Weakly adaptive comparison searching

AbstractWe consider schemes of discrete search in the set {1,…,n} using only comparison queries, i.e. those of the form x<a? for aϵ{1,…,n}. Such a scheme is called i-adaptive if questions may be stated in i series, so that answers are obtained after each series but not between particular questions in it. We describe a worst-case optimal algorithm of i-adaptive search and determine its complexity. The latter turns out to be i·n1i where i may be a function of n. We also consider the closely related version of continuous search with a given error bound

Exemplar Based Deep Discriminative and Shareable Feature Learning for Scene Image Classification

In order to encode the class correlation and class specific information in image representation, we propose a new local feature learning approach named Deep Discriminative and Shareable Feature Learning (DDSFL). DDSFL aims to hierarchically learn feature transformation filter banks to transform raw pixel image patches to features. The learned filter banks are expected to: (1) encode common visual patterns of a flexible number of categories; (2) encode discriminative information; and (3) hierarchically extract patterns at different visual levels. Particularly, in each single layer of DDSFL, shareable filters are jointly learned for classes which share the similar patterns. Discriminative power of the filters is achieved by enforcing the features from the same category to be close, while features from different categories to be far away from each other. Furthermore, we also propose two exemplar selection methods to iteratively select training data for more efficient and effective learning. Based on the experimental results, DDSFL can achieve very promising performance, and it also shows great complementary effect to the state-of-the-art Caffe features.Comment: Pattern Recognition, Elsevier, 201

Invariant template matching in systems with spatiotemporal coding: a vote for instability

We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that can be modeled as parameterized uncertainties such as image blur, luminance, translation, and rotation as well as unmodeled ones. Biological and neural systems require that these perturbations be processed through a minimal number of channels by simple adaptation mechanisms. We found that the most suitable mathematical framework to meet this requirement is that of weakly attracting sets. This framework provides us with a normative and unifying solution to the pattern recognition problem. We analyze the consequences of its explicit implementation in neural systems. Several properties inherent to the systems designed in accordance with our normative mathematical argument coincide with known empirical facts. This is illustrated in mental rotation, visual search and blur/intensity adaptation. We demonstrate how our results can be applied to a range of practical problems in template matching and pattern recognition.Comment: 52 pages, 12 figure

Optimal Hashing-based Time-Space Trade-offs for Approximate Near Neighbors

[See the paper for the full abstract.] We show tight upper and lower bounds for time-space trade-offs for the $c$-Approximate Near Neighbor Search problem. For the $d$-dimensional Euclidean space and $n$-point datasets, we develop a data structure with space $n^{1 + \rho_u + o(1)} + O(dn)$ and query time $n^{\rho_q + o(1)} + d n^{o(1)}$ for every $\rho_u, \rho_q \geq 0$ such that: \begin{equation} c^2 \sqrt{\rho_q} + (c^2 - 1) \sqrt{\rho_u} = \sqrt{2c^2 - 1}. \end{equation} This is the first data structure that achieves sublinear query time and near-linear space for every approximation factor $c > 1$, improving upon [Kapralov, PODS 2015]. The data structure is a culmination of a long line of work on the problem for all space regimes; it builds on Spherical Locality-Sensitive Filtering [Becker, Ducas, Gama, Laarhoven, SODA 2016] and data-dependent hashing [Andoni, Indyk, Nguyen, Razenshteyn, SODA 2014] [Andoni, Razenshteyn, STOC 2015]. Our matching lower bounds are of two types: conditional and unconditional. First, we prove tightness of the whole above trade-off in a restricted model of computation, which captures all known hashing-based approaches. We then show unconditional cell-probe lower bounds for one and two probes that match the above trade-off for $\rho_q = 0$, improving upon the best known lower bounds from [Panigrahy, Talwar, Wieder, FOCS 2010]. In particular, this is the first space lower bound (for any static data structure) for two probes which is not polynomially smaller than the one-probe bound. To show the result for two probes, we establish and exploit a connection to locally-decodable codes.Comment: 62 pages, 5 figures; a merger of arXiv:1511.07527 [cs.DS] and arXiv:1605.02701 [cs.DS], which subsumes both of the preprints. New version contains more elaborated proofs and fixed some typo

Electric communication during courtship and spawning in two sibling species of dwarf stonebasher from southern Africa, Pollimyrus castelnaui and P. marianne (Mormyridae, Teleostei): evidence for a non species-specific communication code?

The fixed part of the electrocommunication signal, the electric organ discharge (EOD) waveform, is well differentiated in the two vicariant dwarf stonebasher species, Pollimyrus castelnaui and P. marianne. However, differentiation regarding the variable, situation-dependent part, i.e., inter-discharge interval (IDI) patterns, has never been studied in a pair of sibling species of mormyrid fish. We here compare the electrical signalling that accompanies different motor behaviours (such as resting and swimming, territorial agonistic interactions, courtship and spawning) in the two species. Double pulse patterns of regularly alternating short IDIs of 8-11 ms and long ones of 16-100 ms accompanied threat displays in both species. In three pairs of P. marianne and five pairs of P. castelnaui, courtship was characterised by nest building, territory patrolling and acoustic displays (advertisment calls) that were accompanied by long discharge breaks in the male and highly regular IDIs around 50 ms in the female of both species. Nest-tending males showed IDI sequences consisting of regularly alternating double pulse patterns, similar to threat displays. During spawning both sexes generated stereotyped IDI sequences of a low discharge rate. All IDI patterns occurring in one species were also found in the other, and no species-specifity was identified at that level. Playback experiments contrasting conspecific and heterospecific IDI sequences (that had been recorded from nocturnally swimming fish) revealed preferences in none of the six experimental subjects. Double pulse patterns, high discharge rate displays (HD) and regularisations of the IDI sequence accompanying specific behaviours occurred in similar form in both dwarf stonebasher species of the present study. Therefore, we conclude that in the speciation of P. castelnaui and P. marianne the fixed part of the EOD, its waveform, was under more differential selection pressure than its variable part, the patterns of IDI