Jeon, Aeri Cho, Jinhwa Jang, Soohyun Lee, Jake Hyun, Hyung-Kwon Ko, Jaemin Jo, and Jinwook Seo. Zadu: A python library for evaluating the reliability of dimensionality reduction embeddings. In 2023 IEEE Visualization and Visual Analytics (VIS), 2023. to appear.

@inproceedings{jeon23vis,
  author={Jeon, Hyeon and Cho, Aeri and Jang, Jinhwa and Lee, Soohyun and Hyun, Jake and Ko, Hyung-Kwon and Jo, Jaemin and Seo, Jinwook},
  booktitle={2023 IEEE Visualization and Visual Analytics (VIS)}, 
  title={ZADU: A Python Library for Evaluating the Reliability of Dimensionality Reduction Embeddings}, 
  year={2023},
  volume={},
  number={},
  pages={},
  doi={},
  note={to appear}
}