---
kind: concept
slug: multi-view-clustering
title: Multi-view clustering
summary: >-
  Clustering samples with several feature sets (views) into one partition. FastMICE ensembles anchor-based graphs built from random view groups. CPM-Nets learns one code per sample from its observed views, so views may be missing. Author-reported: best average NMI rank on 22 datasets, and ACC and NMI gains on six partial-view sets. Trade-offs: k must be given; released code differs from the papers.
tags: [clustering, multi-view, large-scale-clustering, missing-views]
papers: ["2011.06170", "2203.11572"]
related: [ensemble-clustering, k-means-clustering, spectral-clustering, multimodal-fusion]
status: draft
updated_at: 2026-11-01
---

## Overview

Each sample is described by V views, for example colour and texture features
of the same image. The goal is one partition of the N samples into k clusters,
using all views [arxiv:2203.11572 §1]. Many methods build an N-by-N affinity
matrix and run spectral clustering on it. That costs memory and time that grow
quickly with N [arxiv:2203.11572 §1]. The design problem is therefore how to
combine views and how to keep the cost low, while still avoiding the
per-dataset tuning that many methods need [arxiv:2203.11572 §1] [arxiv:2203.11572 §2.1].

Two choices shape the methods that assume every view is present:

- **Where views are fused.** Early fusion merges all views into one model.
  Late fusion clusters each view and merges the results. The paper argues that
  multi-stage fusion is less explored [arxiv:2203.11572 §1] [arxiv:2203.11572 §2.1].
- **How the graph is built.** Anchor-based methods pick a small set of
  representative points, so the graph has N-by-p entries instead of N-by-N.
  Methods differ in whether all views share one anchor set or each view has its
  own [arxiv:2203.11572 §1].

A third case is a view that is missing for some samples, for example when
different exams are run on different patients [arxiv:2011.06170 §1]. Here the
question is how to build one representation per sample from whatever views it
has, instead of imputing or grouping by missing pattern [arxiv:2011.06170 §1].

## Variants

### Random view-group ensemble (FastMICE)

Draw M random groups of views. Each group yields one anchor-based bipartite
graph and one base clustering. The M base clusterings are then fused in one
consensus step [arxiv:2203.11572 §3.1]. Early fusion (one group with all views)
and late fusion (one group per view) are special cases of this scheme
[arxiv:2203.11572 §3.2]. Within a group, each view is also subsampled: a random
fraction of its columns is kept, and the anchors and neighbours are shared among
the views of the group [arxiv:2203.11572 §3.3]. Card:
[Fast Multi-view Clustering via Ensembles](/papers/2203.11572).

The paper's ensemble-size and anchor results are reported as sensitivity
curves in figures, without numbers in the text [arxiv:2203.11572 §4.4]
[arxiv:2203.11572 §4.5] [arxiv:2203.11572 §4.6]. The general ensemble idea is
covered on [Ensemble clustering](/concepts/ensemble-clustering).

### Shared code with missing views (CPM-Nets)

Each sample gets one latent code, built from whichever of its views are
observed. A network per view decodes the code back to that view, and the
reconstruction error counts only the observed views [arxiv:2011.06170 §2.1].
A class-structure loss pulls codes of the same class together, which also
helps the codes separate for clustering [arxiv:2011.06170 §2.2]. For clustering,
the paper runs k-means on the codes and reports accuracy (ACC) and normalised
mutual information (NMI) on six multi-view sets [arxiv:2011.06170 §4.4.2]. At
missing rate η = 0.5, it reports average gains of 3.36% in ACC and 5.11% in NMI
over the second-best method. The text does not say whether these gains are
absolute or relative [arxiv:2011.06170 §4.4.2]. Filling missing values with the
per-view average performs poorly in the same experiment [arxiv:2011.06170 §4.4.2].

The paper also has a GAN variant, CPM-GAN, that imputes missing views before the
codes are clustered [arxiv:2011.06170 §3]. It reports that the version without
the GAN is sometimes slightly better at low missing rates, on Football or CUB
[arxiv:2011.06170 §4.4.2]. On CUB and Animal, the paper also compares with VIGAN,
which needs complete-view samples. The paper gives VIGAN 10% complete data, and
reports higher ACC and NMI for CPM-Nets [arxiv:2011.06170 §4.4.2]. Card:
[Deep Partial Multi-View Learning](/papers/2011.06170).

## When to use which

Every number is author-reported. The two papers study different settings, so
the rows compare the methods by constraint rather than by a single score.

| Situation | Use | Why |
|---|---|---|
| Small sets (a few hundred samples, e.g. BBCSport with 544) and you can afford per-dataset tuning of the baselines | Compare the baselines first | The paper's tables show baselines with higher NMI on some small sets: on BBCSport, MVEC scores 90.57 against 88.95 for FastMICE [arxiv:2203.11572 tab. 3] |
| Very large sets (NUS-WIDE with 30,000 samples and up) | FastMICE | Only four of the ten baselines produced results on NUS-WIDE, and none on YTF-400 (398,191 samples), where only FastMICE completes [arxiv:2203.11572 tab. 3] [arxiv:2203.11572 tab. 7] |
| All views present for every sample, and no time for per-dataset tuning | FastMICE | The paper uses fixed values of M, p and K on all datasets. The cluster count k and the distance still need a choice [arxiv:2203.11572 §4.2] |
| Text data with complete views | FastMICE with cosine distance | The paper uses cosine distance for three text datasets. The official code does not pick it automatically [arxiv:2203.11572 §4.2] |
| Many samples miss one or more views, and you need one representation for clustering | CPM-Nets | It learns one code per sample from the views each sample has, with no grouping by missing pattern and no separate imputation step before clustering [arxiv:2011.06170 §1] [arxiv:2011.06170 §2] |
| Reproducing the CPM-Nets clustering numbers | Read the card before implementing | The paper reports clustering with and without the GAN. The released code has no GAN, and its hyperparameters differ from the paper [arxiv:2011.06170 §4.2] [arxiv:2011.06170 §4.4.2] |
| Need to reproduce a FastMICE number exactly | Check the card first | The paper states no seed, and the official code reseeds from the clock, so repeated runs can differ. The paper averages 20 runs, and its tables report standard deviations [arxiv:2203.11572 tab. 3] [arxiv:2203.11572 §4.2] |

## Implementation sketch

The paper has no algorithm box. This sketch is our summary of its four stages
[arxiv:2203.11572 §3]. Parameter values are the paper's defaults [arxiv:2203.11572 §4.2].

```pseudocode
# Multi-view clustering, FastMICE-style  [arxiv:2203.11572 §3]
# Input: V views (N x d_v each), k clusters; M = 20, p = 1000, K = 5

def multi_view_cluster(views, k):
    base = []
    # Stage 1: M random groups of views, each with 1..V members  [§3.2]
    for group in random_view_groups(num_views, M):
        blocks = []
        for v in group:
            # Keep a random fraction of columns  [§3.3]
            X = keep_random_columns(views[v], ratio=uniform(0.2, 0.8))
            # Pick about p/|group| representatives, then link each sample
            # to its K/|group| nearest  [§3.3]
            blocks.append(anchor_graph(X, p // len(group), K // len(group)))
        # Stack the member graphs side by side  [§3.3]
        B = hstack(blocks)
        # Partition the group graph into k_m clusters, k_m in [k, 2k]  [§3.4]
        base.append(transfer_cut(B, uniform_int(k, 2 * k)))
    # Stage 4: one bipartite graph over all base clusters  [§3.5]
    return transfer_cut(one_hot_union(base), k)
```

The official code differs from the text in several details, such as scaling,
row normalisation and k-means settings. The paper card lists them, so check
them before you copy the sketch [arxiv:2203.11572 §3.4]. For the missing-view
variant, the training and test loops are on its
[card](/papers/2011.06170), not in this sketch.

## Contradictions

No direct disagreement is recorded. The two papers study different settings:
one assumes all views are present, the other handles missing views
[arxiv:2203.11572 §1] [arxiv:2011.06170 §1]. They also use different dataset
sets and metric sets, so their numbers are not comparable [arxiv:2203.11572 tab. 3]
[arxiv:2011.06170 §4.4.2].

## Papers

- [Deep Partial Multi-View Learning](/papers/2011.06170): one shared code per sample from the observed views, with a reconstruction loss on those views and a class-structure loss; reports clustering gains on six partial-view sets.
- [Fast Multi-view Clustering via Ensembles: Towards Scalability, Superiority, and Simplicity](/papers/2203.11572): anchor-based ensemble clustering over random view groups, with near-linear cost and no per-dataset tuning, reported on 22 datasets.