Algorithm Profiling Sample Clauses

Algorithm Profiling. This section describes the algorithmic analysis of the Count-Min algorithm. The Count-Min Algorithm consists of three main functions: the sketch initialization, the update and the estimation. The Count-Min sketch data structure consists of a fixed 2-D array of counters, of width w and depth d, as shown in Figure 4. Each row of counters is associated with a different hash function. The hash function maps items uniformly onto the range {1, 2, . . . w}. For items represented as integers i, the hash functions can be of the form (a*i+b mod p mod w), where p is a prime number larger than the maximum i value (say, p = 231 − 1 or p = 261 − 1), and a, b are values chosen randomly in the range 1 to p − 1. It is important that each hash function is different; otherwise there is no benefit from the repetition.

Algorithm Profiling. This section makes the algorithmic analysis of the Exponential Histogram algorithm. The EH data structure is used for solving the Basic Counting problem. As described above, the Exponential histogram is a data structure that maintains the count of the elements with value 1 in the last N elements seen from the stream. The Exponential Histogram algorithm is based on two processes:

Algorithm Profiling. This section presents an algorithmic analysis of the HY correlation estimator. The HY estimator calculates the correlation between two stock markets using their transaction prices. As the stock transactions are non-synchronous, the HY correlation estimator is calculated over all the overlapping transaction time intervals. Figure 12 shows an example for the calculation of the HY estimator over the transactions of two market stocks The HY estimator calculation is based on the computation of the covariance for all the pairs of the market stocks and the calculation of the transactions of each market stock separately. The direct use of equation of Figure 11 has O(mn) complexity(where m and n are the number of transactions for the first and the second stock respectively).

Algorithm Profiling. In this section we present critical points of the LIBSVM software code that indicate hardware opportunities. In order to do so, we performed profiling of the code using the Linux GNU GCC profiling tool (gprof) so as to detect potential parallelism. Description Time percentage SVM Function Computes xi*xj 70.23% dot_product() Computes the kernel function K(xi,xj) 8.27% kernel_computation() Finds sub problem to be minimized in each iteration 8.27% select_working_set() Computes yi*yj* K(xi,xj) 6.18% get_Q() Solves the optimization problem 3.49% solve() Table 1: SVM profiling analysis Quadratic programming optimization problems, such as the SVM classification algorithm are expensive. In cases where the data sets are high-dimensional and large, the kernel and inner product computations require a massive number of matrix-vector operations. This can be observed in the above table since all functions that appear perform matrix-vector operations. A brief description of each function is given in the Table 1. However, a more detailed description is also presented below.

Algorithm Profiling. Variational inference The first implementation of LDA considered was the Princeton implementation by Xxxxx X. Xxxx xx.xx. [18][19]. This application was chosen as it was written in C and would be compatible with the hardware tools (the Maxeler host code has to be written in C/C++). The profiling showed that the most time consuming function was the digamma function (78% of the processing time). This function is called multiple times by the Variational inference algorithm. This implementation wasn‟t studied further as it is not the one used by the community. This study has been done as Variational Inference is the basic algorithm and the first LDA implementation. Xxxxx sampling The next implementation considered was based on Xxxxx Sampling. It is the algorithm implemented in R project [21] and Mallet [22] tools. Mallet is the most commonly used tool for topic modeling and has many different Inference algorithm implementations for the LDA. The basic LDA implementation is based on Xxxxx Sampling. The profiling of the Java implementation showed that more than 80% of the execution time is used by the Xxxxx Sampling stage. The algorithm iterates through the documents (the number of iterations is given by the user) and for each word, iterates through all the topics (the number of topics is given by the user) and updates the appropriate values. This algorithm looked promising as there are various parallel implementations of Xxxxx sampling on GPUs and multicore platforms [23, 24 , 25]. The most time consuming function is the sample TopicsForOneDoc(); that Implements the Xxxxx sampling. It is called for each document for the number of iterations. The function iterates through the word of each document and updates the topic distributions.Sparse LDA. Both the previous implementations are deprecated as the SparseLDA presented in [26] is mostly used by the community, as it is at least 20x faster than the standard Xxxxx Sampling implementation. In their work they evaluate the performance of several methods for topic inference in previously unseen documents, including methods based on Xxxxx sampling, variational inference, and a new method inspired by text classification. The classification based inference method produces results similar to iterative inference methods, but requires only a single matrix multiplication. Results indicated that SparseLDA can be approximately 20 times faster than traditional LDA and provide twice the speedup of previously published fast samplin...