Outlier detection plays an essential role in many data-driven applications to identify isolated instances that are different from the majority. While many statistical learning and data mining techniques have been used for developing more effective outlier detection algorithms, the interpretation of detected outliers does not receive much attention. Interpretation is becoming increasingly important to help people trust and evaluate the developed models through providing intrinsic reasons why the certain outliers are chosen. It is difficult, if not impossible, to simply apply feature selection for explaining outliers due to the distinct characteristics of various detection models, complicated structures of data in certain applications, and imbalanced distribution of outliers and normal instances. In addition, the role of contrastive contexts where outliers locate, as well as the relation between outliers and contexts, are usually overlooked in interpretation. To tackle the issues above, in this paper, we propose a novel Contextual Outlier INterpretation (COIN) method to explain the abnormality of existing outliers spotted by detectors. The interpretability for an outlier is achieved from three aspects: outlierness score, attributes that contribute to the abnormality, and contextual description of its neighborhoods. Experimental results on various types of datasets demonstrate the flexibility and effectiveness of the proposed framework compared with existing interpretation approaches.

The variability of the clusters generated by clustering techniques in the domain of latitude and longitude variables of fatal crash data are significantly unpredictable. This unpredictability, caused by the randomness of fatal crash incidents, reduces the accuracy of crash frequency (i.e., counts of fatal crashes per cluster) which is used to measure traffic safety in practice. In this paper, a quantitative measure of traffic safety that is not significantly affected by the aforementioned variability is proposed. It introduces a fatal point -- a segment with the highest frequency of fatality -- concept based on cluster characteristics and detects them by imposing rounding errors to the hundredth decimal place of the longitude. The frequencies of the cluster and the cluster's fatal point are combined to construct a low-sensitive quantitative measure of traffic safety for the cluster. The performance of the proposed measure of traffic safety is then studied by varying the parameter k of k-means clustering with the expectation that other clustering techniques can be adopted in a similar fashion. The 2015 North Carolina fatal crash dataset of Fatality Analysis Reporting System (FARS) is used to evaluate the proposed fatal point concept and perform experimental analysis to determine the effectiveness of the proposed measure. The empirical study shows that the average traffic safety, measured by the proposed quantitative measure over several clusters, is not significantly affected by the variability, compared to that of the standard crash frequency.

We address the problem of bootstrapping language acquisition for an artificial system similarly to what is observed in experiments with human infants. Our method works by associating meanings to words in manipulation tasks, as a robot interacts with objects and listens to verbal descriptions of the interactions. The model is based on an affordance network, i.e., a mapping between robot actions, robot perceptions, and the perceived effects of these actions upon objects. We extend the affordance model to incorporate spoken words, which allows us to ground the verbal symbols to the execution of actions and the perception of the environment. The model takes verbal descriptions of a task as the input and uses temporal co-occurrence to create links between speech utterances and the involved objects, actions, and effects. We show that the robot is able form useful word-to-meaning associations, even without considering grammatical structure in the learning process and in the presence of recognition errors. These word-to-meaning associations are embedded in the robot's own understanding of its actions. Thus, they can be directly used to instruct the robot to perform tasks and also allow to incorporate context in the speech recognition task. We believe that the encouraging results with our approach may afford robots with a capacity to acquire language descriptors in their operation's environment as well as to shed some light as to how this challenging process develops with human infants.

Machine learning and predictive analytics are pervasive in our lives today. AI impacts nearly everything we do and interact with including retail and wholesale pricing, consumer habits and behaviors, marketing and advertising, politics, entertainment, sports, medicine, business logistics and planning, fraud and risk detection, airline and truck route planning, pricing strategy, gaming, AI speech recognition, AI image recognition, self-driving cars, and robotics. Yet whether you are creating a self-driving car, predicting customer churn, or cresting a product recommendation system, all machine learning projects follow the same process and the same five basic phases. Data is the new oil. It is quickly becoming the most valuable commodity in the world. Data is like oil because it fuels machine learning projects. Without data, there is no machine learning and no predictive analytics. And just like grades of oil, there are grades of data. Supreme data is like rocket fuel for machine learning models, and buyers pay a premium for it.

This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in the span of the data that has minimum projection on the other data points and non-vanishing projection on d. The obtained directions are subsequently leveraged to identify a neighborhood set for each data point. An alternating direction method of multipliers framework is provided to efficiently solve for the optimal directions. The proposed method is shown to notably outperform the existing subspace clustering methods, particularly for unwieldy scenarios involving high levels of noise and close subspaces, and yields the state-of-the-art results for the problem of face clustering using subspace segmentation.

In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. This paper presents a new approach dubbed Innovation Pursuit (iPursuit) to the problem of subspace clustering using a new geometrical idea whereby subspaces are identified based on their relative novelties. We present two frameworks in which the idea of innovation pursuit is used to distinguish the subspaces. Underlying the first framework is an iterative method that finds the subspaces consecutively by solving a series of simple linear optimization problems, each searching for a direction of innovation in the span of the data potentially orthogonal to all subspaces except for the one to be identified in one step of the algorithm. A detailed mathematical analysis is provided establishing sufficient conditions for iPursuit to correctly cluster the data. The proposed approach can provably yield exact clustering even when the subspaces have significant intersections. It is shown that the complexity of the iterative approach scales only linearly in the number of data points and subspaces, and quadratically in the dimension of the subspaces. The second framework integrates iPursuit with spectral clustering to yield a new variant of spectral-clustering-based algorithms. The numerical simulations with both real and synthetic data demonstrate that iPursuit can often outperform the state-of-the-art subspace clustering algorithms, more so for subspaces with significant intersections, and that it significantly improves the state-of-the-art result for subspace-segmentation-based face clustering.

Big spatio-temporal datasets, available through both open and administrative data sources, offer significant potential for social science research. The magnitude of the data allows for increased resolution and analysis at individual level. While there are recent advances in forecasting techniques for highly granular temporal data, little attention is given to segmenting the time series and finding homogeneous patterns. In this paper, it is proposed to estimate behavioral profiles of individuals' activities over time using Gaussian Process-based models. In particular, the aim is to investigate how individuals or groups may be clustered according to the model parameters. Such a Bayesian non-parametric method is then tested by looking at the predictability of the segments using a combination of models to fit different parts of the temporal profiles. Model validity is then tested on a set of holdout data. The dataset consists of half hourly energy consumption records from smart meters from more than 100,000 households in the UK and covers the period from 2015 to 2016. The methodological approach developed in the paper may be easily applied to datasets of similar structure and granularity, for example social media data, and may lead to improved accuracy in the prediction of social dynamics and behavior.

Correlation matrices are omnipresent in multivariate data analysis. When the number $d$ of variables is large, the sample estimates of correlation matrices are typically noisy and conceal underlying dependence patterns. We consider the case when the variables can be grouped into $K$ clusters with exchangeable dependence; an assumption often made in applications in finance and econometrics. Under this partial exchangeability condition, the corresponding correlation matrix has a block structure and the number of unknown parameters is reduced from $d(d-1)/2$ to at most $K(K+1)/2$. We propose a robust algorithm based on Kendall's rank correlation to identify the clusters without assuming the knowledge of $K$ a priori or anything about the margins except continuity. The corresponding block-structured estimator performs considerably better than the sample Kendall rank correlation matrix when $K < d$. Even in the unstructured case $K = d$, though there is no gain asymptotically, the new estimator can be much more efficient in finite samples. When the data are elliptical, the results extend to linear correlation matrices and their inverses. The procedure is illustrated on financial stock returns.

Epanechnikov Mean Shift is a simple yet empirically very effective algorithm for clustering. It localizes the centroids of data clusters via estimating modes of the probability distribution that generates the data points, using the `optimal' Epanechnikov kernel density estimator. However, since the procedure involves non-smooth kernel density functions, the convergence behavior of Epanechnikov mean shift lacks theoretical support as of this writing---most of the existing analyses are based on smooth functions and thus cannot be applied to Epanechnikov Mean Shift. In this work, we first show that the original Epanechnikov Mean Shift may indeed terminate at a non-critical point, due to the non-smoothness nature. Based on our analysis, we propose a simple remedy to fix it. The modified Epanechnikov Mean Shift is guaranteed to terminate at a local maximum of the estimated density, which corresponds to a cluster centroid, within a finite number of iterations. We also propose a way to avoid running the Mean Shift iterates from every data point, while maintaining good clustering accuracies under non-overlapping spherical Gaussian mixture models. This further pushes Epanechnikov Mean Shift to handle very large and high-dimensional data sets. Experiments show surprisingly good performance compared to the Lloyd's K-means algorithm and the EM algorithm.

Pairwise "same-cluster" queries are one of the most widely used forms of supervision in semi-supervised clustering. However, it is impractical to ask human oracles to answer every query correctly. In this paper, we study the influence of allowing "not-sure" answers from a weak oracle and propose an effective algorithm to handle such uncertainties in query responses. Two realistic weak oracle models are considered where ambiguity in answering depends on the distance between two points. We show that a small query complexity is adequate for effective clustering with high probability by providing better pairs to the weak oracle. Experimental results on synthetic and real data show the effectiveness of our approach in overcoming supervision uncertainties and yielding high quality clusters.