HLoOP -- Hyperbolic 2-space Local Outlier Probabilities

Hyperbolic geometry has recently garnered considerable attention in machine learning due to its capacity to embed hierarchical graph structures with low distortions for further downstream processing. This paper introduces a simple framework to detect local outliers for datasets grounded in hyperbolic 2-space referred to as HLoOP (Hyperbolic Local Outlier Probability). Within a Euclidean space, well-known techniques for local outlier detection are based on the Local Outlier Factor (LOF) and its variant, the LoOP (Local Outlier Probability), which incorporates probabilistic concepts to model the outlier level of a data vector. The developed HLoOP combines the idea of finding nearest neighbors, density-based outlier scoring with a probabilistic, statistically oriented approach. Therefore, the method consists in computing the Riemmanian distance of a data point to its nearest neighbors following a Gaussian probability density function expressed in a hyperbolic space. This is achieved by defining a Gaussian cumulative distribution in this space. The HLoOP algorithm is tested on the WordNet dataset yielding promising results. Code and data will be made available on request for reproductibility.

Managing network congestion with a Kohonen-based RED queue

The behaviour of the TCP AIMD algorithm is known to cause queue length oscillations when congestion occurs at a router output link. Indeed, due to these queueing variations, end-to-end applications experience large delay jitter. Many studies have proposed efficient Active Queue Management (AQM) mechanisms in order to reduce queue oscillations and stabilize the queue length. These AQM are mostly improvements of the Random Early Detection (RED) model. Unfortunately, these enhancements do not react in a similar manner for various network conditions and are strongly sensitive to their initial setting parameters. Although this paper proposes a solution to overcome the difficulties of setting these parameters by using a Kohonen neural network model, another goal of this study is to investigate whether cognitive intelligence could be placed in the core network to solve such stability problem. In our context, we use results from the neural network area to demonstrate that our proposal, named Kohonen-RED (KRED), enables a stable queue length without complex parameters setting and passive measurements.