Shortest path distance in random k-nearest neighbor graphs

Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are detrimental to machine learning. We also study the behavior of the shortest path distance in weighted kNN graphs.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

Predictors and their domain for statistical downscaling of climate in Bangladesh

Reliable projection of future rainfall in Bangladesh is very important for the assessment of possible impacts of climate change and implementation of necessary adaptation and mitigation measures. Statistical downscaling methods are widely used for downscaling coarse resolution general circulation model (GCM) output at local scale. Selection of predictors and their spatial domain is very important to facilitate downscaling future climate projected by GCMs. The present paper reports the finding of the study conducted to identify the GCM predictors and demarcate their climatic domain for statistical downscaling in Bangladesh at local or regional scale. Twenty-six large scale atmospheric variables which are widely simulated GCM predictors from 45 grid points around the country were analysed using various statistical methods for this purpose. The study reveals that large-scale atmospheric variables at the grid points located in the central-west part of Bangladesh have the highest influence on rainfall. It is expected that the finding of the study will help different meteorological and agricultural organizations of Bangladesh to project rainfall and temperature at local scale in order to provide various agricultural or hydrological services

Historical trends and future projection of climate at Dhaka city of Bangladesh

Dhaka, the capital city of Bangladesh is considered as one of the most vulnerable cities of the world to climate change. A study has been carried out to assess the historical changes as well as future changes in the climate of Dhaka city in order to propose necessary mitigation and adaptation measures. Statistical downscaling model (SDSM) was used for the projection of future changes in daily rainfall and temperature and non-parametric trend analysis was used to assess the changes in rainfall, temperature and related extremes. The impacts of projected changes in climate on urban infrastructure and livelihood in Dhaka city was finally assessed to propose necessary adaptation measures. The study revealed that night time temperature in Dhaka city has increased significantly at a rate of 0.22ºC/decade in last fifty year, which is support to increase continually in the future. Different temperature related extreme events are also found to increase significantly in Dhaka. On the other hand, no significant change in rainfall or rainfall related extremes are observed. Therefore, it can be remarked that imminent impacts of climate change will be due to the increase in temperature and temperature related extremes. The public health and the water and energy supply are likely to be imminent affected sector in the city due to climate change

Phase transition in the family of p-resistances

We study the family of p-resistances on graphs for p 1. This family generalizes the standard resistance distance. We prove that for any fixed graph, for p =1 the p-resistance coincides with the shortest path distance, for p =2it coincides with the standard resistance distance, and for p!1it converges to the inverse of the minimal s-t-cut in the graph. Secondly, we consider the special case of random geometric graphs (such as k-nearest neighbor graphs) when the number n of vertices in the graph tends to infinity. We prove that an interesting phase transition takes place. There exist two critical thresholds p ⇤ and p ⇤ ⇤ such that if p<p ⇤ , then the p-resistance depends on meaningful global properties of the graph, whereas if p>p ⇤ ⇤ , it only depends on trivial local quantities and does not convey any useful information. We can explicitly compute the critical values: p ⇤ = 1 + 1/(d 1) and p ⇤ ⇤ = 1 + 1/(d 2) where d is the dimension of the underlying space (we believe that the fact that there is a small gap between p ⇤ and p ⇤ ⇤ is an artifact of our proofs). We also relate our findings to Laplacian regularization and suggest to use q-Laplacians as regularizers, where q satisfies 1/p ⇤ +1/q =1.

Regime shift in monsoon rainfall of Bangladesh: a sequential data processing approach

As the economy and livelihoods of Bangladesh heavily depends on agriculture, any changes in monsoon rainfall have severe implications for the country. There is a growing concern on monsoon rainfall pattern change in Bangladesh in recent years like other parts of Indian summer monsoon region. A study has been carried out in this paper to analyze the monsoon rainfall time series of Bangladesh to decipher if there any shift in monsoon rainfall regime of Bangladesh. Sixty four years rainfall data recorded at twenty-nine locations distributed over Bangladesh were analyzed using a sequential regime shift detection method for this purpose. The proposed method employed Student’s t-test to detect difference between two subsequent regimes with a cut-off length of one to determine the regime shift. The result shows that monsoon rainfall has increased, mostly in recent years in many locations of Bangladesh. Though increased monsoon rainfall will be helpful for rain-fed agriculture in Bangladesh, at the same time it will also cause more frequent floods, urban water logging, water-borne diseases, etc

Multitask Learning for Brain-Computer Interfaces

Brain-computer interfaces (BCIs) are limited in their applicability in everyday settings by the current necessity to record subjectspecific calibration data prior to actual use of the BCI for communication. In this paper, we utilize the framework of multitask learning to construct a BCI that can be used without any subject-specific calibration process. We discuss how this out-of-the-box BCI can be further improved in a computationally efficient manner as subject-specific data becomes available. The feasibility of the approach is demonstrated on two sets of experimental EEG data recorded during a standard two-class motor imagery paradigm from a total of 19 healthy subjects. Specifically, we show that satisfactory classification results can be achieved with zero training data, and combining prior recordings with subjectspecific calibration data substantially outperforms using subject-specific data only. Our results further show that transfer between recordings under slightly different experimental setups is feasible.

Density-preserving quantization with application to graph downsampling

We consider the problem of vector quantization of i.i.d. samples drawn from a density p on R d. It is desirable that the representatives selected by the quantization algorithm have the same distribution p as the original sample points. However, quantization algorithms based on Euclidean distance, such as k-means, do not have this property. We provide a solution to this problem that takes the unweighted k-nearest neighbor graph on the sample as input. In particular, it does not need to have access to the data points themselves. Our solution generates quantization centers that are “evenly spaced”. We exploit this property to downsample geometric graphs and show that our method produces sparse downsampled graphs. Our algorithm is easy to implement, and we provide theoretical guarantees on the performance of the proposed algorithm

Efficiency of different organic surfactants on nitrate adsorption in water

Organoclays are modified clays in which the natural inorganic interlayer cations are replaced by organic cations. The net amount of organic cations adsorbed to the clay can exceed the cation exchange capacity of the clay, thus providing binding sites for exchangeable anions. Therefore, organic surfactants are efficient in the treatment of contaminated water. Here a review has been carried out to understand the efficiency of various organic surfactants, viz. hexadecyl trimethylammonium, hexadecyl pyridinium and benzethonium on nitrate reduction in drinking water. This study revealed that hexadecyl pyridinium are more efficient to remove nitrate in drinking water than other organic surfactants