10,245 research outputs found
Batch kernel SOM and related Laplacian methods for social network analysis
Large graphs are natural mathematical models for describing the structure of
the data in a wide variety of fields, such as web mining, social networks,
information retrieval, biological networks, etc. For all these applications,
automatic tools are required to get a synthetic view of the graph and to reach
a good understanding of the underlying problem. In particular, discovering
groups of tightly connected vertices and understanding the relations between
those groups is very important in practice. This paper shows how a kernel
version of the batch Self Organizing Map can be used to achieve these goals via
kernels derived from the Laplacian matrix of the graph, especially when it is
used in conjunction with more classical methods based on the spectral analysis
of the graph. The proposed method is used to explore the structure of a
medieval social network modeled through a weighted graph that has been directly
built from a large corpus of agrarian contracts
SOM-VAE: Interpretable Discrete Representation Learning on Time Series
High-dimensional time series are common in many domains. Since human
cognition is not optimized to work well in high-dimensional spaces, these areas
could benefit from interpretable low-dimensional representations. However, most
representation learning algorithms for time series data are difficult to
interpret. This is due to non-intuitive mappings from data features to salient
properties of the representation and non-smoothness over time. To address this
problem, we propose a new representation learning framework building on ideas
from interpretable discrete dimensionality reduction and deep generative
modeling. This framework allows us to learn discrete representations of time
series, which give rise to smooth and interpretable embeddings with superior
clustering performance. We introduce a new way to overcome the
non-differentiability in discrete representation learning and present a
gradient-based version of the traditional self-organizing map algorithm that is
more performant than the original. Furthermore, to allow for a probabilistic
interpretation of our method, we integrate a Markov model in the representation
space. This model uncovers the temporal transition structure, improves
clustering performance even further and provides additional explanatory
insights as well as a natural representation of uncertainty. We evaluate our
model in terms of clustering performance and interpretability on static
(Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST
images, a chaotic Lorenz attractor system with two macro states, as well as on
a challenging real world medical time series application on the eICU data set.
Our learned representations compare favorably with competitor methods and
facilitate downstream tasks on the real world data.Comment: Accepted for publication at the Seventh International Conference on
Learning Representations (ICLR 2019
How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?
In numerous applicative contexts, data are too rich and too complex to be
represented by numerical vectors. A general approach to extend machine learning
and data mining techniques to such data is to really on a dissimilarity or on a
kernel that measures how different or similar two objects are. This approach
has been used to define several variants of the Self Organizing Map (SOM). This
paper reviews those variants in using a common set of notations in order to
outline differences and similarities between them. It discusses the advantages
and drawbacks of the variants, as well as the actual relevance of the
dissimilarity/kernel SOM for practical applications
Self-Organizing Time Map: An Abstraction of Temporal Multivariate Patterns
This paper adopts and adapts Kohonen's standard Self-Organizing Map (SOM) for
exploratory temporal structure analysis. The Self-Organizing Time Map (SOTM)
implements SOM-type learning to one-dimensional arrays for individual time
units, preserves the orientation with short-term memory and arranges the arrays
in an ascending order of time. The two-dimensional representation of the SOTM
attempts thus twofold topology preservation, where the horizontal direction
preserves time topology and the vertical direction data topology. This enables
discovering the occurrence and exploring the properties of temporal structural
changes in data. For representing qualities and properties of SOTMs, we adapt
measures and visualizations from the standard SOM paradigm, as well as
introduce a measure of temporal structural changes. The functioning of the
SOTM, and its visualizations and quality and property measures, are illustrated
on artificial toy data. The usefulness of the SOTM in a real-world setting is
shown on poverty, welfare and development indicators
Evaluating a Self-Organizing Map for Clustering and Visualizing Optimum Currency Area Criteria
Optimum currency area (OCA) theory attempts to define the geographical region in which it would maximize economic efficiency to have a single currency. In this paper, the focus is on prospective and current members of the Economic and Monetary Union. For this task, a self-organizing neural network, the Self-organizing map (SOM), is combined with hierarchical clustering for a two-level approach to clustering and visualizing OCA criteria. The output of the SOM is a topologically preserved two-dimensional grid. The final models are evaluated based on both clustering tendencies and accuracy measures. Thereafter, the two-dimensional grid of the chosen model is used for visual assessment of the OCA criteria, while its clustering results are projected onto a geographic map.Self-organizing maps, Optimum Currency Area, projection, clustering, geospatial visualization
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