SCALABLE APPROXIMATION OF KERNEL FUZZY C-MEANS

Virtually every sector of business and industry that uses computing, including financial analysis, search engines, and electronic commerce, incorporate Big Data analysis into their business model. Sophisticated clustering algorithms are popular for deducing the nature of data by assigning labels to unlabeled data. We address two main challenges in Big Data. First, by definition, the volume of Big Data is too large to be loaded into a computer’s memory (this volume changes based on the computer used or available, but there is always a data set that is too large for any computer). Second, in real-time applications, the velocity of new incoming data prevents historical data from being stored and future data from being accessed. Therefore, we propose our Streaming Kernel Fuzzy c-Means (stKFCM) algorithm, which reduces both computational complexity and space complexity significantly. The proposed stKFCM only requires O(n2) memory where n is the (predetermined) size of a data subset (or data chunk) at each time step, which makes this algorithm truly scalable (as n can be chosen based on the available memory). Furthermore, only 2n2 elements of the full N × N (where N >> n) kernel matrix need to be calculated at each time-step, thus reducing both the computation time in producing the kernel elements and also the complexity of the FCM algorithm. Empirical results show that stKFCM, even with relatively very small n, can provide clustering performance as accurately as kernel fuzzy c-means run on the entire data set while achieving a significant speedup.

Big Manistee River Tributaries as Potential Arctic Grayling Habitat

The Big Manistee River was one of the most well known Michigan rivers to historically support a population of Arctic grayling (Thymallus arctics). Overfishing, competition with introduced fish, and habitat loss due to logging are believed to have caused their decline and ultimate extirpation from the Big Manistee River around 1900 and from the State of Michigan by 1936. Grayling are a species of great cultural importance to Little River Band of Ottawa Indian tribal heritage and although past attempts to reintroduce Arctic grayling have been unsuccessful, a continued interest in their return led to the assessment of environmental conditions of tributaries within a 21 kilometer section of the Big Manistee River to determine if suitable habitat exists. Although data describing historical conditions in the Big Manistee River is limited, we reviewed the literature to determine abiotic conditions prior to Arctic grayling disappearance and the habitat conditions in rivers in western and northwestern North America where they currently exist. We assessed abiotic habitat metrics from 23 sites distributed across 8 tributaries within the Manistee River watershed. Data collected included basic water parameters, streambed substrate composition, channel profile and areal measurements of channel geomorphic unit, and stream velocity and discharge measurements. These environmental condition values were compared to literature values, habitat suitability thresholds, and current conditions of rivers with Arctic grayling populations to assess the feasibility of the abiotic habitat in Big Manistee River tributaries to support Arctic grayling. Although the historic grayling habitat in the region was disturbed during the era of major logging around the turn of the 20th century, our results indicate that some important abiotic conditions within Big Manistee River tributaries are within the range of conditions that support current and past populations of Arctic grayling. Seven tributaries contained between 20-30% pools by area, used by grayling for refuge. All but two tributaries were composed primarily of pebbles, with the remaining two dominated by fine substrates (sand, silt, clay). Basic water parameters and channel depth were within the ranges of those found for populations of Arctic grayling persisting in Montana, Alaska, and Canada for all tributaries. Based on the metrics analyzed in this study, suitable abiotic grayling habitat does exist in Big Manistee River tributaries.