DBSCAN and OPTICS are powerful algorithms for identifying clusters of points in domains where few assumptions can be made about the structure of the data. In this paper, we leverage these strengths and introduce a new algorithm, LINSCAN, designed to seek lineated clusters that are difficult to find and isolate with existing methods. In particular, by embedding points as normal distributions approximating their local neighborhoods and leveraging a distance function derived from the Kullback Leibler Divergence, LINSCAN can detect and distinguish lineated clusters that are spatially close but have orthogonal covariances. We demonstrate how LINSCAN can be applied to seismic data to identify active faults, including intersecting faults, and determine their orientation. Finally, we discuss the properties a generalization of DBSCAN and OPTICS must have in order to retain the stability benefits of these algorithms.

We show that several major algorithms of reinforcement learning (RL) fit into the framework of categorical cybernetics, that is to say, parametrised bidirectional processes. We build on our previous work in which we show that value iteration can be represented by precomposition with a certain optic. The outline of the main construction in this paper is: (1) We extend the Bellman operators to parametrised optics that apply to action-value functions and depend on a sample. (2) We apply a representable contravariant functor, obtaining a parametrised function that applies the Bellman iteration. (3) This parametrised function becomes the backward pass of another parametrised optic that represents the model, which interacts with an environment via an agent. Thus, parametrised optics appear in two different ways in our construction, with one becoming part of the other. As we show, many of the major classes of algorithms in RL can be seen as different extremal cases of this general setup: dynamic programming, Monte Carlo methods, temporal difference learning, and deep RL. We see this as strong evidence that this approach is a natural one and believe that it will be a fruitful way to think about RL in the future.

The rise of AI-powered classification techniques has ushered in a new era for data-driven Fault Detection and Diagnosis in smart building systems. While extensive research has championed supervised FDD approaches, the real-world application of unsupervised methods remains limited. Among these, cluster analysis stands out for its potential with Building Management System data. This study introduces an unsupervised learning strategy to detect faults in terminal air handling units and their associated systems. The methodology involves pre-processing historical sensor data using Principal Component Analysis to streamline dimensions. This is then followed by OPTICS clustering, juxtaposed against k-means for comparison. The effectiveness of the proposed strategy was gauged using several labeled datasets depicting various fault scenarios and real-world building BMS data. Results showed that OPTICS consistently surpassed k-means in accuracy across seasons. Notably, OPTICS offers a unique visualization feature for users called reachability distance, allowing a preview of detected clusters before setting thresholds. Moreover, according to the results, while PCA is beneficial for reducing computational costs and enhancing noise reduction, thereby generally improving the clarity of cluster differentiation in reachability distance. It also has its limitations, particularly in complex fault scenarios. In such cases, PCA's dimensionality reduction may result in the loss of critical information, leading to some clusters being less discernible or entirely undetected. These overlooked clusters could be indicative of underlying faults, and their obscurity represents a significant limitation of PCA when identifying potential fault lines in intricate datasets.

Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The goal of this process is to provide a useful aid to the researcher that will help her/him to identify patterns among the data. Dealing with large databases, such patterns may not be easily detectable without the contribution of a clustering algorithm. This article provides a deep description of the most widely used clustering methodologies accompanied by useful presentations concerning suitable parameter selection and initializations. Simultaneously, this article not only represents a review highlighting the major elements of examined clustering techniques but emphasizes the comparison of these algorithms' clustering efficiency based on 3 datasets, revealing their existing weaknesses and capabilities through accuracy and complexity, during the confrontation of discrete and continuous observations. The produced results help us extract valuable conclusions about the appropriateness of the examined clustering techniques in accordance with the dataset's size.

Density Based Clustering are a type of Clustering methods using in data mining for extracting previously unknown patterns from data sets. There are a number of density based clustering methods such as DBSCAN, OPTICS, DENCLUE, VDBSCAN, DVBSCAN, DBCLASD and ST-DBSCAN. In this paper, a study of these methods is done along with their characteristics, advantages and disadvantages and most importantly, their applicability to different types of data sets to mine useful and appropriate patterns.

Optics and lenses are abstract categorical gadgets that model systems with bidirectional data flow. In this paper we observe that the denotational definition of optics - identifying two optics as equivalent by observing their behaviour from the outside - is not suitable for operational, software oriented approaches where optics are not merely observed, but built with their internal setups in mind. We identify operational differences between denotationally isomorphic categories of cartesian optics and lenses: their different composition rule and corresponding space-time tradeoffs, positioning them at two opposite ends of a spectrum. With these motivations we lift the existing categorical constructions and their relationships to the 2-categorical level, showing that the relevant operational concerns become visible. We define the 2-category $\textbf{2-Optic}(\mathcal{C})$ whose 2-cells explicitly track optics' internal configuration. We show that the 1-category $\textbf{Optic}(\mathcal{C})$ arises by locally quotienting out the connected components of this 2-category. We show that the embedding of lenses into cartesian optics gets weakened from a functor to an oplax functor whose oplaxator now detects the different composition rule. We determine the difficulties in showing this functor forms a part of an adjunction in any of the standard 2-categories. We establish a conjecture that the well-known isomorphism between cartesian lenses and optics arises out of the lax 2-adjunction between their double-categorical counterparts. In addition to presenting new research, this paper is also meant to be an accessible introduction to the topic.

That popularity was evident both within and outside the venue as well: Long lines of spectators led up to the entrance, and the seats were packed when the games began. Fans cheered as the final two teams arrived in white Mercedes vans and crowded around barricades to gawk at influencers, players, Riot executives and popular Twitch streamers like Michael "Shroud" Grzesiek and Tarik Celik on a makeshift red carpet. Many of the streamers later set up in skyboxes above the venue to co-stream the games, providing unique running commentary over the game footage and further boosting viewership numbers. The singer Ashnikko also made an appearance, performing their song "Fire Again" onstage before the match began.

The NFT space has ongoing issues with fraud, including through bad actors wholesale lifting art from one project and using it in a second project -- a process often referred to as "copyminting." They are derivative projects that have a few too many similarities to the original project to be considered anything other than a ripoff. While most of these duplicate projects do very little sales volume relative to the original, they may damage the underlying brand, contribute to the overall distrust of the NFT space, or trick less savvy buyers into spending money on something that's the jpg equivalent of a street vendor shilling fake Rolex watches. To help combat this fraud, a few companies are emerging that specialize in fraud detection in NFTs. They tend to leverage blockchain data to help determine which project came first and apply some image detection to find metadata matches.

As we know that Clustering is a powerful unsupervised knowledge discovery tool used nowadays to segment our data points into groups of similar features types. However, each algorithm of clustering works according to the parameters. Similarity-based techniques (K-means clustering algorithm working is based on similarity of the data points and is tasked with designating how many clusters are available, while hierarchical clustering algorithms decide when to assign finished clusters manually. Generally used density-based clustering technique is DBSCAN which requires two parameters about how it defines its Core Points, but finding the parameters is an extremely difficult task. DBSCAN's relatively algorithm is called OPTICS (Ordering Points to Identify Cluster Structure).