Hidden Markov Model

Hidden Markov Model (HMM) adalah peluasan dari rantai Markov di mana statenya tidak dapat diamati secara langsung (tersembunyi), tetapi hanya dapat diobservasi melalui suatu himpunan pengamatan lain. Pada HMM terdapat tiga permasalahan mendasar yang harus diselesaikan yakni evaluation problem, decoding problem, dan learning problem. Dalam paper ini, akan dijelaskan tentang Hidden Markov Model(HMM) dan solusi dari ketiga masalah mendasar dalam HMM tersebut, yakni evaluation problem dengan algoritma forward, decoding problem dengan algoritma viterbi, dan learning problem dengan algoritma Baum‐Welch. Kata kunci : Hidden Markov Model, evaluation problem, decoding problem, learning proble

Struktur Simplektik pada Aljabar Lie Affine aff(2,R)

In this research, we studied the affine Lie algebra aff(2,R). The aim of this research is to determine the 1-form in affine Lie algebra aff(2,R) which is associated with its symplectic structure so that affine Lie algebra aff(2,R) is a Frobenius Lie algebra. Realized the elements of the affine Lie algebra aff(2,R) in matrix form, then calculated the Lie brackets and formed the structure matrix of the affine Lie algebra aff(2,R). 1-form of the affine Lie algebra aff(2,R) is obtained from the determinant of the structure matrix of the affine Lie algebra aff(2,R). Furthermore, proved that the 2-form is symplectic and related to the 1-form. The result obtained is that the affine Lie algebra aff(2,R) has 1-form α=ε_12^*+ε_23^* on aff(2,R)^* which is related to its symplectic structure, β=ε_11^*∧ε_12^*+ε_12^*∧ε_22^*+ε_21^*∧ε_13^*+ε_22^*∧ε_23^* such that the affine Lie algebra aff(2,R) is a Frobenius Lie algebra. For further research, it can be developed into an affine Lie algebra with dimensions n(n+1)

Klasifikasi Aljabar Lie Forbenius-Quasi Dari Aljabar Lie Filiform Berdimensi ≤ 5

In this research, we studied quasi-Frobenius Lie algebras and filiform Lie algebras of dimensions ≤ 5 over real field. The primary objective of this research is to classify the classification of filiform Lie algebras of dimensions ≤ 5 into quasi-Frobenius Lie algebras. The method employed in this research involves constructing a skew-symmetric 2-form in real Lie algebra, which also a nondegenerate 2-cocycle. The outcomes of this research reveal that there exists a class of filiform Lie algebras of dimensions $\le 5$ that can be classified as a quasi-Frobenius real Lie algebra. Furthermore, this research can be developed to classify higher dimensional filiform Lie algebras as quasi-Frobenius real Lie algebras

Markov average-based weighted fuzzy time series model to predict PT Kimia farma Tbk stock price

The COVID-19 pandemic impacted various activities in Indonesia, including the stock market. Despite the declining economic condition, people are increasingly interested in investing. Among other companies available on the Indonesia Stock Exchange, companies in the health sector have a particular appeal to potential investors, one of which is pharmaceutical companies. This research used a Markov Average-Based Weighted Fuzzy Time Series model applied to PT Kimia Farma Tbk stock price data. This model develops the previous Markov chain–Fuzzy Time Series model, which has not calculated the weights for recurring events and used the Sturgess rule to determine the interval length. In this research, each recurring event has given a different weight that provides different probability values for transitions from one state to another. The Average-Based method is used to determine the interval length that can reflect the fluctuation of the data used. The stock price prediction of PT Kimia Farma Tbk using this model is categorized as very accurate with a MAPE of 2.632%

Robust Optimization Model for Twitter Sentiment Analysis of PeduliLindungi Application

Technological advances during the COVID-19 pandemic in Indonesia gave rise to the PeduliLindungi application which is developed by the government to prevent the spread of COVID-19. The advantages and disadvantages of developing PeduliLindungi can be seen from the responses and opinions from users, one of which is through the Twitter. A person's opinion about PeduliLindungi based on the tweet can be classified into positive, negative, or neutral categories using a Machine Learning approach with the Support Vector Machine (SVM) algorithm. In this paper, multiobjective optimization modeling is used to maximize the performance metrics, which are the value of Accuracy, Precision, Recall, and F1-Score. The value of the performance metrics is considered to contain uncertainty factors. Therefore, the optimization problem is solved by using Robust Optimization to handle the uncertainty factor. The data uncertainty is assumed to be belongs to polyhedral uncertainty set thus the resulted robust is computationally tractable. Numerical experiment is presented to complete the discussion

DISTRIBUSI STASIONER RANTAI MARKOV UNTUK PREDIKSI CURAH HUJAN DI WILAYAH JAWA BARAT

Abstrak: Curah hujan adalah fenomena alam yang termasuk salah satu variabel iklim dan diamati setiap waktu di setiap tempat.Data curah hujan merupakan data time series, yang bersifat acak. Di dalamnya merupakan data perpindahan dari satu waktu ke waktu lainnya yang dapat dinyatakan sebagai keadaan intensitas rendah, sedang atau tinggi.Prediksi curah hujan sangat diperlukan untuk kehidupan masyarakat dan mendukung perekonomian. Selain itu prediksi curah hujan merupakan antisipasi pencegahan jika intensitas hujan tinggi akan terjadi dalam waktu panjang. Salah satu metode prediksi curah hujan yang dapat digunakan adalah pendekatan proses stokastik. Rantai Markov merupakan bagian dari proses stokastik  yang dapat digunakan untuk prediksi curah hujan waktu sekarang berdasarkan satu waktu sebelumnya. Fokus penelitian ini adalah penerapan Rantai Markov untuk prediksi curah hujan.Melalui rantai Markov diperoleh peluang jangka panjang untuk fenomena curah hujan. Dalam penelitian ini dikaji distribusi stasioner dan limit peluang rantai Markov dan penerapannya untuk prediksi curah hujan di wilayah Jawa Barat. Untuk jangka panjang diprediksi curah hujan untuk kota Bogor dan Tasikmalaya cenderung tinggi, sementara untuk kota Bandung, Sumedang, dan Indramayu curah hujan cenderung rendah. Hasil  penelitian ini diharapkan dapat menjadi bahan rekomendasi bagi pihak yang terkait langsung dalam mengambil langkah pecegahan akibat curah hujan.Kata kunci:curah hujan, distribusi stasioner, prediksi, rantai Marko

Non-homogeneous continuous time Markov chain model for information dissemination on Indonesian Twitter users

Nonhomogeneous Continuous-Time Markov Chain (NH-CTMC) is a stochastic process that can be used to model problems where the future state depends only on the current state and is independent of the past. The transition intensity in NH-CTMC is not constant but is a function of time. In this paper, NH-CTMC is employed to model information dissemination on Twitter, where transitions occur only from followee groups to follower groups. Information is considered spread on Twitter when followers retweet posts from their followees. The tweet-retweet process on Twitter satisfies the Markov property, as a retweet from a follower depends only on the tweet posted just before by the corresponding followee. The probability of a tweet spreading is determined by the transition intensity, assumed to be a Sigmoid function whose parameters are estimated using Maximum Likelihood Estimation (MLE). This method is applied to Twitter data from Indonesia related to discussions on Covid-19 vaccination. The results indicate that information about Covid-19 vaccination on Twitter spreads rapidly from followees to followers in the first 20 hours, and then slows down after 40 hours. The NH-CTMC model outperforms the Homogeneous Continuous-Time Markov Chain (H-CTMC) approach, where the transition intensity (tweet spreading intensity) is assumed to be constant

Information diffusion model with homogeneous continuous time Markov chain on Indonesian Twitter users

In this paper, a homogeneous continuous time Markov chain (CTMC) is used to model information diffusion or dissemination, also to determine influencers on Twitter dynamically. The tweeting process can be modeled with a homogeneous CTMC since the properties of Markov chains are fulfilled. In this case, the tweets that are received by followers only depend on the tweets from the previous followers. Knowledge Discovery in Database (KDD) in Data Mining is used to be research methodology including pre-processing, data mining process using homogeneous CTMC, and post-processing to get the influencers using visualization that predicts the number of affected users. We assume the number of affected users follows a logarithmic function. Our study examines the Indonesian Twitter data users with tweets about covid19 vaccination resulted in dynamic influencer rankings over time. From these results, it can also be seen that the users with the highest number of followers are not necessarily the top influencer.publishedVersio

Prediksi Trend Pergerakan Harga Saham dengan Hidden Markov Model (HMM) dan Support Vector Machine (SVM)

Prediksi trend pergerakan harga saham sangatlah dibutuhkan untuk meningkatkan potensi keuntungan sekaligus mengurang kemungkinan rugi. Berbagai metode telah digunakan untuk memprediksi trend pergerakan harga saham. Pada paper ini, dibahas metode Hidden Markov Model (HMM) dan Support Vector Machine (SVM) sebagai alat untuk memprediksi trend naik turunnya harga close Indeks LQ45. Akurasi prediksi dengan HMM sebesar 50,98%, sementara dengan SVM sebesar 55,56%

PERAMALAN JUMLAH PENUMPANG KERETA REL LISTRIK JABODETABEK MENGGUNAKAN PROSES POISSON NONHOMOGEN

The train is one of the alternative transportations for the community to carry out their activities in terms of work and tourism for long distances. One of the public transportation companies, namely, PT. Indonesian Commuter Train (KCI) is trusted as a provider of Electric Rail Trains (ERT) in order to optimally meet the needs of the community. The number of ERT passengers has an influence in planning the capacity of the train. For this reason, it is necessary to know the number of KRL passengers for the future. In this study we have forecasted the number of KRL passengers using the Nonhomogeneous Poisson process, where the intensity function is determined by a simple linear regression method. The results of forecasting the number of Jabodetabek ERT passengers using the Nonhomogeneous Poisson process, show that the number of Jabodetabek ERT passengers in November 2021 to April 2022 has decreased. The results of this forecasting fall into the fairly accurate category with a Mean Absolute Percentage Error (MAPE) value of 28%