K-Means algorithm is a popular clustering method. However, it has two limitations: 1) it gets stuck easily in spurious local minima, and 2) the number of clusters k has to be given a priori. To solve these two issues, a multi-prototypes convex merging based K-Means clustering algorithm (MCKM) is presented. First, based on the structure of the spurious local minima of the K-Means problem, a multi-prototypes sampling (MPS) is designed to select the appropriate number of multi-prototypes for data with arbitrary shapes. A theoretical proof is given to guarantee that the multi-prototypes selected by MPS can achieve a constant factor approximation to the optimal cost of the K-Means problem. Then, a merging technique, called convex merging (CM), merges the multi-prototypes to get a better local minima without k being given a priori. Specifically, CM can obtain the optimal merging and estimate the correct k. By integrating these two techniques with K-Means algorithm, the proposed MCKM is an efficient and explainable clustering algorithm for escaping the undesirable local minima of K-Means problem without given k first. Experimental results performed on synthetic and real-world data sets have verified the effectiveness of the proposed algorithm.
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In this paper, a new fast algorithm for path planning and a collision prediction framework for two dimensional dynamically changing environments are introduced. The method is called Time Distance (TD) and benefits from the space-time space idea. First, the TD concept is defined as the time interval that must be spent in order for an object to reach another object or a location. Next, TD functions are derived as a function of location, velocity and geometry of objects. To construct the configuration-time space, TD functions in conjunction with another function named "Z-Infinity" are exploited. Finally, an explicit formula for creating the length optimal collision free path is presented. Length optimization in this formula is achieved using a function named "Route Function" which minimizes a cost function. Performance of the path planning algorithm is evaluated in simulations. Comparisons indicate that the algorithm is fast enough and capable to generate length optimal paths as the most effective methods do. Finally, as another usage of the TD functions, a collision prediction framework is presented. This framework consists of an explicit function which is a function of TD functions and calculates the TD of the vehicle with respect to all objects of the environment.
The task of image-level weakly-supervised semantic segmentation (WSSS) has gained popularity in recent years, as it reduces the vast data annotation cost for training segmentation models. The typical approach for WSSS involves training an image classification network using global average pooling (GAP) on convolutional feature maps. This enables the estimation of object locations based on class activation maps (CAMs), which identify the importance of image regions. The CAMs are then used to generate pseudo-labels, in the form of segmentation masks, to supervise a segmentation model in the absence of pixel-level ground truth. In case of the SEAM baseline, a previous work proposed to improve CAM learning in two ways: (1) Importance sampling, which is a substitute for GAP, and (2) the feature similarity loss, which utilizes a heuristic that object contours almost exclusively align with color edges in images. In this work, we propose a different probabilistic interpretation of CAMs for these techniques, rendering the likelihood more appropriate than the multinomial posterior. As a result, we propose an add-on method that can boost essentially any previous WSSS method, improving both the region similarity and contour quality of all implemented state-of-the-art baselines. This is demonstrated on a wide variety of baselines on the PASCAL VOC dataset. Experiments on the MS COCO dataset show that performance gains can also be achieved in a large-scale setting. Our code is available at //github.com/arvijj/hfpl.
A robotic platform for mobile manipulation needs to satisfy two contradicting requirements for many real-world applications: A compact base is required to navigate through cluttered indoor environments, while the support needs to be large enough to prevent tumbling or tip over, especially during fast manipulation operations with heavy payloads or forceful interaction with the environment. This paper proposes a novel robot design that fulfills both requirements through a versatile footprint. It can reconfigure its footprint to a narrow configuration when navigating through tight spaces and to a wide stance when manipulating heavy objects. Furthermore, its triangular configuration allows for high-precision tasks on uneven ground by preventing support switches. A model predictive control strategy is presented that unifies planning and control for simultaneous navigation, reconfiguration, and manipulation. It converts task-space goals into whole-body motion plans for the new robot. The proposed design has been tested extensively with a hardware prototype. The footprint reconfiguration allows to almost completely remove manipulation-induced vibrations. The control strategy proves effective in both lab experiment and during a real-world construction task.
In this paper, we consider waveform design for dualfunction radar-communication systems based on multiple-inputmultiple-out arrays. To achieve better Rician target detection performance, we use the relative entropy associated with the formulated detection problem as the design metric. We also impose a multiuser interference energy constraint on the waveforms to ensure the achievable sum-rate of the communications. Two algorithms are presented to tackle the nonlinear non-convex waveform design problem. In the first algorithm, we derive a quadratic function to minorize the objective function. To tackle the quadratically constrained quadratic programming problem at each iteration, a semidefinite relaxation approach followed by a rank-one decomposition procedure and an efficient alternating direction method of multipliers (ADMM) are proposed, respectively. In the second algorithm, we present a novel ADMM algorithm to tackle the optimization problem and employ an efficient minorization-maximization approach in the inner loop of the ADMM algorithm. Numerical results demonstrate the superiority of both algorithms. Moreover, the presented algorithms can be extended to synthesize peak-to-average-power ratio constrained waveforms, which allows the radio frequency amplifier to operate at an increased efficiency.
Many real-world systems often involve physical components or operating environments with highly nonlinear and uncertain dynamics. A number of different control algorithms can be used to design optimal controllers for such systems, assuming a reasonably high-fidelity model of the actual system. However, the assumptions made on the stochastic dynamics of the model when designing the optimal controller may no longer be valid when the system is deployed in the real-world. The problem addressed by this paper is the following: Suppose we obtain an optimal trajectory by solving a control problem in the training environment, how do we ensure that the real-world system trajectory tracks this optimal trajectory with minimal amount of error in a deployment environment. In other words, we want to learn how we can adapt an optimal trained policy to distribution shifts in the environment. Distribution shifts are problematic in safety-critical systems, where a trained policy may lead to unsafe outcomes during deployment. We show that this problem can be cast as a nonlinear optimization problem that could be solved using heuristic method such as particle swarm optimization (PSO). However, if we instead consider a convex relaxation of this problem, we can learn policies that track the optimal trajectory with much better error performance, and faster computation times. We demonstrate the efficacy of our approach on tracking an optimal path using a Dubin's car model, and collision avoidance using both a linear and nonlinear model for adaptive cruise control.
This study considers the control problem with signal temporal logic (STL) specifications. Prior works have adopted smoothing techniques to address this problem within a feasible time frame and solve the problem by applying sequential quadratic programming (SQP) methods naively. However, one of the drawbacks of this approach is that solutions can easily become trapped in local minima that do not satisfy the specification. In this study, we propose a new optimization method, termed CCP-based SQP, based on the convex-concave procedure (CCP). Our framework includes a new robustness decomposition method that decomposes the robustness function into a set of constraints, resulting in a form of difference of convex (DC) program that can be solved efficiently. We solve this DC program sequentially as a quadratic program by only approximating the disjunctive parts of the specifications. Our experimental results demonstrate that our method has a superior performance compared to the state-of-the-art SQP methods in terms of both robustness and computational time.
Comparison-based learning addresses the problem of learning when, instead of explicit features or pairwise similarities, one only has access to comparisons of the form: \emph{Object $A$ is more similar to $B$ than to $C$.} Recently, it has been shown that, in Hierarchical Clustering, single and complete linkage can be directly implemented using only such comparisons while several algorithms have been proposed to emulate the behaviour of average linkage. Hence, finding hierarchies (or dendrograms) using only comparisons is a well understood problem. However, evaluating their meaningfulness when no ground-truth nor explicit similarities are available remains an open question. In this paper, we bridge this gap by proposing a new revenue function that allows one to measure the goodness of dendrograms using only comparisons. We show that this function is closely related to Dasgupta's cost for hierarchical clustering that uses pairwise similarities. On the theoretical side, we use the proposed revenue function to resolve the open problem of whether one can approximately recover a latent hierarchy using few triplet comparisons. On the practical side, we present principled algorithms for comparison-based hierarchical clustering based on the maximisation of the revenue and we empirically compare them with existing methods.
In order to perform highly dynamic and agile maneuvers, legged robots typically spend time in underactuated domains (e.g. with feet off the ground) where the system has limited command of its acceleration and a constrained amount of time before transitioning to a new domain (e.g. foot touchdown). Meanwhile, these transitions can have instantaneous, unbounded effects on perturbations. These properties make it difficult for local feedback controllers to effectively recover from disturbances as the system evolves through underactuated domains and hybrid impact events. To address this, we utilize the fundamental solution matrix that characterizes the evolution of perturbations through a hybrid trajectory and its 2-norm, which represents the worst-case growth of perturbations. In this paper, the worst-case perturbation analysis is used to explicitly reason about the tracking performance of a hybrid trajectory and is incorporated in an iLQR framework to optimize a trajectory while taking into account the closed-loop convergence of the trajectory under an LQR tracking controller. The generated convergent trajectories are able to recover more effectively from perturbations, are more robust to large disturbances, and use less feedback control effort than trajectories generated with traditional optimization methods.
In this paper, we propose a one-stage online clustering method called Contrastive Clustering (CC) which explicitly performs the instance- and cluster-level contrastive learning. To be specific, for a given dataset, the positive and negative instance pairs are constructed through data augmentations and then projected into a feature space. Therein, the instance- and cluster-level contrastive learning are respectively conducted in the row and column space by maximizing the similarities of positive pairs while minimizing those of negative ones. Our key observation is that the rows of the feature matrix could be regarded as soft labels of instances, and accordingly the columns could be further regarded as cluster representations. By simultaneously optimizing the instance- and cluster-level contrastive loss, the model jointly learns representations and cluster assignments in an end-to-end manner. Extensive experimental results show that CC remarkably outperforms 17 competitive clustering methods on six challenging image benchmarks. In particular, CC achieves an NMI of 0.705 (0.431) on the CIFAR-10 (CIFAR-100) dataset, which is an up to 19\% (39\%) performance improvement compared with the best baseline.
Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit the given data to reveal the underlying cluster structure. Some types of losses---such as k-means, or its non-linear version: kernelized k-means (centroid based), and DBSCAN (density based)---are popular choices due to their good empirical performance on a range of applications. Although every so often the clustering output using these standard losses fails to reveal the underlying structure, and the practitioner has to custom-design their own variation. In this work we take an intrinsically different approach to clustering: rather than fitting a dataset to a specific clustering loss, we train a recurrent model that learns how to cluster. The model uses as training pairs examples of datasets (as input) and its corresponding cluster identities (as output). By providing multiple types of training datasets as inputs, our model has the ability to generalize well on unseen datasets (new clustering tasks). Our experiments reveal that by training on simple synthetically generated datasets or on existing real datasets, we can achieve better clustering performance on unseen real-world datasets when compared with standard benchmark clustering techniques. Our meta clustering model works well even for small datasets where the usual deep learning models tend to perform worse.
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