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Artificial Intelligence in Health ISM: A new multi-view space-learning model

Table 6. Computational time observed in the TEA‑seq A-MVC requires a specialized algorithm to select the
multi‑omic single‑cell data anchor points that are best distributed across clusters.
Since clusters must be sufficiently populated with A-MVC
Method Time (min) anchors for the method to work, the number of anchors
MVMDS 5.31 must be set higher than the number of clusters. In contrast,
ISM 1.17 ISM attribute anchors are found automatically through the
ILSM 1.31 process of parsimonization. This process requires the setting
GFA 23.14 of a sparsity parameter to relax the reciprocal of the HHI,
MOFA+ 19.38 which may otherwise lead to excessive sparsity. In the
MOWGLI (20%) 82.31 examples considered in this article, this value is experiment
NMF 0.55 independent and is set to 0.8. Further reducing the sparsity
parameter risks a lack of overlap between the simplicial
Note: The parallelization of separate factorizations was not activated for cones, potentially rendering the tensor decomposition
ILSM, hence the slightly higher computational time compared to ISM.
Abbreviations: GFA: Group factor analysis; ILSM: Integrated latent ineffective. Therefore, until more experience is gained with
sources model; ISM: Integrated sources model; MOFA+: Multi-Omics ISM, we do not recommend changing this parameter.
Factor Analysis+; MOWGLI: Multi-Omics Wasserstein inteGrative
anaLysIs; MVMDS: Multi-view multidimensional scaling; Just as NMF and NTF factors are more interpretable
NMF: Non-negative matrix factorization. and meaningful due to the non-negativity of their
loadings, ISM produces latent factors whose interpretation
However, the proportion of known categories retrieved is greatly facilitated by the non-negativity and sparsity of
and other metrics depend on the data being analyzed. the attribute loadings. This is illustrated by the example
For example, for the Reuters data, only three out of six of the Signature 915 dataset. It is noteworthy that all non-
categories are recognized at best using ISM or MVMDS, negative approaches result in a high sparsity index of the
suggesting that latent-space-based methods may not be the view-mapping, in contrast to the mixed-sign approaches.
most effective approaches with bag-of-words data. The ISM has only three hyperparameters, which are

In contrast to the other approaches studied, MVMDS very few compared to alternative methods: The sparsity
and ISM are the only approaches that perform relatively well coefficient, the embedding dimension, and the rank
on all the datasets analyzed, demonstrating their versatility. dimension. As mentioned, the sparsity coefficient should
The main advantages of ISM over MVMDS are its speed be kept at its default value of 0.8. Regarding the rank and
and increased sparsity in the latent-space representation. embedding dimensions chosen for the ISM model, an
Regarding missing data, the ISM implementation uses objective and natural choice was the known number of
an NTF package that can handle missing data, unlike classes for our examples, as we expect each factor to be
distinctly assigned to a particular class. The only exception
MVMDS.
was the UCI digit dataset, where reducing the embedding
To the best of our knowledge, ISM is the first approach dimension by one unit significantly reduced the error rate.
that uses NMF to transform heterogeneous views into However, this is only possible in a supervised setting where
a 3D array and then uses NTF to extract consistent classes are known. More generally, as with all factorization
information from the transformed views. However, methods, the factorization rank must be determined in
apparent commonalities with anchor-based MVC methods advance.
(A-MVC) are worth mentioning to further illustrate the This raises the issue of the subjectivity of the choice
originality of ISM: made, especially in an unsupervised setting where cross-
(i) In the first step, ISM relies on anchors, akin to A-MVC. validation cannot be used. For PCA, MVMDS, MOFA+,
ISM anchors correspond to zero-loading attributes in and GFA, setting the rank by inspecting the scree plot of
the latent spaces defined by the H , whereas A-MVC the variance ratio is indeed a subjective choice due to the
v
anchors are observations well distributed over existing variety of possible criteria that can be used to identify
clusters. Both act as intermediaries to derive either a an “elbow” in the scree plot. We tried a range of values
latent space or cluster labels shared by all views. around the “observed” elbow. The observed changes in
(ii) In the second step, ISM applies NTF on the embedded the close neighborhood metric had no impact on the
views. A-MVC applies NTF on a tensor of anchor conclusions about the performance of ISM relative to other
graphs, albeit with added constraints that ensure approaches (Tables S1 and S2). Since GFA and MOFA+
orthogonality and consistency in the cluster labels include automatic rank detection (ARD), increasing
across all views. the rank should not adversely affect performance, as

Volume 1 Issue 3 (2024) 108 doi: 10.36922/aih.3427