ImageSig: A signature transform for ultra-lightweight image recognition

This paper introduces a new lightweight method for image recognition. ImageSig is based on computing signatures and does not require a convolutional structure or an attention-based encoder. It is striking to the authors that it achieves: a) an accuracy for 64 X 64 RGB images that exceeds many of the state-of-the-art methods and simultaneously b) requires orders of magnitude less FLOPS, power and memory footprint. The pretrained model can be as small as 44.2 KB in size. ImageSig shows unprecedented performance on hardware such as Raspberry Pi and Jetson-nano. ImageSig treats images as streams with multiple channels. These streams are parameterized by spatial directions. We contribute to the functionality of signature and rough path theory to stream-like data and vision tasks on static images beyond temporal streams. With very few parameters and small size models, the key advantage is that one could have many of these "detectors" assembled on the same chip; moreover, the feature acquisition can be performed once and shared between different models of different tasks - further accelerating the process. This contributes to energy efficiency and the advancements of embedded AI at the edge

Best network chirplet-chain: Near-optimal coherent detection of unmodeled gravitation wave chirps with a network of detectors

The searches of impulsive gravitational waves (GW) in the data of the ground-based interferometers focus essentially on two types of waveforms: short unmodeled bursts and chirps from inspiralling compact binaries. There is room for other types of searches based on different models. Our objective is to fill this gap. More specifically, we are interested in GW chirps with an arbitrary phase/frequency vs. time evolution. These unmodeled GW chirps may be considered as the generic signature of orbiting/spinning sources. We expect quasi-periodic nature of the waveform to be preserved independent of the physics which governs the source motion. Several methods have been introduced to address the detection of unmodeled chirps using the data of a single detector. Those include the best chirplet chain (BCC) algorithm introduced by the authors. In the next years, several detectors will be in operation. The joint coherent analysis of GW by multiple detectors can improve the sight horizon, the estimation of the source location and the wave polarization angles. Here, we extend the BCC search to the multiple detector case. The method amounts to searching for salient paths in the combined time-frequency representation of two synthetic streams. The latter are time-series which combine the data from each detector linearly in such a way that all the GW signatures received are added constructively. We give a proof of principle for the full sky blind search in a simplified situation which shows that the joint estimation of the source sky location and chirp frequency is possible.Comment: 22 pages, revtex4, 6 figure

Extracting information from the signature of a financial data stream

Market events such as order placement and order cancellation are examples of the complex and substantial flow of data that surrounds a modern financial engineer. New mathematical techniques, developed to describe the interactions of complex oscillatory systems (known as the theory of rough paths) provides new tools for analysing and describing these data streams and extracting the vital information. In this paper we illustrate how a very small number of coefficients obtained from the signature of financial data can be sufficient to classify this data for subtle underlying features and make useful predictions. This paper presents financial examples in which we learn from data and then proceed to classify fresh streams. The classification is based on features of streams that are specified through the coordinates of the signature of the path. At a mathematical level the signature is a faithful transform of a multidimensional time series. (Ben Hambly and Terry Lyons \cite{uniqueSig}), Hao Ni and Terry Lyons \cite{NiLyons} introduced the possibility of its use to understand financial data and pointed to the potential this approach has for machine learning and prediction. We evaluate and refine these theoretical suggestions against practical examples of interest and present a few motivating experiments which demonstrate information the signature can easily capture in a non-parametric way avoiding traditional statistical modelling of the data. In the first experiment we identify atypical market behaviour across standard 30-minute time buckets sampled from the WTI crude oil future market (NYMEX). The second and third experiments aim to characterise the market "impact" of and distinguish between parent orders generated by two different trade execution algorithms on the FTSE 100 Index futures market listed on NYSE Liffe

Detecting early signs of depressive and manic episodes in patients with bipolar disorder using the signature-based model

Recurrent major mood episodes and subsyndromal mood instability cause substantial disability in patients with bipolar disorder. Early identification of mood episodes enabling timely mood stabilisation is an important clinical goal. Recent technological advances allow the prospective reporting of mood in real time enabling more accurate, efficient data capture. The complex nature of these data streams in combination with challenge of deriving meaning from missing data mean pose a significant analytic challenge. The signature method is derived from stochastic analysis and has the ability to capture important properties of complex ordered time series data. To explore whether the onset of episodes of mania and depression can be identified using self-reported mood data.Comment: 12 pages, 3 tables, 10 figure

Fourteen candidate RR Lyrae star streams in the inner Galaxy

We apply the GC3 stream-finding method to RR Lyrae stars (RRLS) in the Catalina survey. We find two RRLS stream candidates at $>4\sigma$ confidence and another 12 at $>3.5\sigma$ confidence over the Galactocentric distance range $4 < D/{\rm kpc} < 26$. Of these, only two are associated with known globular clusters (NGC 1261 and Arp2). The remainder are candidate `orphan' streams, consistent with the idea that globular cluster streams are most visible close to dissolution. Our detections are likely a lower bound on the total number of dissolving globulars in the inner galaxy, since many globulars have few RRLS while only the brightest streams are visible over the Galactic RRLS background, particularly given the current lack of kinematical information. We make all of our candidate streams publicly available and provide a new GALSTREAMS Python library for the footprints of all known streams and overdensities in the Milky Way.Comment: 18 pages, 4 figures. Accepted for publication at MNRAS. GALSTREAMS Milky Way Streams Footprint Library are available at https://github.com/cmateu/galstreams . All RRL data and code used in the paper are available at https://cmateu.github.io/Cecilia_Mateu_WebPage/CatalinaGC3_Streams.htm