arXiv subjects

Ali Mohades

Publications and source records attributed to Ali Mohades.

17 recordsLinked to original sources

arXiv2025

Cardinality Sparsity: Applications in Matrix-Matrix Multiplications and Machine Learning

High-dimensional data has become ubiquitous across the sciences but presents computational and statistical challenges. A common approach to addressing these challenges is through sparsity. In this paper, we introduce a new concept of sparsity, called cardinality sparsity. Broadly speaking, we define a tensor as sparse if it contains only a small number of unique values. We demonstrate that cardinality sparsity can improve deep learning and tensor regression both statistically and computationally. Along the way, we generalize recent statistical theories in these fields. Most importantly, we show that cardinality sparsity has a strikingly powerful application beyond high-dimensional data analysis: it can significantly speed up matrix-matrix multiplications. For instance, we demonstrate that cardinality sparsity leads to algorithms for binary-matrix multiplication that outperform state-of-the-art algorithms by a substantial margin. Additionally, another crucial aspect of this sparsity is minimizing memory usage. By executing matrix multiplication in the compressed domain, we can significantly lower the amount of memory needed to store the input data.

math.ST↗

arXiv2023

Two-Stage Classifier for Campaign Negativity Detection using Axis Embeddings: A Case Study on Tweets of Political Users during 2021 Presidential Election in Iran

In elections around the world, the candidates may turn their campaigns toward negativity due to the prospect of failure and time pressure. In the digital age, social media platforms such as Twitter are rich sources of political discourse. Therefore, despite the large amount of data that is published on Twitter, the automatic system for campaign negativity detection can play an essential role in understanding the strategy of candidates and parties in their campaigns. In this paper, we propose a hybrid model for detecting campaign negativity consisting of a two-stage classifier that combines the strengths of two machine learning models. Here, we have collected Persian tweets from 50 political users, including candidates and government officials. Then we annotated 5,100 of them that were published during the year before the 2021 presidential election in Iran. In the proposed model, first, the required datasets of two classifiers based on the cosine similarity of tweet embeddings with axis embeddings (which are the average of embedding in positive and negative classes of tweets) from the training set (85\%) are made, and then these datasets are considered the training set of the two classifiers in the hybrid model. Finally, our best model (RF-RF) was able to achieve 79\% for the macro F1 score and 82\% for the weighted F1 score. By running the best model on the rest of the tweets of 50 political users that were published one year before the election and with the help of statistical models, we find that the publication of a tweet by a candidate has nothing to do with the negativity of that tweet, and the presence of the names of political persons and political organizations in the tweet is directly related to its negativity.

cs.LG↗

arXiv2023

A Hybrid Architecture for Out of Domain Intent Detection and Intent Discovery

Intent Detection is one of the tasks of the Natural Language Understanding (NLU) unit in task-oriented dialogue systems. Out of Scope (OOS) and Out of Domain (OOD) inputs may run these systems into a problem. On the other side, a labeled dataset is needed to train a model for Intent Detection in task-oriented dialogue systems. The creation of a labeled dataset is time-consuming and needs human resources. The purpose of this article is to address mentioned problems. The task of identifying OOD/OOS inputs is named OOD/OOS Intent Detection. Also, discovering new intents and pseudo-labeling of OOD inputs is well known by Intent Discovery. In OOD intent detection part, we make use of a Variational Autoencoder to distinguish between known and unknown intents independent of input data distribution. After that, an unsupervised clustering method is used to discover different unknown intents underlying OOD/OOS inputs. We also apply a non-linear dimensionality reduction on OOD/OOS representations to make distances between representations more meaning full for clustering. Our results show that the proposed model for both OOD/OOS Intent Detection and Intent Discovery achieves great results and passes baselines in English and Persian languages.

cs.CL↗

arXiv2023

A Persian Benchmark for Joint Intent Detection and Slot Filling

Natural Language Understanding (NLU) is important in today's technology as it enables machines to comprehend and process human language, leading to improved human-computer interactions and advancements in fields such as virtual assistants, chatbots, and language-based AI systems. This paper highlights the significance of advancing the field of NLU for low-resource languages. With intent detection and slot filling being crucial tasks in NLU, the widely used datasets ATIS and SNIPS have been utilized in the past. However, these datasets only cater to the English language and do not support other languages. In this work, we aim to address this gap by creating a Persian benchmark for joint intent detection and slot filling based on the ATIS dataset. To evaluate the effectiveness of our benchmark, we employ state-of-the-art methods for intent detection and slot filling.

cs.CL↗

arXiv2022

Implementation of polygon guarding algorithms for art gallery problems

Victor Klee introduce the art gallery problem during a conference in Stanford in August 1976 with that question: "How many guards are required to guard an art gallery?" In 1987, Ghosh provided an approximation algorithm for vertex guards problem that achieved $ O(\log n) $ approximation ratio. In 2017, Bhattacharya et. al presented an approximation algorithm for guarding weak visibility polygons. In our paper, we first implement these algorithms and then we test them for different types of polygons. We compare their performance in terms of number of guards used by them. In the last part, we have provided a new algorithm that uses Ghosh's idea. Experiments show that this algorithm assigns near optimal guards for guarding the input polygons.

cs.CG↗

arXiv2022

Clustering Geometrically-Modeled Points in the Aggregated Uncertainty Model

The $k$-center problem is to choose a subset of size $k$ from a set of $n$ points such that the maximum distance from each point to its nearest center is minimized. Let $Q=\{Q_1,\ldots,Q_n\}$ be a set of polygons or segments in the region-based uncertainty model, in which each $Q_i$ is an uncertain point, where the exact locations of the points in $Q_i$ are unknown. The geometric objects segments and polygons can be models of a point set. We define the uncertain version of the $k$-center problem as a generalization in which the objective is to find $k$ points from $Q$ to cover the remaining regions of $Q$ with minimum or maximum radius of the cluster to cover at least one or all exact instances of each $Q_i$, respectively. We modify the region-based model to allow multiple points to be chosen from a region and call the resulting model the aggregated uncertainty model. All these problems contain the point version as a special case, so they are all NP-hard with a lower bound 1.822. We give approximation algorithms for uncertain $k$-center of a set of segments and polygons. We also have implemented some of our algorithms on a data-set to show our theoretical performance guarantees can be achieved in practice.

cs.CG↗

arXiv2021

PREDICT: Persian Reverse Dictionary

Finding the appropriate words to convey concepts (i.e., lexical access) is essential for effective communication. Reverse dictionaries fulfill this need by helping individuals to find the word(s) which could relate to a specific concept or idea. To the best of our knowledge, this resource has not been available for the Persian language. In this paper, we compare four different architectures for implementing a Persian reverse dictionary (PREDICT). We evaluate our models using (phrase,word) tuples extracted from the only Persian dictionaries available online, namely Amid, Moein, and Dehkhoda where the phrase describes the word. Given the phrase, a model suggests the most relevant word(s) in terms of the ability to convey the concept. The model is considered to perform well if the correct word is one of its top suggestions. Our experiments show that a model consisting of Long Short-Term Memory (LSTM) units enhanced by an additive attention mechanism is enough to produce suggestions comparable to (or in some cases better than) the word in the original dictionary. The study also reveals that the model sometimes produces the synonyms of the word as its output which led us to introduce a new metric for the evaluation of reverse dictionaries called Synonym Accuracy accounting for the percentage of times the event of producing the word or a synonym of it occurs. The assessment of the best model using this new metric also indicates that at least 62% of the times, it produces an accurate result within the top 100 suggestions.

cs.CL↗

arXiv2021

An upper bound for min-max angle of polygons

Let $S$ be a set of $n$ points in the plane, $\wp(S)$ be the set of all simple polygons crossing $S$, $γ_P$ be the maximum angle of polygon $P \in \wp(S)$ and $θ=min_{P\in\wp(S)} γ_P$. In this paper, we prove that $θ\leq 2π-\frac{2π}{r.m}$ where $m$ and $r$ are the number of edges and inner points of the convex hull of $S$, respectively. We also propose an algorithm to construct a polygon with the said upper bound on its angles. Constructing a simple polygon with angular constraint on a given set of points in the plane can be used for path planning in robotics. Moreover, we improve our upper bound on $θ$ and prove that this is tight for $r=1$.

cs.CG↗

arXiv2020

Computing The Packedness of Curves

A polygonal curve $P$ with $n$ vertices is $c$-packed, if the sum of the lengths of the parts of the edges of the curve that are inside any disk of radius $r$ is at most $cr$, for any $r>0$. Similarly, the concept of $c$-packedness can be defined for any scaling of a given shape. Assuming $L$ is the diameter of $P$ and $δ$ is the minimum distance between points on disjoint edges of $P$, we show the approximation factor of the existing $O(\frac{\log (L/δ)}εn^3)$ time algorithm is $1+ε$-approximation algorithm. The massively parallel versions of these algorithms run in $O(\log (L/δ))$ rounds. We improve the existing $O((\frac{n}{ε^3})^{\frac 4 3}\polylog \frac n ε)$ time $(6+ε)$-approximation algorithm by providing a $(4+ε)$-approximation $O(n(\log^2 n)(\log^2 \frac{1}ε)+\frac{n}ε)$ time algorithm, and the existing $O(n^2)$ time $2$-approximation algorithm improving the existing $O(n^2\log n)$ time $2$-approximation algorithm. Our exact $c$-packedness algorithm takes $O(n^5)$ time, which is the first exact algorithm for disks. We show using $α$-fat shapes instead of disks adds a factor $α^2$ to the approximation. We also give a data-structure for computing the curve-length inside query disks. It has $O(n^6\log n)$ construction time, uses $O(n^6)$ space, and has query time $O(\log n+k)$, where $k$ is the number of intersected segments with the query shape. We also give a massively parallel algorithm for relative $c$-packedness with $O(1)$ rounds.

cs.CG↗

arXiv2019

A Time-space Trade-off for Computing the Geodesic Center of a Simple Polygon

In this paper we study the problem of computing the geodesic center of a simple polygon when the available workspace is limited. For an $n$-vertex simple polygon, we give a time-space trade-off algorithm that finds the geodesic center in $O(T(n, s) \log^2 n+ \frac{n^2}{s} \log n)$ expected time and uses $O(s)$ additional words of space where $s\in Ω(\log n) \cap O(n)$, and $T(n, s)$ is the time needed for constructing the shortest path tree of a given point inside a simple polygon, in depth-first order, with $O(s)$ extra space. Applying the best current known time-space trade-off of Oh and Ahn (Algorithmica 2019) for shortest path tree, our algorithm runs in $O(\frac{n^2}{s} \log^3 n)$ expected time.

cs.CG↗

arXiv2019

Fast Frechet Distance Between Curves With Long Edges

Computing the Fréchet distance between two polygonal curves takes roughly quadratic time. In this paper, we show that for a special class of curves the Fréchet distance computations become easier. Let $P$ and $Q$ be two polygonal curves in $\mathbb{R}^d$ with $n$ and $m$ vertices, respectively. We prove four results for the case when all edges of both curves are long compared to the Fréchet distance between them: (1) a linear-time algorithm for deciding the Fréchet distance between two curves, (2) an algorithm that computes the Fréchet distance in $O((n+m)\log (n+m))$ time, (3) a linear-time $\sqrt{d}$-approximation algorithm, and (4) a data structure that supports $O(m\log^2 n)$-time decision queries, where $m$ is the number of vertices of the query curve and $n$ the number of vertices of the preprocessed curve.

cs.CG↗

arXiv2019

An efficient approximation for point-set diameter in higher dimensions

In this paper, we study the problem of computing the diameter of a set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+\varepsilon)$-approximation algorithm with $O(n+ 1/\varepsilon^{d-1})$ time and $O(n)$ space, where $0 < \varepsilon\leqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(\varepsilon))$-approximation algorithm with $O(n+ 1/\varepsilon^{\frac{2d}{3}-\frac{1}{3}})$ running time. These results provide some improvements in comparison with existing algorithms in terms of simplicity and data structure.

cs.CG↗

arXiv2018

Largest and Smallest Area Triangles on Imprecise Points

Assume we are given a set of parallel line segments in the plane, and we wish to place a point on each line segment such that the resulting point set maximizes or minimizes the area of the largest or smallest triangle in the set. We analyze the complexity of the four resulting computational problems, and we show that three of them admit polynomial-time algorithms, while the fourth is NP-hard. Specifically, we show that maximizing the largest triangle can be done in $O(n^2)$ time (or in $O(n \log n)$ time for unit segments); minimizing the largest triangle can be done in $O(n^2 \log n)$ time; maximizing the smallest triangle is NP-hard; but minimizing the smallest triangle can be done in $O(n^2)$ time. We also discuss to what extent our results can be generalized to polygons with $k>3$ sides.

cs.CG↗

arXiv2017

Maximum-Area Quadrilateral in a Convex Polygon, Revisited

In this note we show by example that the algorithm presented in 1979 by Dobkin and Snyder for finding the largest-area k-gon that is inscribed in a convex polygon fails to find the optimal solution for k=4. This question, posed by Keikha et al. where they showed that the Dobkin Snyder algorithm fails for k=3.

cs.CG↗

arXiv2017

Maximum-Area Triangle in a Convex Polygon, Revisited

We revisit the following problem: Given a convex polygon $P$, find the largest-area inscribed triangle. We show by example that the linear-time algorithm presented in 1979 by Dobkin and Snyder for solving this problem fails. We then proceed to show that with a small adaptation, their approach does lead to a quadratic-time algorithm. We also present a more involved $O(n\log n)$ time divide-and-conquer algorithm. Also we show by example that the algorithm presented in 1979 by Dobkin and Snyder for finding the largest-area $k$-gon that is inscribed in a convex polygon fails to find the optimal solution for $k=4$. Finally, we discuss the implications of our discoveries on the literature.

cs.CG↗

arXiv2017

Improper Filter Reduction

Combinatorial filters have been the subject of increasing interest from the robotics community in recent years. This paper considers automatic reduction of combinatorial filters to a given size, even if that reduction necessitates changes to the filter's behavior. We introduce an algorithmic problem called improper filter reduction, in which the input is a combinatorial filter F along with an integer k representing the target size. The output is another combinatorial filter F' with at most k states, such that the difference in behavior between F and F' is minimal. We present two metrics for measuring the distance between pairs of filters, describe dynamic programming algorithms for computing these distances, and show that improper filter reduction is NP-hard under these metrics. We then describe two heuristic algorithms for improper filter reduction, one greedy sequential approach, and one randomized global approach based on prior work on weighted improper graph coloring. We have implemented these algorithms and analyze the results of three sets of experiments.

cs.RO↗

arXiv2014

Alpha-Concave Hull, a Generalization of Convex Hull

Bounding hull, such as convex hull, concave hull, alpha shapes etc. has vast applications in different areas especially in computational geometry. Alpha shape and concave hull are generalizations of convex hull. Unlike the convex hull, they construct non-convex enclosure on a set of points. In this paper, we introduce another generalization of convex hull, named alpha-concave hull, and compare this concept with convex hull and alpha shape. We show that the alpha-concave hull is also a generalization of an NP-complete problem named min-area TSP. We prove that computing the alpha-concave hull is NP-hard on a set of points.

cs.CG↗