Neighbor embedding has been a quantum leap in nonlinear dimensionality reduction, revolutionizing the way data can be visualized.Neighbor embedding typically adapts to the local density in the highdimensional data space with adaptive bandwidths in entropic affinities, while it resolves scale indeterminacies by having unit bandwidths in the low-dimensional embedding space.In this paper, multi-scale stochastic neighbor embedding (Ms.SNE) is improved by allowing it to adapt lowdimensional bandwidths in a data-driven way instead of having fixed ones.In practice, Ms.SNE goes through a multi-scale optimization process; coordinates and bandwidths are optimized separately, in an alternate fashion, to avoid interferences: (i) bandwidths are optimized from previous coordinates and (ii) coordinates are optimized given the new bandwidths.Experimentally, twice adaptive bandwidths improve Ms.SNE's capability to preserve neighborhoods on all scales, i.e., local and global data structure; this claim is supported with quantitative results on several benchmarks. Neighbor embedding for data visualizationDimensionality reduction (DR) [1] yields nonlinear embeddings [2] that allow for visualization and exploratory analysis of data in many domains, such as computational biology [3], to cite just one example.Modern DR involves mostly methods of neighbor embedding (NE) [4], like Student t-distributed stochastic NE (t-SNE) [5] or uniform manifold approximation and projection (UMAP) [6].These methods are very robust to the curse of dimensionalty [7] and produce local embeddings; sparsity of small-size neighborhoods is also the key to accelerate these methods [8,6,9,10].However, sparsity might also cause the loss of the global structure of data [11,6,12,10,2,13,14].This depends on how the final embedding does reminisce [12] about its initialization with PCA [15] or Laplacian eigenmaps [16], either due to early stopping [5] or explicit regularization [13].Another workaround consists in having neighborhoods on two [9, 10] or more scales [11], even though acceleration can become more difficult.A less investigated feature of NE is a form of uniformization of data density in the low-dimensional (LD) embedding.It results from the use of entropic affinities

Local methods of dimensionality reduction like neighborhood embedding (NE) and t-SNE in particular outperform older global approaches such as stress-based multi-dimensional scaling (MDS).Stochastic neighborhoods are less sensitive than distances to statistical variations between spaces with strongly different dimensionalities, making a match across them very difficult.Here, we take inspiration from those stochastic neighborhoods in order to devise a pseudo-distance that is less prone to concentration than the Euclidean distance.For two points in the high-dimensional data space, it is defined as the symmetrized Kullback-Leibler divergence across the (stochastic) neighborhoods of the two points (SKLAN).Plugging the SKLAN in a method of stress-based MDS, we compare quantitatively t-SNE, MDS with all Euclidean distances, and MDS with SKLAN & Euclidean distances on several data sets.The results show that SKLAN allows MDS to perform competitively with t-SNE.

As a local method of dimensionality reduction, t-SNE requires careful initialization in order to preserve the data global structure to the best extent.In regular t-SNE, the low-dimensional embedding is initialized either randomly or with PCA; next, gradient descent refines the embedding coordinates in two phases.In the first one, called early exaggeration, attractive forces between points are artificially strengthened to delay any detrimental effect of repulsive forces while points are still poorly organized.In this paper, a novel initialization of t-SNE is proposed.It works by hierarchizing the data points into a space-partitioning binary tree and successive runs of t-SNE with 4, 8, 16, ..., N points.Between two runs, the prototypical point in each tree branch is split into its two children prototypes, with some little random noise, and the embedding is rescaled to account for the increased population.Experimental results show the effectiveness of the method.The proposed method is compatible with any method of neighbor embedding (t-SNE, UMAP, etc.) provided early exaggeration can be disabled and initial coordinates can be fed into.

To minimise its loss function, the popular method of nonlinear dimensionality reduction t-SNE requires O(N 2 ) computations.As its applications often involve large datasets, fast approximations have been developed, such as Barnes-Hut t-SNE and FIt-SNE.Most fast approximations to t-SNE require the embedding dimensionality to be small, typically 2 or 3, limiting the use of t-SNE to data visualisation.Additionally, the effective computation time of the current accelerated t-SNE algorithms stays too high for a comfortable interactive visual exploration of data.This paper proposes an accelerated approximation to t-SNE with iterations of complexity O(N K), which does not rely on the use of a model to capture information about the low-dimensional space, relieving the computational burden of high dimensionality of the embedding space.For this purpose, the proposed method approximates neighbour sets and keeps track of smoothed estimations of long-range interactions in O(N K) time.The method is qualitatively tested on a handful of datasets and shows comparable results to existing fast neighbour embedding methods in the context of data visualisation.Code is available at https://github.com/PierreLambert3/c_fast_hSNE.git.

Most recent deep neural network architectures for tabular data operate at the feature level and process multiple latent representations simultaneously.While the dimension of these representations is set through hyper-parameter tuning, their number is typically fixed and equal to the number of features in the original data.In this paper, we explore the impact of varying the number of latent representations on model performance.Our results suggest that increasing the number of representations beyond the number of features can help capture more complex interactions, whereas reducing their number can improve performance in cases where there are many uninformative features.

Student t-distributed stochastic neighbor embedding (t-SNE) finds low-dimensional data representations allowing visual exploration of data sets.t-SNE minimises a cost function with a custom two-phase gradient descent.The first phase is called early exaggeration and involves a hyper-parameter whose value can be tricky and time-consuming to set.This paper proposes another way to optimise the cost function without early exaggeration.Empirical evaluation shows that the proposed method of optimization converges faster and yields competitive results in terms of neighborhood preservation.

Multidimensional scaling is a statistical process that aims to embed high-dimensional data into a lower-dimensional, more manageable space.Common MDS algorithms tend to have some limitations when facing large data sets due to their high time and spatial complexities.This paper attempts to tackle the problem by using a stochastic approach to MDS which uses gradient descent to optimise a loss function defined on randomly designated quartets of points.This method mitigates the quadratic memory usage by computing distances on the fly, and has iterations in O(N ) time complexity, with N samples.Experiments show that the proposed method provides competitive results in reasonable time.Public codes are available at https://github.com/PierreLambert3/SQuaD-MDS.git. Multidimensional scaling and its limitationsDimensionality reduction (DR) is the process of mapping high-dimensional (HD) observations into a lower-dimensional (LD) space such that the LD embedding is a faithful representation of the HD data.The main DR uses are in machine learning, to curb the curse of dimensionality, and in visualisation.Mapped data can reveal structures that would lay hidden from the human perception if left in HD.Typically, some information is lost by the DR and, therefore, each DR method has a take on what kind of information should be preserved and what can be lost.Used frequently in visualisation, t-SNE [1] aims at retaining the neighbourhood of each point according to a distance metric and a perplexity, which reflects the size of the neighbourhood to preserve.While t-SNE excels at retaining local structures, sufficiently remote points tend to be considered equally distant by the algorithm and, therefore, the larger-scale structures can be distorted.Such distortions can lead to erroneous conclusions by the human user, who might overestimate the dissimilarity between two clusters that are distant in the LD embedding.For this reason, using multiple DR paradigms in conjunction is a good practice in visualisation: another embedding that preserves distances instead of neighbourhoods would have prevented this erroneous conclusion.This paper considers metric multidimensional scaling (MDS): a DR technique that produces a LD embedding such that the pairwise distances in LD reflect those in HD.MDS minimises a cost function which, in its simplest form, is the sum of the squared differences between distances in HD and the Euclidean distances in LD.A common strategy to optimize this cost function is based on 417

Fast multi-scale neighbor embedding (f-ms-NE) is an algorithm that maps high-dimensional data to a low-dimensional space by preserving the multi-scale data neighborhoods.To lower its time complexity, f-ms-NE uses random subsamplings to estimate the data properties at multiple scales.To improve this estimation and study the f-ms-NE sensitivity to randomness, this paper generalizes the f-ms-NE cost function by averaging several subsamplings.Experiments reveal that this can slightly improve the quality of the embeddings while maintaining reasonable computation times.Codes are available at https://github.com/cdebodt/Fast_Multi-scale_NE.

This paper deals with the open-loop characterization of a micromanipulation system actuated by thermocapillary convective flows. Micrometric size objects placed at the air/liquid interface are actuated by heating the surface of the liquid using a laser. The heat generates a surface tension gradient at the interface which induces thermocapillary convective flows that are used to move the objects. In this paper, the performances of this approach are analyzed based on open-loop experiments. Several actuation strategies are proposed and discussed. The experimental results highlight the potential of this approach since velocities up to several millimeters per second are obtained. However the precision of the positioning is not ensured by open-loop actuation, so closed-loop control will be necessary in future works. As a first step towards closed-loop control, this paper proposes a model of the system. This model is based on the open-loop experimental results, but the proposed methodology can be applied to any setup that use thermocapillary convective flows for particle manipulation.

We present a pick-and-place approach driven by capillarity for highly precise and cost-effective assembly of mesoscopic components onto structured substrates. Based on competing liquid bridges, the technology seamlessly combines programmable capillary grasping, handling, and passive releasing with capillary self-alignment of components onto prepatterned assembly sites. The performance of the capillary gripper is illustrated by comparing the measured lifting capillary forces with those predicted by a hydrostatic model of the liquid meniscus. Two component release strategies, based on either axial or shear capillary forces, are discussed and experimentally validated. The release-and-assembly process developed for a continuously moving assembly substrate provides a roll-to-roll-compatible technology for high-resolution and high-throughput component assembly.

This paper presents a new microrobotic platform actuated by capillary effects, combining surface tension and pressure effects. The device has 6 degrees of freedom (DOFs), among which, three are actuated: the z-axis translation having a stroke of a few hundreds of microns and θxand θytilting up to about 15°. The platform is submerged in a liquid and placed on microbubbles whose shapes (e.g., height) are driven by fluidic parameters (pressure and volume). The modeling of this new type of compliant robot is described and compared with experimental measurements. This paper paves the way for an interesting actuation and robotic solution for submerged devices on the microscale.

This paper presents a new actuation mean for a parallel microrobot based on capillary effect, combining surface tension and pressure effects. The device presented is a compliant moving table having 6 degrees of freedom (dof) among which three are actuated: z axis translation having a stroke of a few hundreds of microns, and θxand θytilt angles up to about 15°. The structure is immersed in a liquid and the actuation principle is based on fluidic parameters (pressure and volume). A model to calculate the stiffness of the system is presented and validated by experimental measurements. Some issues inherent to this type of actuation are also addressed. The presented device is an illustration of a promising solution for microrobotic actuation using capillary effects in a liquid media.

To understand robotic grasping at the nanoscale, contact mechanics between nano grippers and nano samples was studied. Contact mechanics models were introduced to simulate elastic contacts between various profiles of flat surface, sphere and cylinder for different types of nano samples and nano grippers. Analyses and evaluation instances indicate that friction forces, commonly used in macro grasping to overcome the gravity, at nanoscale is often not enough to overcome relatively strong adhesion forces to pick up the nano sample deposited on a substrate due to tiny contact area of the grasping. Two-finger grippers are proposed for the stable nanoscale grasping and a nonparallel gripper with a 'V' configuration was demonstrated with better grasping capabilities than a parallel one. To achieve the robotic nanoscale grasping, a nano gripper constructed from two individually actuated and sensed tips is presented. Pick-and-place manipulation of silicon nanowires validate the theoretical analyses and capabilities of the proposed nano gripper.

The context of this paper is to study the use of capillary microgripper in submerged mediums which requires the use of microbubbles. This paper presents a model and experimentations of the generation of bubbles. In the microsystems which uses liquid, gas bubbles can generate forces due to the surface tension at their interface. To use these bubbles, it is necessary to generate them in a controlled way. In this paper, we propose to study the generation of a bubble having a defined volume, using a syringe pump based device. We first build a mathematical model to predict the growth of the bubble in the liquid. Indeed, the compressibility of the gas and the effect of surface tension are of major importance at microscale, and our model will demonstrate the existence of an instability during the bubble growth. We proceed with a dimensionless study that will allow to predict the existence of the instability on the basis of a dimensionless number. Finally, we present experimental results to validate the mathematical model.

This contribution presents the experimental validation of a computational model of capillary forces based on the Laplace equation for the meniscus geometry and on the Kelvin equation for capillary condensation. We apply this to a tip of AFM cantilever ended by a 100 nm curvature tip, and describe the effect of both humidity rate and relative tilt between the cantilever and the substrate. We propose to pick and place components at the considered scale (100 nm) by varying the capillary force.