arXiv subjects

Nassir Mohammad

Publications and source records attributed to Nassir Mohammad.

5 recordsLinked to original sources

arXiv2026

Seed-Guided Semi-Supervised Clustering by A-Contrario Anomaly Detection

This paper introduces a semi-supervised clustering framework grounded in the statistical duality between grouping principles and anomaly detection. We address the challenge of robust cluster definition in noisy environments -- a task where partitioning algorithms often over-assign outliers and density-based methods remain sensitive to heuristic global parameters. Drawing on \textit{a-contrario} statistical reasoning and Gestalt proximity principles, we define a cluster as a maximal subset of data points containing no anomalies relative to a null hypothesis of uniform randomness. Central to this approach is the Perception algorithm, which utilises a principled expectation-based threshold ($\mathbb{E} < 1$) to identify outliers without manual parameter tuning. By treating clustering as the dual of anomaly detection, we employ an iterative ``clustering-by-exclusion'' mechanism. The algorithm is seed-guided, leveraging minimal user-provided labels to initialise robust cluster medians and form initial groups, which are subsequently expanded by admitting non-anomalous points. This approach naturally isolates fringe points, isolated noise, and emerging unknown clusters. We evaluate the method on synthetic and real-world benchmarks, including image and text datasets represented through raw, linear-reduced, and neighbourhood-preserving embeddings. Results demonstrate that with as few as 10--30 seeds per cluster, the proposed method achieves competitive and often very strong performance under a practical low-tuning benchmarking protocol, while maintaining linear scalability with respect to both observations and dimensionality for a fixed number of seeded clusters and iterations.

cs.LG↗

arXiv2023

A Computational Theory and Semi-Supervised Algorithm for Clustering

A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping principle and measure; all other examples are considered to be fringe points, isolated anomalies, anomalous clusters or unknown clusters. More precisely, after appropriate modelling under the assumption of uniform random distribution, any example whose expectation of occurrence is <1 with respect to a group is considered an anomaly; otherwise it is assigned a membership of that group. Thus, clustering is conceived as the dual of anomaly detection. The representation of data is taken to be the Euclidean distance of a point to a cluster median. This is due to the robustness properties of the median to outliers, its approximate location of centrality and so that decision boundaries are general purpose. The kernel of the clustering method is the perception anomaly detection algorithm, resulting in a parameter-free, fast, and efficient clustering algorithm. Acknowledging that clustering is an interactive and iterative process, the algorithm relies on a small fraction of known relationships between examples. These relationships serve as seeds to define the user's objectives and guide the clustering process. The method then expands the clusters accordingly, leaving the remaining examples for exploration and subsequent iterations. Results are presented on synthetic and realworld data sets, demonstrating the advantages over the most popular unsupervised and semi-supervised clustering methods.

cs.LG↗

arXiv2022

Anomaly Detection using Principles of Human Perception

In the fields of statistics and unsupervised machine learning a fundamental and well-studied problem is anomaly detection. Anomalies are difficult to define, yet many algorithms have been proposed. Underlying the approaches is the nebulous understanding that anomalies are rare, unusual or inconsistent with the majority of data. The present work provides a philosophical treatise to clearly define anomalies and develops an algorithm for their efficient detection with minimal user intervention. Inspired by the Gestalt School of Psychology and the Helmholtz principle of human perception, anomalies are assumed to be observations that are unexpected to occur with respect to certain groupings made by the majority of the data. Under appropriate random variable modelling anomalies are directly found in a set of data by a uniform and independent random assumption of the distribution of constituent elements of the observations, with anomalies corresponding to those observations where the expectation of the number of occurrences of the elements in a given view is $<1$. Starting from fundamental principles of human perception an unsupervised anomaly detection algorithm is developed that is simple, real-time and parameter-free. Experiments suggest it as a competing choice for univariate data with promising results on the detection of global anomalies in multivariate data.

cs.CR↗

arXiv2022

A Vision Inspired Neural Network for Unsupervised Anomaly Detection in Unordered Data

A fundamental problem in the field of unsupervised machine learning is the detection of anomalies corresponding to rare and unusual observations of interest; reasons include for their rejection, accommodation or further investigation. Anomalies are intuitively understood to be something unusual or inconsistent, whose occurrence sparks immediate attention. More formally anomalies are those observations-under appropriate random variable modelling-whose expectation of occurrence with respect to a grouping of prior interest is less than one; such a definition and understanding has been used to develop the parameter-free perception anomaly detection algorithm. The present work seeks to establish important and practical connections between the approach used by the perception algorithm and prior decades of research in neurophysiology and computational neuroscience; particularly that of information processing in the retina and visual cortex. The algorithm is conceptualised as a neuron model which forms the kernel of an unsupervised neural network that learns to signal unexpected observations as anomalies. Both the network and neuron display properties observed in biological processes including: immediate intelligence; parallel processing; redundancy; global degradation; contrast invariance; parameter-free computation, dynamic thresholds and non-linear processing. A robust and accurate model for anomaly detection in univariate and multivariate data is built using this network as a concrete application.

cs.LG↗

arXiv2009

Colorization of Natural Images via L1 Optimization

Natural images in the colour space YUV have been observed to have a non-Gaussian, heavy tailed distribution (called 'sparse') when the filter G(U)(r) = U(r) - sum_{s \in N(r)} w{(Y)_{rs}} U(s), is applied to the chromacity channel U (and equivalently to V), where w is a weighting function constructed from the intensity component Y [1]. In this paper we develop Bayesian analysis of the colorization problem using the filter response as a regularization term to arrive at a non-convex optimization problem. This problem is convexified using L1 optimization which often gives the same results for sparse signals [2]. It is observed that L1 optimization, in many cases, over-performs the famous colorization algorithm by Levin et al [3].

cs.CV↗