Consensus clustering is a method of aggregating (potentially conflicting) results from multiple clustering algorithms. Also called cluster ensembles or aggregation of clustering (or partitions), it refers to the situation in which a number of different (input) clusterings have been obtained for a particular dataset and it is desired to find a single (consensus) clustering which is a better fit in some sense than the existing clusterings. Consensus clustering is thus the problem of reconciling clustering information about the same data set coming from different sources or from different runs of the same algorithm. When cast as an optimization problem, consensus clustering is known as median partition, and has been shown to be NP-complete, even when the number of input clusterings is three. Consensus clustering for unsupervised learning is analogous to ensemble learning in supervised learning. == Issues with existing clustering techniques == Current clustering techniques do not address all the requirements adequately. Dealing with large number of dimensions and large number of data items can be problematic because of time complexity; Effectiveness of the method depends on the definition of "distance" (for distance-based clustering) If an obvious distance measure doesn't exist, we must "define" it, which is not always easy, especially in multidimensional spaces. The result of the clustering algorithm (that, in many cases, can be arbitrary itself) can be interpreted in different ways. == Justification for using consensus clustering == There are potential shortcomings for all existing clustering techniques. This may cause interpretation of results to become difficult, especially when there is no knowledge about the number of clusters. Clustering methods are also very sensitive to the initial clustering settings, which can cause non-significant data to be amplified in non-reiterative methods. An extremely important issue in cluster analysis is the validation of the clustering results, that is, how to gain confidence about the significance of the clusters provided by the clustering technique (cluster numbers and cluster assignments). Lacking an external objective criterion (the equivalent of a known class label in supervised analysis), this validation becomes somewhat elusive. Iterative descent clustering methods, such as the SOM and k-means clustering circumvent some of the shortcomings of hierarchical clustering by providing for univocally defined clusters and cluster boundaries. Consensus clustering provides a method that represents the consensus across multiple runs of a clustering algorithm, to determine the number of clusters in the data, and to assess the stability of the discovered clusters. The method can also be used to represent the consensus over multiple runs of a clustering algorithm with random restart (such as K-means, model-based Bayesian clustering, SOM, etc.), so as to account for its sensitivity to the initial conditions. It can provide data for a visualization tool to inspect cluster number, membership, and boundaries. However, they lack the intuitive and visual appeal of hierarchical clustering dendrograms, and the number of clusters must be chosen a priori. == The Monti consensus clustering algorithm == The Monti consensus clustering algorithm is one of the most popular consensus clustering algorithms and is used to determine the number of clusters, K {\displaystyle K} . Given a dataset of N {\displaystyle N} total number of points to cluster, this algorithm works by resampling and clustering the data, for each K {\displaystyle K} and a N × N {\displaystyle N\times N} consensus matrix is calculated, where each element represents the fraction of times two samples clustered together. A perfectly stable matrix would consist entirely of zeros and ones, representing all sample pairs always clustering together or not together over all resampling iterations. The relative stability of the consensus matrices can be used to infer the optimal K {\displaystyle K} . More specifically, given a set of points to cluster, D = { e 1 , e 2 , . . . e N } {\displaystyle D=\{e_{1},e_{2},...e_{N}\}} , let D 1 , D 2 , . . . , D H {\displaystyle D^{1},D^{2},...,D^{H}} be the list of H {\displaystyle H} perturbed (resampled) datasets of the original dataset D {\displaystyle D} , and let M h {\displaystyle M^{h}} denote the N × N {\displaystyle N\times N} connectivity matrix resulting from applying a clustering algorithm to the dataset D h {\displaystyle D^{h}} . The entries of M h {\displaystyle M^{h}} are defined as follows: M h ( i , j ) = { 1 , if points i and j belong to the same cluster 0 , otherwise {\displaystyle M^{h}(i,j)={\begin{cases}1,&{\text{if}}{\text{ points i and j belong to the same cluster}}\\0,&{\text{otherwise}}\end{cases}}} Let I h {\displaystyle I^{h}} be the N × N {\displaystyle N\times N} identicator matrix where the ( i , j ) {\displaystyle (i,j)} -th entry is equal to 1 if points i {\displaystyle i} and j {\displaystyle j} are in the same perturbed dataset D h {\displaystyle D^{h}} , and 0 otherwise. The indicator matrix is used to keep track of which samples were selected during each resampling iteration for the normalisation step. The consensus matrix C {\displaystyle C} is defined as the normalised sum of all connectivity matrices of all the perturbed datasets and a different one is calculated for every K {\displaystyle K} . C ( i , j ) = ( ∑ h = 1 H M h ( i , j ) ∑ h = 1 H I h ( i , j ) ) {\displaystyle C(i,j)=\left({\frac {\textstyle \sum _{h=1}^{H}M^{h}(i,j)\displaystyle }{\sum _{h=1}^{H}I^{h}(i,j)}}\right)} That is the entry ( i , j ) {\displaystyle (i,j)} in the consensus matrix is the number of times points i {\displaystyle i} and j {\displaystyle j} were clustered together divided by the total number of times they were selected together. The matrix is symmetric and each element is defined within the range [ 0 , 1 ] {\displaystyle [0,1]} . A consensus matrix is calculated for each K {\displaystyle K} to be tested, and the stability of each matrix, that is how far the matrix is towards a matrix of perfect stability (just zeros and ones) is used to determine the optimal K {\displaystyle K} . One way of quantifying the stability of the K {\displaystyle K} th consensus matrix is examining its CDF curve (see below). == Over-interpretation potential of the Monti consensus clustering algorithm == Monti consensus clustering can be a powerful tool for identifying clusters, but it needs to be applied with caution as shown by Şenbabaoğlu et al. It has been shown that the Monti consensus clustering algorithm is able to claim apparent stability of chance partitioning of null datasets drawn from a unimodal distribution, and thus has the potential to lead to over-interpretation of cluster stability in a real study. If clusters are not well separated, consensus clustering could lead one to conclude apparent structure when there is none, or declare cluster stability when it is subtle. Identifying false positive clusters is a common problem throughout cluster research, and has been addressed by methods such as SigClust and the GAP-statistic. However, these methods rely on certain assumptions for the null model that may not always be appropriate. Şenbabaoğlu et al demonstrated the original delta K metric to decide K {\displaystyle K} in the Monti algorithm performed poorly, and proposed a new superior metric for measuring the stability of consensus matrices using their CDF curves. In the CDF curve of a consensus matrix, the lower left portion represents sample pairs rarely clustered together, the upper right portion represents those almost always clustered together, whereas the middle segment represent those with ambiguous assignments in different clustering runs. The proportion of ambiguous clustering (PAC) score measure quantifies this middle segment; and is defined as the fraction of sample pairs with consensus indices falling in the interval (u1, u2) ∈ [0, 1] where u1 is a value close to 0 and u2 is a value close to 1 (for instance u1=0.1 and u2=0.9). A low value of PAC indicates a flat middle segment, and a low rate of discordant assignments across permuted clustering runs. One can therefore infer the optimal number of clusters by the K {\displaystyle K} value having the lowest PAC. == Related work == Clustering ensemble (Strehl and Ghosh): They considered various formulations for the problem, most of which reduce the problem to a hyper-graph partitioning problem. In one of their formulations they considered the same graph as in the correlation clustering problem. The solution they proposed is to compute the best k-partition of the graph, which does not take into account the penalty for merging two nodes that are far apart. Clustering aggregation (Fern and Brodley): They applied the clustering aggregation idea to a collection of soft clusterings they obtained by random projections. They used an agglomerative algorithm
Plug computer
A plug computer is a small-form-factor computer whose chassis contains the AC power plug, and thus plugs directly into the wall. Alternatively, the computer may resemble an AC adapter or a similarly small device. Plug computers are often configured for use in the home or office as compact computer. == Description == Plug computers consist of a high-performance, low-power system-on-a-chip processor, with several I/O hardware ports (USB ports, Ethernet connectors, etc.). Most versions do not have provisions for connecting a display and are best suited to running media servers, back-up services, or file sharing and remote access functions; thus acting as a bridge between in-home protocols (such as Digital Living Network Alliance (DLNA) and Server Message Block (SMB)) and cloud-based services. There are, however, plug computer offerings that have analog VGA monitor and/or HDMI connectors, which, along with multiple USB ports, permit the use of a display, keyboard, and mouse, thus making them full-fledged, low-power alternatives to desktop and laptop computers. They typically run any of a number of Linux distributions. Plug computers typically consume little power and are inexpensive. == History == A number of other devices of this type began to appear at the 2009 Consumer Electronics Show. On January 6, 2009 CTERA Networks launched a device called CloudPlug that provides online backup at local disk speeds and overlays a file sharing service. The device also transforms any external USB hard drive into a network-attached storage device. On January 7, 2009, Cloud Engines unveiled the Pogoplug network access server. On January 8, 2009, Axentra announced availability of their HipServ platform. On February 23, 2009, Marvell Technology Group announced its plans to build a mini-industry around plug computers. On August 19, 2009, CodeLathe announced availability of their TonidoPlug network access server. On November 13, 2009 QuadAxis launched its plug computing device product line and development platform, featuring the QuadPlug and QuadPC and running QuadMix, a modified Linux. On January 5, 2010, Iomega announced their iConnect network access server. On January 7, 2010 Pbxnsip launched its plug computing device the sipJack running pbxnsip: an IP Communications platform.
Adam Tauman Kalai
Adam Tauman Kalai is an American computer scientist who specializes in artificial intelligence and works at OpenAI. == Education and career == Kalai graduated from Harvard University in 1996 with a BA in computer science and received a MA and PhD, both in computer science, from Carnegie Mellon University in 1999 and 2001, respectively. His doctoral advisor was Avrim Blum. After graduation, Kalai did his postdoctoral research at Massachusetts Institute of Technology under Santosh Vempala until 2003. Kalai became a faculty member at the Toyota Technological Institute at Chicago from 2003 to 2006, followed by a stint as an assistant professor at Georgia Institute of Technology from 2007 to 2008. He joined Microsoft Research in 2008 and subsequently moved to OpenAI in 2023. == Contributions == Kalai is known for his algorithm for generating random factored numbers (see Bach's algorithm), for co-inventing the cooperative-competitive value (coco value), for efficiently learning learning mixtures of Gaussians, for the Blum-Kalai-Wasserman algorithm for learning parity with noise, and for the intractability of the folk theorem in game theory. More recently, Kalai is known for identifying and reducing gender bias in word embeddings, which are a representation of words commonly used in AI systems. In 2026, he coauthored a Nature paper on hallucinations in large language models. == Personal life == Kalai is the son of game theorist Ehud Kalai and is married to cryptographer Yael Tauman Kalai.
Forrest N. Iandola
Forrest N. Iandola is an American computer scientist specializing in efficient AI. == Career == Iandola earned a PhD in Electrical Engineering and Computer Science from UC Berkeley in 2016, advised by Kurt Keutzer. As part of his dissertation, he co-authored SqueezeNet, a deep neural network for image classification optimized for smartphones and other mobile devices. Iandola and Keutzer went on to co-found DeepScale. The firm squeezes deep neural networks onto low-cost automotive-grade processors for use in driver assistance systems. Tesla acquired DeepScale in 2019. In 2020, he co-authored SqueezeBERT, an efficient neural network for natural language processing. In 2022, he joined Meta as an AI research scientist. His research at Meta includes developing efficient AI models, such as EfficientSAM and MobileLLM.
AI Text-to-image Tools: Free vs Paid (2026)
Shopping for the best AI text-to-image tool? An AI text-to-image tool is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI text-to-image tool slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
Visual hull
A visual hull is a geometric entity created by shape-from-silhouette 3D reconstruction technique introduced by A. Laurentini. This technique assumes the foreground object in an image can be separated from the background. Under this assumption, the original image can be thresholded into a foreground/background binary image, which we call a silhouette image. The foreground mask, known as a silhouette, is the 2D projection of the corresponding 3D foreground object. Along with the camera viewing parameters, the silhouette defines a back-projected generalized cone that contains the actual object; this cone is called a silhouette cone. The intersection of the two silhouette cones defines a visual hull. which is a bounding geometry of the actual 3D object. When the reconstructed geometry is only used for rendering from a different viewpoint, the implicit reconstruction together with rendering can be done using graphics hardware. == In two dimensions == A technique used in some modern touchscreen devices employs cameras placed in the corners situated opposite infrared LEDs. The one-dimensional projection (shadow) of objects on the surface may be used to reconstruct the convex hull of the object. Visual hull generation method has also been used within experimental tele-meeting systems that aim to allow a user in a remote location to interact with virtual objects. The method uses multiple cameras to capture the real-world movements and interactions of the "sender", employing hardware-accelerated volumetric visual hull representation to create 3D volume from 2D multi-view images. Its ultimate aim is to allow 3D collaboration between the two users in the virtual realm, with the visual hull technique reducing the computational power required to allow this type of interaction and enabling the use of consumer goods such as the Wii Remote as a tool for interaction.
Isolation forest
Isolation forest is an unsupervised learning algorithm for anomaly detection that works on the principle of isolating anomalies, instead of the most common techniques of profiling normal points. In statistics, an anomaly (a.k.a. outlier) is an observation or event that deviates so much from other events to arouse suspicion it was generated by a different mean. For example, the graph in Fig.1 represents ingress traffic to a web server, expressed as the number of requests in 3-hours intervals, for a period of one month. It is quite evident by simply looking at the picture that some points (marked with a red circle) are unusually high, to the point of inducing suspect that the web server might have been under attack at that time. On the other hand, the flat segment indicated by the red arrow also seems unusual and might possibly be a sign that the server was down during that time period. Anomalies in a big dataset may follow very complicated patterns, which are difficult to detect "by eye" in the great majority of cases. This is the reason why the field of anomaly detection is well suited for the application of machine learning techniques. The most common techniques employed for anomaly detection are based on the construction of a profile of what is "normal": anomalies are reported as those instances in the dataset that do not conform to the normal profile. Isolation Forest uses a different approach: instead of trying to build a model of normal instances, it explicitly isolates anomalous points in the dataset. The main advantage of this approach is the possibility of exploiting sampling techniques to an extent that is not allowed to the profile-based methods, creating a very fast algorithm with a low memory demand. == History == The Isolation Forest (iForest) algorithm was initially proposed by Fei Tony Liu, Kai Ming Ting and Zhi-Hua Zhou in 2008. The authors took advantage of two quantitative properties of anomalous data points in a sample, that is: they are the minority consisting of fewer instances and they have attribute-values that are very different from those of normal instances Since anomalies are typically few and very different from the other points in the sample, they must be easier to "isolate" compared to normal points. On the basis of this principle, Isolation Forest builds an ensemble of "Isolation Trees" (iTrees) for the data set and marks as anomalies the points that have short average path lengths on the iTrees. In a later paper, published in 2012 the same authors described a set of experiments to prove that iForest: has a low linear time complexity and a small memory requirement is able to deal with high dimensional data with irrelevant attributes can be trained with or without anomalies in the training set can provide detection results with different levels of granularity without re-training In 2013 Zhiguo Ding and Minrui Fei proposed a framework based on iForest to resolve the problem of detecting anomalies in streaming data. More application of iForest to streaming data are described in papers by Swee Chuan Tan et al., G. A. Susto et al. and Yu Weng et al. One of the main problems of the application of iForest to anomaly detection was not with the model itself, but rather in the way the "anomaly score" was computed. This problem was highlighted by Sahand Hariri, Matias Carrasco Kind and Robert J. Brunner in a 2018 paper, wherein they proposed an improved iForest model named Extended Isolation Forest (EIF). In the same paper the authors describe the improvements made to the original model and how they are able to enhance the consistency and reliability of the anomaly score produced for a given data point. == Algorithm == At the basis of the Isolation Forest algorithm there is the tendency of anomalous instances in a dataset to be easier to separate from the rest of the sample (isolate), compared to normal points. In order to isolate a data point the algorithm recursively generates partitions on the sample by randomly selecting an attribute and then randomly selecting a split value for the attribute, between the minimum and maximum values allowed for that attribute. An example of random partitioning in a 2D dataset of normally distributed points is given in Fig. 2 for a non-anomalous point and Fig. 3 for a point that's more likely to be an anomaly. It is apparent from the pictures how anomalies require fewer random partitions to be isolated, compared to normal points. From a mathematical point of view, recursive partitioning can be represented by a tree structure named Isolation Tree, while the number of partitions required to isolate a point can be interpreted as the length of the path, within the tree, to reach a terminating node starting from the root. For example, the path length of point xi in Fig. 2 is greater than the path length of xj in Fig. 3. More formally, let X = { x1, ..., xn } be a set of d-dimensional points and X' ⊂ X a subset of X. An Isolation Tree (iTree) is defined as a data structure with the following properties: for each node T in the Tree, T is either an external-node with no child, or an internal-node with one "test" and exactly two daughter nodes (Tl, Tr) a test at node T consists of an attribute q and a split value p such that the test q < p determines the traversal of a data point to either Tl or Tr. In order to build an iTree, the algorithm recursively divides X' by randomly selecting an attribute q and a split value p, until either (i) the node has only one instance or (ii) all data at the node have the same values. When the iTree is fully grown, each point in X is isolated at one of the external nodes. Intuitively, the anomalous points are those (easier to isolate, hence) with the smaller path length in the tree, where the path length h(xi) of point x i ∈ X {\displaystyle x_{i}\in X} is defined as the number of edges xi traverses from the root node to get to an external node. A probabilistic explanation of iTree is provided in the iForest original paper. == Properties of Isolation Forest == Sub-sampling: since iForest does not need to isolate all of normal instances, it can frequently ignore the big majority of the training sample. As a consequence, iForest works very well when the sampling size is kept small, a property that is in contrast with the great majority of existing methods, where large sampling size is usually desirable. Swamping: when normal instances are too close to anomalies, the number of partitions required to separate anomalies increases, a phenomena known as swamping, which makes it more difficult for iForest to discriminate between anomalies and normal points. One of the main reasons for swamping is the presence of too many data for the purpose of anomaly detection, which implies one possible solution to the problem is sub-sampling. Since iForest respond very well to sub-sampling in terms of performance, the reduction of the number of points in the sample is also a good way to reduce the effect of swamping. Masking: when the number of anomalies is high it is possible that some of those aggregate in a dense and large cluster, making it more difficult to separate the single anomalies and, in turn, to detect such points as anomalous. Similarly to swamping, this phenomena (known as "masking") is also more likely when the number of points in the sample is big, and can be alleviated through sub-sampling. High Dimensional Data: one of the main limitation to standard, distance-based methods is their inefficiency in dealing with high dimensional datasets:. The main reason for that is, in a high dimensional space every point is equally sparse, so using a distance-based measure of separation is pretty ineffective. Unfortunately, high-dimensional data also affects the detection performance of iForest, but the performance can be vastly improved by adding a features selection test like Kurtosis to reduce the dimensionality of the sample space. Normal Instances Only: iForest performs well even if the training set does not contain any anomalous point, the reason being that iForest describes data distributions in such a way that high values of the path length h(xi) correspond to the presence of data points. As a consequence, the presence of anomalies is pretty irrelevant to iForest's detection performance. == Anomaly Detection with Isolation Forest == Anomaly detection with Isolation Forest is a process composed of two main stages: in the first stage, a training dataset is used to build iTrees as described in previous sections. in the second stage, each instance in test set is passed through the iTrees build in the previous stage, and a proper "anomaly score" is assigned to the instance using the algorithm described below Once all the instances in the test set have been assigned an anomaly score, it is possible to mark as "anomaly" any point whose score is greater than a predefined threshold, which depends on the domain the analysis is being applied to. === Anomaly Score === Th